├── .gitignore
├── LICENSE
├── README.md
├── setup.py
├── tests
├── BeAu
│ ├── FORCE_CONSTANTS
│ ├── POSCAR
│ └── SPOSCAR
├── LiCaAs
│ ├── FORCE_CONSTANTS
│ ├── POSCAR
│ └── SPOSCAR
├── MgB2
│ ├── FORCE_CONSTANTS
│ ├── POSCAR
│ └── SPOSCAR
├── SrTiO3
│ ├── BORN
│ ├── FORCE_CONSTANTS
│ ├── POSCAR
│ └── SPOSCAR
└── graphene
│ ├── FORCE_CONSTANTS
│ ├── POSCAR
│ └── SPOSCAR
└── topophonon
├── __init__.py
├── model.py
├── runExamples.py
├── structure.py
├── topology.py
├── units.py
└── utils.py
/.gitignore:
--------------------------------------------------------------------------------
1 | *__pycache__*
2 | *.swp
3 | *.egg-info/
4 | dist/
5 | build/
6 | token*
--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # TopoPhonon
2 | #### topoPhonon is a python package that allows users to phononic calculate topological properties, by building phonon tight-binding model.
3 | * Build tight-binding models from user's input, FORCE_CONSTANTS files or Phonopy API. The last method is much faster, but need to import Phonopy package and manually create phonopy.harmonic.dynamical_matrix.DynamicalMatrix object.
4 | * Calculate berry phase, berry curvature, wannier charge center evolution around Weyl points from tight-binding models.
5 | * Build slab/ribbon models for surface/edge.
6 | * Plot 3d band surfaces.
7 |
8 | ## Installation:
9 |
10 | `pip install topophonon`
11 |
12 | ## Basic usage:
13 |
14 | Use one line of code to build a tight-binding model:
15 | `model = read_from_files(path)`
16 | where the path should contain POSCAR, SPOSCAR and FORCE_CONSTANTS files.
17 |
18 | From the model just built, build a slab model with `multi` layers along `fin_dir`:
19 | `model_2d = model.cut_piece(multi, fin_dir)`
20 | `model_2d = model_2d.atom_projected_band(q_path, node_names)`
21 |
22 | Create a Topology object:
23 | `tp = Topology(model)`
24 | Plot the energy surfaces of `band1` and `band2` and find the degenerate points on z=0 plane:
25 | `model.plot_3d_band([band1, band2], center, xy_range)`
26 | Then plot Wannier charge center evolution around `center` for `band_indices`:
27 | `tp.wcc_evol_sphere(band_indices, center)`
28 | and the Berry curvature distribution on $k_i$=`kz` plane, where $k_i$ = $k_z, k_y, k_z$ if `dirc` = 0, 1, 2, respectively:
29 | `tp.Berry_curvature_proj(band_indices, dirc, kz)`
30 |
31 |
32 | #### More examples can be found in topophonon/runExamples.py file
33 |
--------------------------------------------------------------------------------
/setup.py:
--------------------------------------------------------------------------------
1 | import setuptools
2 |
3 | with open("README.md", "r") as fh:
4 | long_description = fh.read()
5 |
6 | setuptools.setup(
7 | name="topoPhonon",
8 | version="1.0.3",
9 | python_requires=">=3.8",
10 | install_requires=[
11 | "matplotlib>=3.5.2",
12 | "numpy>=1.23.1",
13 | "tqdm>=4.64.1",
14 | "scipy>=1.6.2"
15 | ],
16 | author="He (Alan) Zhu",
17 | author_email="zhu00336@umn.edu",
18 | description=" topoPhonon package is a python package that allows users to"
19 | "phononic calculate topological properties, by building phonon tight-binding"
20 | "model.",
21 | long_description=long_description,
22 | long_description_content_type="text/markdown",
23 | url="https://github.com/cnncnnzh/topoPhonon",
24 | packages=setuptools.find_packages(),
25 | classifiers=[
26 | "Programming Language :: Python :: 3",
27 | "License :: OSI Approved :: GNU General Public License v3 (GPLv3)",
28 | "Operating System :: OS Independent",
29 | ],
30 | )
31 |
--------------------------------------------------------------------------------
/tests/BeAu/POSCAR:
--------------------------------------------------------------------------------
1 | Be4 Au4
2 | 1.0
3 | 4.723566 0.000000 0.000000
4 | 0.000000 4.723566 0.000000
5 | 0.000000 0.000000 4.723566
6 | Be Au
7 | 4 4
8 | direct
9 | 0.153453 0.346547 0.653453 Be
10 | 0.346547 0.653453 0.153453 Be
11 | 0.653453 0.153453 0.346547 Be
12 | 0.846547 0.846547 0.846547 Be
13 | 0.844944 0.655056 0.344944 Au
14 | 0.655056 0.344944 0.844944 Au
15 | 0.344944 0.844944 0.655056 Au
16 | 0.155056 0.155056 0.155056 Au
17 |
--------------------------------------------------------------------------------
/tests/BeAu/SPOSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 9.4471319999999999 0.0000000000000000 0.0000000000000000
4 | 0.0000000000000000 9.4471319999999999 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 9.4471319999999999
6 | Be Au
7 | 32 32
8 | Direct
9 | 0.0767265000000000 0.1732735000000000 0.3267265000000000
10 | 0.5767265000000000 0.1732735000000000 0.3267265000000000
11 | 0.0767265000000000 0.6732735000000000 0.3267265000000000
12 | 0.5767265000000000 0.6732735000000000 0.3267265000000000
13 | 0.0767265000000000 0.1732735000000000 0.8267264999999999
14 | 0.5767265000000000 0.1732735000000000 0.8267264999999999
15 | 0.0767265000000000 0.6732735000000000 0.8267264999999999
16 | 0.5767265000000000 0.6732735000000000 0.8267264999999999
17 | 0.1732735000000000 0.3267265000000000 0.0767265000000000
18 | 0.6732735000000000 0.3267265000000000 0.0767265000000000
19 | 0.1732735000000000 0.8267264999999999 0.0767265000000000
20 | 0.6732735000000000 0.8267264999999999 0.0767265000000000
21 | 0.1732735000000000 0.3267265000000000 0.5767265000000000
22 | 0.6732735000000000 0.3267265000000000 0.5767265000000000
23 | 0.1732735000000000 0.8267264999999999 0.5767265000000000
24 | 0.6732735000000000 0.8267264999999999 0.5767265000000000
25 | 0.3267265000000000 0.0767265000000000 0.1732735000000000
26 | 0.8267264999999999 0.0767265000000000 0.1732735000000000
27 | 0.3267265000000000 0.5767265000000000 0.1732735000000000
28 | 0.8267264999999999 0.5767265000000000 0.1732735000000000
29 | 0.3267265000000000 0.0767265000000000 0.6732735000000000
30 | 0.8267264999999999 0.0767265000000000 0.6732735000000000
31 | 0.3267265000000000 0.5767265000000000 0.6732735000000000
32 | 0.8267264999999999 0.5767265000000000 0.6732735000000000
33 | 0.4232735000000000 0.4232735000000000 0.4232735000000000
34 | 0.9232735000000001 0.4232735000000000 0.4232735000000000
35 | 0.4232735000000000 0.9232735000000001 0.4232735000000000
36 | 0.9232735000000001 0.9232735000000001 0.4232735000000000
37 | 0.4232735000000000 0.4232735000000000 0.9232735000000001
38 | 0.9232735000000001 0.4232735000000000 0.9232735000000001
39 | 0.4232735000000000 0.9232735000000001 0.9232735000000001
40 | 0.9232735000000001 0.9232735000000001 0.9232735000000001
41 | 0.4224720000000000 0.3275280000000000 0.1724720000000000
42 | 0.9224720000000000 0.3275280000000000 0.1724720000000000
43 | 0.4224720000000000 0.8275280000000000 0.1724720000000000
44 | 0.9224720000000000 0.8275280000000000 0.1724720000000000
45 | 0.4224720000000000 0.3275280000000000 0.6724720000000000
46 | 0.9224720000000000 0.3275280000000000 0.6724720000000000
47 | 0.4224720000000000 0.8275280000000000 0.6724720000000000
48 | 0.9224720000000000 0.8275280000000000 0.6724720000000000
49 | 0.3275280000000000 0.1724720000000000 0.4224720000000000
50 | 0.8275280000000000 0.1724720000000000 0.4224720000000000
51 | 0.3275280000000000 0.6724720000000000 0.4224720000000000
52 | 0.8275280000000000 0.6724720000000000 0.4224720000000000
53 | 0.3275280000000000 0.1724720000000000 0.9224720000000000
54 | 0.8275280000000000 0.1724720000000000 0.9224720000000000
55 | 0.3275280000000000 0.6724720000000000 0.9224720000000000
56 | 0.8275280000000000 0.6724720000000000 0.9224720000000000
57 | 0.1724720000000000 0.4224720000000000 0.3275280000000000
58 | 0.6724720000000000 0.4224720000000000 0.3275280000000000
59 | 0.1724720000000000 0.9224720000000000 0.3275280000000000
60 | 0.6724720000000000 0.9224720000000000 0.3275280000000000
61 | 0.1724720000000000 0.4224720000000000 0.8275280000000000
62 | 0.6724720000000000 0.4224720000000000 0.8275280000000000
63 | 0.1724720000000000 0.9224720000000000 0.8275280000000000
64 | 0.6724720000000000 0.9224720000000000 0.8275280000000000
65 | 0.0775280000000000 0.0775280000000000 0.0775280000000000
66 | 0.5775280000000000 0.0775280000000000 0.0775280000000000
67 | 0.0775280000000000 0.5775280000000000 0.0775280000000000
68 | 0.5775280000000000 0.5775280000000000 0.0775280000000000
69 | 0.0775280000000000 0.0775280000000000 0.5775280000000000
70 | 0.5775280000000000 0.0775280000000000 0.5775280000000000
71 | 0.0775280000000000 0.5775280000000000 0.5775280000000000
72 | 0.5775280000000000 0.5775280000000000 0.5775280000000000
73 |
--------------------------------------------------------------------------------
/tests/LiCaAs/POSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 0.0000000000000000 3.3399999999999994 3.3399999999999994
4 | 3.3399999999999994 0.0000000000000000 3.3399999999999994
5 | 3.3399999999999994 3.3399999999999994 0.0000000000000000
6 | Ca Li As
7 | 1 1 1
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.0000000000000000
10 | 0.5000000000000000 0.5000000000000000 0.5000000000000000
11 | 0.2500000000000000 0.2500000000000000 0.2500000000000000
12 |
--------------------------------------------------------------------------------
/tests/LiCaAs/SPOSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 0.0000000000000000 13.3599999999999977 13.3599999999999977
4 | 13.3599999999999977 0.0000000000000000 13.3599999999999977
5 | 13.3599999999999977 13.3599999999999977 0.0000000000000000
6 | Ca Li As
7 | 64 64 64
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.0000000000000000
10 | 0.2500000000000000 0.0000000000000000 0.0000000000000000
11 | 0.5000000000000000 0.0000000000000000 0.0000000000000000
12 | 0.7500000000000000 0.0000000000000000 0.0000000000000000
13 | 0.0000000000000000 0.2500000000000000 0.0000000000000000
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27 | 0.5000000000000000 0.0000000000000000 0.2500000000000000
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29 | 0.0000000000000000 0.2500000000000000 0.2500000000000000
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178 | 0.3125000000000000 0.5625000000000000 0.5625000000000000
179 | 0.5625000000000000 0.5625000000000000 0.5625000000000000
180 | 0.8125000000000000 0.5625000000000000 0.5625000000000000
181 | 0.0625000000000000 0.8125000000000000 0.5625000000000000
182 | 0.3125000000000000 0.8125000000000000 0.5625000000000000
183 | 0.5625000000000000 0.8125000000000000 0.5625000000000000
184 | 0.8125000000000000 0.8125000000000000 0.5625000000000000
185 | 0.0625000000000000 0.0625000000000000 0.8125000000000000
186 | 0.3125000000000000 0.0625000000000000 0.8125000000000000
187 | 0.5625000000000000 0.0625000000000000 0.8125000000000000
188 | 0.8125000000000000 0.0625000000000000 0.8125000000000000
189 | 0.0625000000000000 0.3125000000000000 0.8125000000000000
190 | 0.3125000000000000 0.3125000000000000 0.8125000000000000
191 | 0.5625000000000000 0.3125000000000000 0.8125000000000000
192 | 0.8125000000000000 0.3125000000000000 0.8125000000000000
193 | 0.0625000000000000 0.5625000000000000 0.8125000000000000
194 | 0.3125000000000000 0.5625000000000000 0.8125000000000000
195 | 0.5625000000000000 0.5625000000000000 0.8125000000000000
196 | 0.8125000000000000 0.5625000000000000 0.8125000000000000
197 | 0.0625000000000000 0.8125000000000000 0.8125000000000000
198 | 0.3125000000000000 0.8125000000000000 0.8125000000000000
199 | 0.5625000000000000 0.8125000000000000 0.8125000000000000
200 | 0.8125000000000000 0.8125000000000000 0.8125000000000000
201 |
--------------------------------------------------------------------------------
/tests/MgB2/POSCAR:
--------------------------------------------------------------------------------
1 | Mg1 B2
2 | 1.0
3 | 1.5368400079881850 -2.6618849769400956 0.0000000000000000
4 | 1.5368400079881850 2.6618849769400956 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 3.5343499999999999
6 | Mg B
7 | 1 2
8 | direct
9 | 0.0000000000000000 0.0000000000000000 0.0000000000000000 Mg2+
10 | 0.3333333333333333 0.6666666666666666 0.5000000000000000 B-
11 | 0.6666666666666667 0.3333333333333334 0.5000000000000000 B-
12 |
--------------------------------------------------------------------------------
/tests/MgB2/SPOSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 4.6105200239645550 -7.9856549308202869 0.0000000000000000
4 | 4.6105200239645550 7.9856549308202869 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 10.6030499999999996
6 | Mg B
7 | 27 54
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.0000000000000000
10 | 0.3333333333333333 0.0000000000000000 0.0000000000000000
11 | 0.6666666666666666 0.0000000000000000 0.0000000000000000
12 | 0.0000000000000000 0.3333333333333333 0.0000000000000000
13 | 0.3333333333333333 0.3333333333333333 0.0000000000000000
14 | 0.6666666666666666 0.3333333333333333 0.0000000000000000
15 | 0.0000000000000000 0.6666666666666666 0.0000000000000000
16 | 0.3333333333333333 0.6666666666666666 0.0000000000000000
17 | 0.6666666666666666 0.6666666666666666 0.0000000000000000
18 | 0.0000000000000000 0.0000000000000000 0.3333333333333333
19 | 0.3333333333333333 0.0000000000000000 0.3333333333333333
20 | 0.6666666666666666 0.0000000000000000 0.3333333333333333
21 | 0.0000000000000000 0.3333333333333333 0.3333333333333333
22 | 0.3333333333333333 0.3333333333333333 0.3333333333333333
23 | 0.6666666666666666 0.3333333333333333 0.3333333333333333
24 | 0.0000000000000000 0.6666666666666666 0.3333333333333333
25 | 0.3333333333333333 0.6666666666666666 0.3333333333333333
26 | 0.6666666666666666 0.6666666666666666 0.3333333333333333
27 | 0.0000000000000000 0.0000000000000000 0.6666666666666666
28 | 0.3333333333333333 0.0000000000000000 0.6666666666666666
29 | 0.6666666666666666 0.0000000000000000 0.6666666666666666
30 | 0.0000000000000000 0.3333333333333333 0.6666666666666666
31 | 0.3333333333333333 0.3333333333333333 0.6666666666666666
32 | 0.6666666666666666 0.3333333333333333 0.6666666666666666
33 | 0.0000000000000000 0.6666666666666666 0.6666666666666666
34 | 0.3333333333333333 0.6666666666666666 0.6666666666666666
35 | 0.6666666666666666 0.6666666666666666 0.6666666666666666
36 | 0.1111111111111111 0.2222222222222222 0.1666666666666667
37 | 0.4444444444444444 0.2222222222222222 0.1666666666666667
38 | 0.7777777777777778 0.2222222222222222 0.1666666666666667
39 | 0.1111111111111111 0.5555555555555555 0.1666666666666667
40 | 0.4444444444444444 0.5555555555555555 0.1666666666666667
41 | 0.7777777777777778 0.5555555555555555 0.1666666666666667
42 | 0.1111111111111111 0.8888888888888888 0.1666666666666667
43 | 0.4444444444444444 0.8888888888888888 0.1666666666666667
44 | 0.7777777777777778 0.8888888888888888 0.1666666666666667
45 | 0.1111111111111111 0.2222222222222222 0.5000000000000000
46 | 0.4444444444444444 0.2222222222222222 0.5000000000000000
47 | 0.7777777777777778 0.2222222222222222 0.5000000000000000
48 | 0.1111111111111111 0.5555555555555555 0.5000000000000000
49 | 0.4444444444444444 0.5555555555555555 0.5000000000000000
50 | 0.7777777777777778 0.5555555555555555 0.5000000000000000
51 | 0.1111111111111111 0.8888888888888888 0.5000000000000000
52 | 0.4444444444444444 0.8888888888888888 0.5000000000000000
53 | 0.7777777777777778 0.8888888888888888 0.5000000000000000
54 | 0.1111111111111111 0.2222222222222222 0.8333333333333333
55 | 0.4444444444444444 0.2222222222222222 0.8333333333333333
56 | 0.7777777777777778 0.2222222222222222 0.8333333333333333
57 | 0.1111111111111111 0.5555555555555555 0.8333333333333333
58 | 0.4444444444444444 0.5555555555555555 0.8333333333333333
59 | 0.7777777777777778 0.5555555555555555 0.8333333333333333
60 | 0.1111111111111111 0.8888888888888888 0.8333333333333333
61 | 0.4444444444444444 0.8888888888888888 0.8333333333333333
62 | 0.7777777777777778 0.8888888888888888 0.8333333333333333
63 | 0.2222222222222222 0.1111111111111111 0.1666666666666667
64 | 0.5555555555555556 0.1111111111111111 0.1666666666666667
65 | 0.8888888888888890 0.1111111111111111 0.1666666666666667
66 | 0.2222222222222222 0.4444444444444445 0.1666666666666667
67 | 0.5555555555555556 0.4444444444444445 0.1666666666666667
68 | 0.8888888888888890 0.4444444444444445 0.1666666666666667
69 | 0.2222222222222222 0.7777777777777778 0.1666666666666667
70 | 0.5555555555555556 0.7777777777777778 0.1666666666666667
71 | 0.8888888888888890 0.7777777777777778 0.1666666666666667
72 | 0.2222222222222222 0.1111111111111111 0.5000000000000000
73 | 0.5555555555555556 0.1111111111111111 0.5000000000000000
74 | 0.8888888888888890 0.1111111111111111 0.5000000000000000
75 | 0.2222222222222222 0.4444444444444445 0.5000000000000000
76 | 0.5555555555555556 0.4444444444444445 0.5000000000000000
77 | 0.8888888888888890 0.4444444444444445 0.5000000000000000
78 | 0.2222222222222222 0.7777777777777778 0.5000000000000000
79 | 0.5555555555555556 0.7777777777777778 0.5000000000000000
80 | 0.8888888888888890 0.7777777777777778 0.5000000000000000
81 | 0.2222222222222222 0.1111111111111111 0.8333333333333333
82 | 0.5555555555555556 0.1111111111111111 0.8333333333333333
83 | 0.8888888888888890 0.1111111111111111 0.8333333333333333
84 | 0.2222222222222222 0.4444444444444445 0.8333333333333333
85 | 0.5555555555555556 0.4444444444444445 0.8333333333333333
86 | 0.8888888888888890 0.4444444444444445 0.8333333333333333
87 | 0.2222222222222222 0.7777777777777778 0.8333333333333333
88 | 0.5555555555555556 0.7777777777777778 0.8333333333333333
89 | 0.8888888888888890 0.7777777777777778 0.8333333333333333
90 |
--------------------------------------------------------------------------------
/tests/SrTiO3/BORN:
--------------------------------------------------------------------------------
1 | # epsilon and Z* of atoms 1 2 3
2 | 6.64926200 0.00000000 0.00000000 0.00000000 6.64926200 0.00000000 0.00000000 0.00000000 6.11385800
3 | 2.52014000 0.00000000 0.00000000 0.00000000 2.52014000 0.00000000 0.00000000 0.00000000 2.55590000
4 | 7.57259000 0.0000000 0.00000000 0.00000000 7.5725900 0.0000000 0.00000000 0.00000000 6.72493000
5 | -6.0885400 0.00000000 0.00000000 0.00000000 -2.0270600 0.00000000 0.00000000 0.00000000 -1.9174100
6 | -1.9771300 0.00000000 0.00000000 0.00000000 -1.9771300 0.00000000 0.00000000 0.00000000 -5.4465300
7 |
--------------------------------------------------------------------------------
/tests/SrTiO3/FORCE_CONSTANTS:
--------------------------------------------------------------------------------
1 | 5 40
2 | 1 1
3 | 4.704595199557503 -0.000000000000000 -0.000000000000000
4 | 0.000000000000000 4.704595199557503 -0.000000000000002
5 | -0.000000000000000 -0.000000000000000 4.485885335299562
6 | 1 2
7 | -1.890730948258053 -0.000000000000000 0.000000000000000
8 | -0.000000000000000 0.547714801002520 -0.000000000000000
9 | 0.000000000000000 -0.000000000000000 0.570971952577310
10 | 1 3
11 | 0.547714801002520 -0.000000000000000 -0.000000000000000
12 | 0.000000000000000 -1.890730948258053 -0.000000000000000
13 | -0.000000000000000 0.000000000000000 0.570971952577310
14 | 1 4
15 | -0.486079374004213 -0.000000000000000 0.000000000000000
16 | -0.000000000000000 -0.486079374004213 -0.000000000000000
17 | 0.000000000000000 0.000000000000000 0.258518497194545
18 | 1 5
19 | 0.521468517589092 -0.000000000000000 -0.000000000000000
20 | 0.000000000000000 0.521468517589092 0.000000000000001
21 | -0.000000000000000 0.000000000000000 -1.768284494449445
22 | 1 6
23 | -0.476245653478604 -0.000000000000000 0.000000000000000
24 | -0.000000000000000 0.224721916436587 0.000000000000000
25 | 0.000000000000000 0.000000000000000 -0.508247112730179
26 | 1 7
27 | 0.224721916436587 -0.000000000000000 -0.000000000000000
28 | 0.000000000000000 -0.476245653478604 0.000000000000000
29 | -0.000000000000000 0.000000000000000 -0.508247112730179
30 | 1 8
31 | -0.211646850063797 -0.000000000000000 0.000000000000000
32 | -0.000000000000000 -0.211646850063797 0.000000000000000
33 | 0.000000000000000 -0.000000000000000 -0.240806037871811
34 | 1 9
35 | -0.309593042603971 -1.159123009408847 -0.970640279683619
36 | -1.159123009408846 -0.309593042603971 -0.970640279683619
37 | -1.117400234436002 -1.117400234436002 -0.377423946932123
38 | 1 10
39 | -0.309593042603971 1.159123009408847 0.970640279683619
40 | 1.159123009408846 -0.309593042603971 -0.970640279683619
41 | 1.117400234436002 -1.117400234436002 -0.377423946932123
42 | 1 11
43 | -0.309593042603971 1.159123009408847 -0.970640279683619
44 | 1.159123009408847 -0.309593042603972 0.970640279683619
45 | -1.117400234436002 1.117400234436002 -0.377423946932123
46 | 1 12
47 | -0.309593042603971 -1.159123009408847 0.970640279683619
48 | -1.159123009408847 -0.309593042603972 0.970640279683619
49 | 1.117400234436002 1.117400234436002 -0.377423946932123
50 | 1 13
51 | -0.352607290262666 -1.060605254565362 1.261904512200948
52 | -1.060605254565362 -0.352607290262666 1.261904512200949
53 | 1.116879806321487 1.116879806321487 -0.358620080521345
54 | 1 14
55 | -0.352607290262666 1.060605254565362 -1.261904512200948
56 | 1.060605254565362 -0.352607290262666 1.261904512200949
57 | -1.116879806321487 1.116879806321487 -0.358620080521344
58 | 1 15
59 | -0.352607290262666 1.060605254565362 1.261904512200948
60 | 1.060605254565362 -0.352607290262665 -1.261904512200948
61 | 1.116879806321487 -1.116879806321488 -0.358620080521344
62 | 1 16
63 | -0.352607290262666 -1.060605254565362 -1.261904512200948
64 | -1.060605254565362 -0.352607290262665 -1.261904512200948
65 | -1.116879806321487 -1.116879806321487 -0.358620080521344
66 | 1 17
67 | -0.887697864690520 0.000000000000000 -0.000000000000000
68 | -0.000000000000000 0.017580615445362 0.382197480235645
69 | 0.000000000000000 0.362570068477175 -0.019870349116948
70 | 1 18
71 | 0.572455436180187 -0.000000000000000 -0.000000000000000
72 | 0.000000000000000 -0.017022229344683 0.106227257836854
73 | -0.000000000000000 0.142448459181037 -0.089311783308099
74 | 1 19
75 | -0.887697864690520 -0.000000000000000 -0.000000000000000
76 | -0.000000000000000 0.017580615445362 -0.382197480235645
77 | 0.000000000000000 -0.362570068477175 -0.019870349116948
78 | 1 20
79 | 0.572455436180187 0.000000000000000 -0.000000000000000
80 | 0.000000000000000 -0.017022229344683 -0.106227257836854
81 | -0.000000000000000 -0.142448459181037 -0.089311783308099
82 | 1 21
83 | -0.937294515847271 0.000000000000000 -0.000000000000000
84 | -0.000000000000000 0.227386358276690 -0.543639437140165
85 | 0.000000000000000 -0.536028320235383 0.308593335620740
86 | 1 22
87 | 0.710190199529597 -0.000000000000000 0.000000000000000
88 | 0.000000000000000 -0.016587414657866 -0.159150365987511
89 | -0.000000000000000 -0.125313648736842 0.056104608078109
90 | 1 23
91 | -0.937294515847271 -0.000000000000000 -0.000000000000000
92 | -0.000000000000000 0.227386358276690 0.543639437140165
93 | 0.000000000000000 0.536028320235383 0.308593335620740
94 | 1 24
95 | 0.710190199529597 0.000000000000000 0.000000000000000
96 | 0.000000000000000 -0.016587414657866 0.159150365987511
97 | -0.000000000000000 0.125313648736842 0.056104608078109
98 | 1 25
99 | 0.017580615445362 -0.000000000000000 0.382197480235645
100 | -0.000000000000000 -0.887697864690520 0.000000000000000
101 | 0.362570068477175 0.000000000000000 -0.019870349116948
102 | 1 26
103 | 0.017580615445362 -0.000000000000000 -0.382197480235645
104 | 0.000000000000000 -0.887697864690520 0.000000000000000
105 | -0.362570068477175 0.000000000000000 -0.019870349116948
106 | 1 27
107 | -0.017022229344683 -0.000000000000000 0.106227257836854
108 | -0.000000000000000 0.572455436180187 0.000000000000000
109 | 0.142448459181037 0.000000000000000 -0.089311783308099
110 | 1 28
111 | -0.017022229344683 -0.000000000000000 -0.106227257836854
112 | 0.000000000000000 0.572455436180187 0.000000000000000
113 | -0.142448459181037 0.000000000000000 -0.089311783308099
114 | 1 29
115 | 0.227386358276690 -0.000000000000000 -0.543639437140165
116 | 0.000000000000000 -0.937294515847271 -0.000000000000000
117 | -0.536028320235383 0.000000000000000 0.308593335620740
118 | 1 30
119 | 0.227386358276690 -0.000000000000000 0.543639437140165
120 | -0.000000000000000 -0.937294515847271 -0.000000000000000
121 | 0.536028320235383 0.000000000000000 0.308593335620740
122 | 1 31
123 | -0.016587414657866 -0.000000000000000 -0.159150365987511
124 | 0.000000000000000 0.710190199529597 -0.000000000000000
125 | -0.125313648736842 0.000000000000000 0.056104608078109
126 | 1 32
127 | -0.016587414657866 -0.000000000000000 0.159150365987511
128 | -0.000000000000000 0.710190199529597 -0.000000000000000
129 | 0.125313648736842 0.000000000000000 0.056104608078109
130 | 1 33
131 | 0.110880594047042 0.437291100684541 -0.255870459455850
132 | 0.437291100684541 0.110880594047042 -0.255870459455849
133 | -0.051800062013907 -0.051800062013907 -0.866490168094702
134 | 1 34
135 | 0.110880594047042 -0.437291100684541 0.255870459455850
136 | -0.437291100684541 0.110880594047042 -0.255870459455849
137 | 0.051800062013907 -0.051800062013907 -0.866490168094702
138 | 1 35
139 | 0.110880594047042 -0.437291100684541 -0.255870459455850
140 | -0.437291100684541 0.110880594047042 0.255870459455850
141 | -0.051800062013907 0.051800062013907 -0.866490168094702
142 | 1 36
143 | 0.110880594047042 0.437291100684541 0.255870459455850
144 | 0.437291100684541 0.110880594047042 0.255870459455850
145 | 0.051800062013907 0.051800062013907 -0.866490168094702
146 | 1 37
147 | -0.016634777764620 0.129976472794948 0.026756594180183
148 | 0.129976472794948 -0.016634777764620 0.026756594180183
149 | 0.015901404588986 0.015901404588986 0.631827814831405
150 | 1 38
151 | -0.016634777764620 -0.129976472794948 -0.026756594180183
152 | -0.129976472794948 -0.016634777764620 0.026756594180183
153 | -0.015901404588986 0.015901404588986 0.631827814831405
154 | 1 39
155 | -0.016634777764620 -0.129976472794948 0.026756594180183
156 | -0.129976472794948 -0.016634777764620 -0.026756594180184
157 | 0.015901404588986 -0.015901404588986 0.631827814831405
158 | 1 40
159 | -0.016634777764620 0.129976472794948 -0.026756594180183
160 | 0.129976472794948 -0.016634777764620 -0.026756594180184
161 | -0.015901404588986 -0.015901404588986 0.631827814831405
162 | 9 1
163 | -0.309496179708956 -1.159248361390632 -1.117690974406605
164 | -1.159248361390632 -0.309496179708956 -1.117690974406605
165 | -0.970996521584653 -0.970996521584653 -0.378027046763985
166 | 9 2
167 | -0.309496179708956 1.159248361390632 1.117690974406605
168 | 1.159248361390632 -0.309496179708956 -1.117690974406605
169 | 0.970996521584653 -0.970996521584653 -0.378027046763985
170 | 9 3
171 | -0.309496179708956 1.159248361390632 -1.117690974406605
172 | 1.159248361390631 -0.309496179708955 1.117690974406605
173 | -0.970996521584653 0.970996521584653 -0.378027046763986
174 | 9 4
175 | -0.309496179708956 -1.159248361390632 1.117690974406605
176 | -1.159248361390631 -0.309496179708955 1.117690974406605
177 | 0.970996521584653 0.970996521584653 -0.378027046763985
178 | 9 5
179 | -0.352523247456696 -1.060633387538547 1.117154667348172
180 | -1.060633387538547 -0.352523247456696 1.117154667348172
181 | 1.262018167983111 1.262018167983111 -0.359402565693185
182 | 9 6
183 | -0.352523247456696 1.060633387538547 -1.117154667348172
184 | 1.060633387538547 -0.352523247456696 1.117154667348171
185 | -1.262018167983111 1.262018167983111 -0.359402565693185
186 | 9 7
187 | -0.352523247456696 1.060633387538547 1.117154667348172
188 | 1.060633387538547 -0.352523247456697 -1.117154667348172
189 | 1.262018167983111 -1.262018167983111 -0.359402565693185
190 | 9 8
191 | -0.352523247456696 -1.060633387538547 -1.117154667348172
192 | -1.060633387538547 -0.352523247456697 -1.117154667348172
193 | -1.262018167983111 -1.262018167983111 -0.359402565693185
194 | 9 9
195 | 18.346968318321832 -0.000000000000000 -0.000000000000000
196 | 0.000000000000000 18.346968318321832 0.000000000000007
197 | 0.000000000000000 -0.000000000000000 20.130025369232996
198 | 9 10
199 | -15.176481952206746 -0.000000000000000 -0.000000000000000
200 | -0.000000000000000 0.222972686508949 0.000000000000000
201 | -0.000000000000000 -0.000000000000000 0.222714447106462
202 | 9 11
203 | 0.222972686508949 -0.000000000000000 -0.000000000000000
204 | 0.000000000000000 -15.176481952206743 -0.000000000000000
205 | 0.000000000000000 -0.000000000000000 0.222714447106461
206 | 9 12
207 | -0.278109040588000 -0.000000000000000 0.000000000000000
208 | -0.000000000000000 -0.278109040588000 0.000000000000000
209 | -0.000000000000000 -0.000000000000000 0.317486776331104
210 | 9 13
211 | 0.213051362041525 -0.000000000000000 -0.000000000000000
212 | 0.000000000000000 0.213051362041525 -0.000000000000005
213 | 0.000000000000000 -0.000000000000000 -12.797206926578582
214 | 9 14
215 | -0.244702737442267 -0.000000000000000 0.000000000000000
216 | -0.000000000000000 0.286254782722525 0.000000000000000
217 | -0.000000000000000 0.000000000000000 -0.216342230489482
218 | 9 15
219 | 0.286254782722525 -0.000000000000000 0.000000000000000
220 | 0.000000000000000 -0.244702737442267 -0.000000000000000
221 | 0.000000000000000 -0.000000000000000 -0.216342230489483
222 | 9 16
223 | -0.294795810935974 -0.000000000000000 -0.000000000000000
224 | -0.000000000000000 -0.294795810935974 -0.000000000000000
225 | -0.000000000000000 -0.000000000000000 -0.292009845482679
226 | 9 17
227 | -0.308840574599676 -0.000000000000000 -0.299339464162100
228 | -0.000000000000000 -1.545434669887570 -0.000000000000001
229 | -0.483131936466583 0.000000000000000 -1.749221028314765
230 | 9 18
231 | -0.308840574599676 -0.000000000000000 0.299339464162100
232 | 0.000000000000000 -1.545434669887570 -0.000000000000001
233 | 0.483131936466583 0.000000000000000 -1.749221028314766
234 | 9 19
235 | 0.065466853055199 -0.000000000000000 -0.027233786383570
236 | 0.000000000000000 1.647852936823362 -0.000000000000000
237 | 0.064190288187125 -0.000000000000000 -0.142227825744294
238 | 9 20
239 | 0.065466853055199 -0.000000000000000 0.027233786383570
240 | -0.000000000000000 1.647852936823362 -0.000000000000000
241 | -0.064190288187125 -0.000000000000000 -0.142227825744294
242 | 9 21
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--------------------------------------------------------------------------------
/tests/SrTiO3/POSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.00000000000000
3 | 3.9289565000000000 0.0000000000000000 0.0000000000000000
4 | 0.0000000000000000 3.9289565000000000 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 3.9856550942854989
6 | Sr Ti O
7 | 1 1 3
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.0240173774801846
10 | 0.5000000000000000 0.5000000000000000 0.5259051370582881
11 | 0.0000000000000000 0.5000000000000000 0.4994707522946911
12 | 0.5000000000000000 0.0000000000000000 0.4994707522946911
13 | 0.5000000000000000 0.5000000000000000 0.0011359808721565
14 |
15 | 0.00000000E+00 0.00000000E+00 0.00000000E+00
16 | 0.00000000E+00 0.00000000E+00 0.00000000E+00
17 | 0.00000000E+00 0.00000000E+00 0.00000000E+00
18 | 0.00000000E+00 0.00000000E+00 0.00000000E+00
19 | 0.00000000E+00 0.00000000E+00 0.00000000E+00
20 |
--------------------------------------------------------------------------------
/tests/SrTiO3/SPOSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 7.8579129999999999 0.0000000000000000 0.0000000000000000
4 | 0.0000000000000000 7.8579129999999999 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 7.9713101885709978
6 | Sr Ti O
7 | 8 8 24
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.0120086887400923
10 | 0.5000000000000000 0.0000000000000000 0.0120086887400923
11 | 0.0000000000000000 0.5000000000000000 0.0120086887400923
12 | 0.5000000000000000 0.5000000000000000 0.0120086887400923
13 | 0.0000000000000000 0.0000000000000000 0.5120086887400923
14 | 0.5000000000000000 0.0000000000000000 0.5120086887400923
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18 | 0.7500000000000000 0.2500000000000000 0.2629525685291441
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20 | 0.7500000000000000 0.7500000000000000 0.2629525685291441
21 | 0.2500000000000000 0.2500000000000000 0.7629525685291441
22 | 0.7500000000000000 0.2500000000000000 0.7629525685291441
23 | 0.2500000000000000 0.7500000000000000 0.7629525685291441
24 | 0.7500000000000000 0.7500000000000000 0.7629525685291441
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27 | 0.0000000000000000 0.7500000000000000 0.2497353761473456
28 | 0.5000000000000000 0.7500000000000000 0.2497353761473456
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47 | 0.2500000000000000 0.7500000000000000 0.5005679904360782
48 | 0.7500000000000000 0.7500000000000000 0.5005679904360782
49 |
--------------------------------------------------------------------------------
/tests/graphene/POSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 2.4600000000000000 0.0000000000000000 0.0000000000000000
4 | 1.2300000000000000 2.1304224933097191 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 10.0000000000000018
6 | C
7 | 2
8 | Direct
9 | 0.0000000000000000 0.0000000000000000 0.5000000000000000
10 | 0.3333333333333333 0.3333333333333333 0.5000000000000000
11 |
--------------------------------------------------------------------------------
/tests/graphene/SPOSCAR:
--------------------------------------------------------------------------------
1 | generated by phonopy
2 | 1.0
3 | 12.3000000000000007 0.0000000000000000 0.0000000000000000
4 | 6.1500000000000004 10.6521124665485960 0.0000000000000000
5 | 0.0000000000000000 0.0000000000000000 10.0000000000000000
6 | C
7 | 50
8 | Direct
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--------------------------------------------------------------------------------
/topophonon/__init__.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | topophonon package is a python package that allows users to calculate topological
4 | properties (berry phase, berry curvature, wannier charge center evolution...), by
5 | building phonon tight bindinbg model.
6 |
7 | @author: zhuhe
8 | """
9 |
10 | import topophonon.structure
11 | import topophonon.model
12 | import topophonon.topology
13 |
14 | __all__ = ['structure', 'model', 'topology', 'masses']
15 |
--------------------------------------------------------------------------------
/topophonon/runExamples.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Wed Sep 7 15:08:31 2022
4 |
5 | @author: zhuhe
6 | """
7 |
8 | from topophonon.structure import Structure
9 | from topophonon.model import read_from_files, Model
10 | from topophonon.topology import Topology
11 |
12 |
13 | ######### LiCaAs #############
14 | print("LiCaAs!!")
15 | # read files from one line of code
16 | model = read_from_files(r"..\tests\LiCaAs")
17 | # specify the k path
18 | k_path = [[0.5, 0.5, 0.5], [0.5, 0.25, 0.75], [0.5, 0.0, 0.5], [0.0, 0.0, 0.0]]
19 | # plot the band structure of the tight binding model
20 | model.atom_projected_band(k_path, node_names=["L", "W", "X", "$\Gamma$"], k_num=80)
21 |
22 | # build a Topology object
23 | tp = Topology(model)
24 | # wannier center evolution of the third band around [0.5,0.222,0.722]
25 | tp.wcc_evol_sphere(
26 | [2],
27 | [0.5, 0.222, 0.722],
28 | r=0.003,
29 | dirc=2,
30 | num=30,
31 | )
32 | # berry curvature distribution
33 | tp.berry_curvature_proj([2], 2, 0.722, center=[0.5, 0.222], xy_range=0.005, num=5)
34 |
35 |
36 | ######### BeAu ##############
37 | print("BeAu!!")
38 | model = read_from_files(r"..\tests\BeAu")
39 |
40 | k_path = [
41 | [0.0, 0.0, 0.0],
42 | [0.0, 0.5, 0.0],
43 | [0.5, 0.5, 0.0],
44 | [0.0, 0.0, 0.0],
45 | [0.5, 0.5, 0.5],
46 | ]
47 | # plot atom-projected band
48 | model.atom_projected_band(
49 | k_path,
50 | node_names=["$\Gamma$", "X", "M", "$\Gamma$", "R"],
51 | k_num=80,
52 | site_comb=[[0, 1, 2, 3], [4, 5, 6, 7]],
53 | unit="cm-1",
54 | )
55 |
56 | tp = Topology(model)
57 | ## wannier center evolution
58 | # at Gamma point
59 | tp.wcc_evol_sphere(
60 | [4],
61 | [0, 0, 0],
62 | r=0.0001,
63 | dirc=2,
64 | num=30,
65 | )
66 | tp.wcc_evol_sphere(
67 | [9],
68 | [0, 0, 0],
69 | r=0.0001,
70 | dirc=2,
71 | num=30,
72 | )
73 | # at R point, 4-fold degenerate points
74 | tp.wcc_evol_sphere(
75 | [0, 1],
76 | [0.5, 0.5, 0.5],
77 | r=0.0001,
78 | dirc=2,
79 | num=30,
80 | )
81 | tp.wcc_evol_sphere(
82 | [8, 9],
83 | [0.5, 0.5, 0.5],
84 | r=0.0001,
85 | dirc=2,
86 | num=30,
87 | )
88 |
89 | # berry curvature distribution at Gamma
90 | tp.berry_curvature_proj([9], 2, 0, xy_range=0.04, num=5)
91 | tp.berry_curvature_proj([10], 2, 0, xy_range=0.01, num=5)
92 | # berry curvature distribution at R
93 | tp.berry_curvature_proj(
94 | [0, 1],
95 | 2,
96 | 0.5,
97 | [0.5, 0.5],
98 | xy_range=0.01,
99 | num=5,
100 | )
101 | tp.berry_curvature_proj(
102 | [8, 9],
103 | 2,
104 | 0.5,
105 | [0.5, 0.5],
106 | xy_range=0.01,
107 | num=5,
108 | )
109 |
110 | ## 2d slab model
111 | # build a 2d slab on z plane with 17 layers along z direction
112 | model_2d = model.cut_piece(17, 2, bottom_shift=0)
113 | # plot the surface band structure
114 | q_path_2d = [
115 | [-0.5, 0.0],
116 | [0.0, -0.5],
117 | [0.5, 0.0],
118 | [0.0, 0.0],
119 | [0.5, 0.5],
120 | [0.5, 0.0],
121 | [0.0, 0.5],
122 | [-0.5, 0.0],
123 | ]
124 | model_2d.atom_projected_band(
125 | q_path_2d,
126 | node_names=["X", "Y", "X", "$\Gamma$", "M", "X", "Y", "X"],
127 | k_num=70,
128 | y_min=100,
129 | y_max=126,
130 | margin_highlight=[0.45, 0],
131 | unit="cm-1",
132 | )
133 | # plot the gaussian smeared surface band structure
134 | model_2d.plot_edge(
135 | q_path_2d, [1, 0], y_min=100, y_max=126, k_num=150, fin_dirc=None, unit="cm-1"
136 | )
137 |
138 |
139 | ######### graphene ##############
140 | print("Graphene!!")
141 | model = read_from_files(r"..\tests\graphene")
142 | # make the model 2d!
143 | model_2d = model.cut_piece(1, 2)
144 | node_names = [r"$\Gamma$", "M", "K", r"$\Gamma$", "K'"]
145 | k_path_2d = [[0.0, 0.0], [0.5, 0.5], [2 / 3, 1 / 3], [0.0, 0.0], [1 / 3, 2 / 3]]
146 | model_2d.atom_projected_band(
147 | k_path_2d, site_comb=[[0], [1]], node_names=node_names, k_num=80
148 | )
149 |
150 |
151 | # plot 3d surface band structures and highlight the degenerate points
152 | model_2d.plot_3d_band([0, 1], [2 / 3, 1 / 3], 0.005, view=[-160, 50])
153 | model_2d.plot_3d_band([4, 5], [0.261, 0.522], 0.005, tol=5.0, view=[-160, 50])
154 |
155 | ## plot edge modes
156 | model_1d = model_2d.cut_piece(30, 1, bottom_shift=0)
157 | k_path_1d = [[0.0], [0.5], [1.0]]
158 | model_1d.plot_edge(k_path_1d, [0, 1], y_min=6, y_max=30, k_num=100, fin_dirc=1, sigma=3)
159 | model_1d.atom_projected_band(
160 | k_path_1d, y_min=0, y_max=50, fin_dirc=1, margin_highlight=[0, 1]
161 | )
162 |
163 | # explicitly specify dim=2
164 | tp = Topology(model_2d, dim=2)
165 | wfs1 = tp.gen_circle_wfs([2 / 3, 1 / 3], r=0.0001)
166 | wfs2 = tp.gen_circle_wfs([0.45, 0.45], r=0.01)
167 | wfs3 = tp.gen_circle_wfs([0.26, 0.52], r=0.01)
168 | print(
169 | "berry phase for dirac point1",
170 | tp.wilson_loop(
171 | [0],
172 | wfs1,
173 | ),
174 | )
175 | print(
176 | "berry phase for dirac point2",
177 | tp.wilson_loop(
178 | [4],
179 | wfs2,
180 | ),
181 | )
182 | print(
183 | "berry phase for dirac point3",
184 | tp.wilson_loop(
185 | [4],
186 | wfs3,
187 | ),
188 | )
189 |
190 |
191 | ######## SrTiO3 with NAC ##########
192 | print("SrTiO3!!")
193 | ## phonopy setup
194 | import phonopy
195 | from phonopy.harmonic.dynamical_matrix import get_dynamical_matrix
196 | from phonopy.phonon.band_structure import BandStructure
197 | from phonopy.phonon.band_structure import get_band_qpoints_and_path_connections
198 |
199 | # create phonopy object
200 | unitcell = r"..\tests\SrTiO3\POSCAR"
201 | supercell = r"..\tests\SrTiO3\SPOSCAR"
202 | born = r"..\tests\SrTiO3\BORN"
203 | force_const = r"..\tests\SrTiO3\FORCE_CONSTANTS"
204 | ph = phonopy.load(
205 | supercell_filename=supercell,
206 | born_filename=born,
207 | force_constants_filename=force_const,
208 | )
209 | # create DynamicalMatrix object
210 | dm = get_dynamical_matrix(
211 | ph.force_constants, ph.supercell, ph.primitive, nac_params=ph.nac_params
212 | )
213 |
214 | ## topoPhonon side
215 | # build a Structure object
216 | structure = Structure(3)
217 | structure.read_POSCAR(unitcell)
218 | structure.read_supercell(supercell)
219 | # build a model object with Phonopy DynamicalMatrix object
220 | model = Model(structure, dm=dm)
221 | k_path = [
222 | [0.0, 0.0, 0.0],
223 | [0.0, 0.5, 0.0],
224 | [0.5, 0.5, 0.0],
225 | [0.0, 0.0, 0.0],
226 | [0.5, 0.5, 0.5],
227 | ]
228 | model.atom_projected_band(
229 | k_path,
230 | node_names=["$\Gamma$", "X", "M", "$\Gamma$", "R"],
231 | site_comb=[[0], [1], [2, 3, 4]],
232 | )
233 |
234 |
235 | ######## MgB2 ##########
236 | print("nodal lines for MgB2!!")
237 | model = read_from_files(r"..\tests\MgB2")
238 | q_path = [
239 | [0.5,0.0,0.0],
240 | [0.0,0.0,0.0],
241 | [1/3,1/3,0.0],
242 | [1/3,1/3,0.5],
243 | [0.0,0.0,0.0],
244 | [0.0,0.0,0.5]
245 | ]
246 | node_names=['M', "$\Gamma$", 'K', 'H', "$\Gamma$", 'A']
247 | # project electron scattering intensity onto the band structure
248 | model.atom_projected_band(
249 | q_path,
250 | node_names=node_names,
251 | k_num=200,
252 | unit='THz',
253 | qi=[1,0,0],
254 | T=1000,
255 | int_factor=1,
256 | max_size=0.1
257 | )
258 | tp = Topology(model)
259 | wfs1 = tp.gen_circle_wfs([1/3,1/3],r=0.01,z=0.2)
260 | print("berry phase around the nodal line")
261 | print("for band1:", tp.wilson_loop([1], wfs1,))
262 | print("for band3:", tp.wilson_loop([3], wfs1,))
263 | print("for band6:", tp.wilson_loop([6], wfs1,))
264 |
--------------------------------------------------------------------------------
/topophonon/structure.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | This module contains the class that describes the crystal structure related
4 | properties
5 | """
6 |
7 | from topophonon.units import masses_dict
8 | import numpy as np
9 | import os
10 | import re
11 | import warnings
12 | from typing import List
13 | from copy import deepcopy
14 |
15 | class Structure():
16 |
17 | #regex for finding coordinates
18 | PATTERN = "(-?\d+\.?\d+)\s*(-?\d+\.?\d+)\s*(-?\d+\.?\d+).*"
19 |
20 |
21 | def __init__(self,
22 | dim: int,
23 | lat: List[List[float]] = None,
24 | coords: List[List[float]] = None,
25 | masses: List[float] = None,
26 | atoms: List[str] = None,
27 | shift: List[float] = [0.0, 0.0, 0.0]):
28 | """
29 | Parameters
30 | ----------
31 | dim : int
32 | dimension of the crystal.
33 | lat : 2d list or ndarray, optional
34 | a matrix defines the lattice parameters in cartesian coordinates.
35 | The default is None
36 | coords : 2d list or ndarray, optional
37 | a list of vectors define the coordinates of atoms in the unit cell.
38 | The default is None
39 | masses : list, optional
40 | a list contains the massses of atoms. If not specified,
41 | default values will be used based on "atoms"
42 | The default is None
43 | atoms : list, optional
44 | a list contains the name of atoms.
45 | The default is None.
46 | """
47 |
48 | self.dim = dim
49 | assert isinstance(self.dim, int) and 1 <= dim <= 3, "dimension must be 1, 2 or 3"
50 | if lat is None:
51 | self.lat = np.zeros((self.dim,self.dim))
52 | else:
53 | self.lat = np.array(lat,dtype=float)
54 | # calculate the reciprocal lattice
55 | # self.k_lat = np.linalg.inv(np.dot(self.lat,self.lat.T))
56 | self.k_lat = np.linalg.inv(self.lat.T)
57 |
58 | if coords is not None:
59 | for coord in coords:
60 | if len(coord) != self.dim:
61 | raise ValueError("The lenght of a coordinate must match dim")
62 | self.coords = coords
63 |
64 | self.prm_dirc = np.array(coords,dtype=float)
65 | self.prm_cart = self._direct_to_cartesian(self.prm_dirc, self.lat)
66 |
67 | if masses is None:
68 | self.masses = None
69 | # set the atoms and default masses
70 | self._set_atoms(atoms)
71 | if masses is not None:
72 | assert isinstance(masses, list), ("the masses must be given in a list")
73 | if self.masses is not None:
74 | warnings.warn("masses are already given, will be overwritten")
75 | self.masses = masses
76 | self.shift = np.array(shift)
77 |
78 |
79 | def _atoms_to_masses(self,
80 | atoms: List[str]):
81 | """
82 | convert a list of atoms to their masses based on their names
83 | """
84 | masses = []
85 | for a in atoms:
86 | assert isinstance(a,str), "the atoms must be given in string type"
87 | assert a.upper() in masses_dict,\
88 | "unrecognized atom type {}".format(a)
89 | masses.append(masses_dict[a.upper()])
90 | self.masses = masses
91 |
92 |
93 | def _set_atoms(self,
94 | atoms: List[str]):
95 | """
96 | set atom list and mass list
97 |
98 | """
99 | if atoms is None:
100 | self.atoms = None
101 | return
102 | warnings.warn("default masses are used")
103 | self.atoms = atoms
104 | self._atoms_to_masses(atoms)
105 |
106 |
107 | def set_lat(self,
108 | lat: np.ndarray):
109 | """
110 | set real space and reciprocal lattice tensor
111 |
112 | Parameters
113 | ----------
114 | lat : 2d ndarray of float
115 | 3 lattice vectors
116 | """
117 |
118 | self.lat = lat
119 | self.k_lat = np.linalg.inv(np.dot(lat, lat.T))
120 |
121 |
122 | @staticmethod
123 | def _direct_to_cartesian(coord: np.ndarray,
124 | lat: np.ndarray) -> np.ndarray :
125 | """
126 | convert a direct coordinate to a cartesian coordinate
127 |
128 | """
129 | return np.dot(coord, lat)
130 |
131 |
132 | @staticmethod
133 | def _cartesian_to_direct(coord: np.ndarray,
134 | lat: np.ndarray) -> np.ndarray :
135 | """
136 | convert a cartesian coordinate to a direct coordinate
137 |
138 | """
139 | return np.dot(coord, np.linalg.inv(lat))
140 |
141 |
142 | def del_atoms(self, indices):
143 | self.masses = [x for i, x in enumerate(self.masses) if i not in indices]
144 | self.atoms = [x for i, x in enumerate(self.atoms) if i not in indices]
145 | self.prm_cart = deepcopy(self.prm_cart[[i for i in range(len(self.prm_cart)) if i not in indices]])
146 | self.prm_dirc = deepcopy(self.prm_dirc[[i for i in range(len(self.prm_dirc)) if i not in indices]])
147 |
148 |
149 | def read_POSCAR(self, poscar: str):
150 | """
151 | read the VASP POSCAR file
152 |
153 | Parameters
154 | ----------
155 | poscar : str
156 | the path of POSCAR file
157 | """
158 |
159 | assert self.dim == 3, "To read files from phonopy, the dimension must be 3"
160 | assert os.path.exists(poscar), "{} not existed".format(poscar)
161 |
162 | self.prm_dirc, self.prm_cart = [], []
163 | # try:
164 | with open(poscar) as p:
165 | # skip the fist line
166 | p.readline()
167 | # the factor of lattice
168 | factor = float(p.readline().strip())
169 | # read the lattice constants
170 | for i in range(3):
171 | r_str = p.readline().strip().split()
172 | r_float = [float(r) * factor for r in r_str]
173 | self.lat[i] = np.array(r_float)
174 | self.k_lat = np.linalg.inv(self.lat.T)
175 | # read atoms
176 | atoms = p.readline().strip().split()
177 | counts = p.readline().strip().split()
178 | all_atoms = []
179 | for i in range(len(counts)):
180 | for _ in range(int(counts[i])):
181 | all_atoms.append(atoms[i])
182 | #convert atoms to masses
183 | if self.masses is None:
184 | self._set_atoms(all_atoms)
185 |
186 | # read the mode
187 | mode = p.readline().strip()
188 |
189 | # read all coordinates
190 | if mode.lower().startswith('c'):
191 | pass
192 |
193 | elif mode.lower().startswith('d'):
194 | for i in range(len(self.atoms)):
195 | coord_str = re.findall(Structure.PATTERN, p.readline())[0]
196 | coord_array = np.array([float(r) for r in coord_str])
197 | self.prm_dirc.append(coord_array)
198 | self.prm_cart.append(
199 | self._direct_to_cartesian(coord_array, self.lat))
200 | self.prm_dirc = np.array(self.prm_dirc)
201 | self.prm_cart = np.array(self.prm_cart)
202 | else:
203 | raise Exception("unknown mode in POSCAR; can be direct or cartesian")
204 | # except:
205 | # raise ValueError("Something goes wrong with {}".format(poscar))
206 |
207 |
208 | def read_supercell(self, sposcar: str):
209 | """
210 | read the supercell file which can be generated by phonopy
211 |
212 | Parameters
213 | ----------
214 | sposcar : str
215 | the path of SPOSCAR file
216 |
217 | """
218 |
219 | assert os.path.exists(sposcar), "{} not existed".format(sposcar)
220 |
221 | #convert the original coordinates to cartesian coordinates
222 | # org_coords_cart = []
223 | # for coord in self.prm_dirc:
224 | # org_coords_cart.append(self._direct_to_cartesian(coord, self.lat))
225 | # org_coords_cart = np.array(org_coords_cart)
226 |
227 | self.super_dirc, self.super_cart = [], []
228 | self.super_lat = np.zeros((self.dim,self.dim))
229 | #Read information in the supercell
230 | try:
231 | with open(sposcar) as p:
232 | p.readline()
233 | factor = float(p.readline().strip())
234 | # read the lattice constants
235 | for i in range(3):
236 | r_str = p.readline().strip().split()
237 | r_float = [float(r) * factor for r in r_str]
238 | self.super_lat[i] = np.array(r_float)
239 | p.readline()
240 | #total number of atoms in the supercell
241 | nums = p.readline().strip().split()
242 | nums = [int(num) for num in nums]
243 | total = sum(nums)
244 | # read the mode
245 | mode = p.readline().strip()
246 |
247 | # read all coordinates
248 | if mode.lower().startswith('c'):
249 | pass
250 | elif mode.lower().startswith('d'):
251 |
252 | for i in range(total):
253 | coord_str = re.findall(Structure.PATTERN, p.readline())[0]
254 | coord = np.array([float(r) for r in coord_str])
255 | self.super_dirc.append(coord)
256 | self.super_cart.append(
257 | self._direct_to_cartesian(coord, self.super_lat))
258 | self.super_dirc = np.array(self.super_dirc)
259 | self.super_cart = np.array(self.super_cart)
260 | except:
261 | raise ValueError("Something goes wrong with {}". format(sposcar))
262 |
263 |
264 | @staticmethod
265 | def _write_structure(file, lat, atoms, count, coords):
266 | with open (file, 'w') as f:
267 | f.write('Output from topoPhonon\n')
268 | f.write(' {:.6f} \n'.format(1))
269 | f.write(" {:.6f} {:.6f} {:.6f}\n {:.6f} {:.6f} {:.6f}\n {:.6f} {:.6f} {:.6f}\n"\
270 | .format(lat[0][0], lat[0][1], lat[0][2],
271 | lat[1][0], lat[1][1], lat[1][2],
272 | lat[2][0], lat[2][1], lat[2][2],))
273 | for atom in atoms:
274 | f.write(" {}".format(atom))
275 | f.write('\n')
276 | for c in count:
277 | f.write(" {}".format(c))
278 | f.write('\n')
279 | f.write('Direct')
280 | f.write('\n')
281 | for coord in coords:
282 | f.write(' {:.6f} {:.6f} {:.6f}\n'.format(coord[0], coord[1], coord[2]))
283 |
284 |
285 | def write_poscar(self, file):
286 | """
287 | output the structure in VASP POSCAR format
288 |
289 | Parameters
290 | ----------
291 | file : str
292 | the path of output POSCAR file
293 |
294 | """
295 | lat = self.lat
296 | atoms, count = np.unique(self.atoms,return_counts=True)
297 | coords = self.prm_dirc
298 | self._write_structure(file, lat, atoms, count, coords)
--------------------------------------------------------------------------------
/topophonon/topology.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sat Aug 20 21:10:49 2022
4 |
5 | @author: zhuhe
6 | """
7 |
8 | import copy
9 | import numpy as np
10 | from scipy.linalg import sqrtm
11 | import warnings
12 | import matplotlib.pyplot as plt
13 | import functools
14 | from copy import deepcopy
15 | from scipy.optimize import basinhopping, minimize
16 |
17 | class Topology():
18 | """
19 | Class with topology-related properties and methods
20 | """
21 |
22 |
23 | def __init__(self, model, dim=None):
24 | self.model = model
25 | self.nb = len(model.structure.masses) * model.dim
26 | if dim is None:
27 | self.dim = model.dim
28 | else:
29 | self.dim = dim
30 |
31 | def _wfs_at_kpt(self, kpt):
32 | """
33 | Return the modified phonon eigenvectors at kpt
34 | """
35 | modified_wf = []
36 | dy_mt, all_freqs, eig_vecs =\
37 | self.model.solve_dynamical_matrix_kpath([kpt], k_num=1)
38 | dim = len(all_freqs[0])
39 | for i in range(dim):
40 | # convert the row vector to column vector
41 | # old_wf = eig_vecs[0][:,i].reshape((-1,1))
42 | # freq = all_freqs[0][i]
43 | # new_wf = np.zeros(dim*2, dtype=complex)
44 | # new_wf[:dim] = np.dot(sqrtm(dy_mt), old_wf).flatten()
45 | # new_wf[dim:] = (-1j * freq * old_wf).flatten()
46 | # modified_wf.append(new_wf)
47 | old_wf = np.array(eig_vecs[0][:,i])
48 | modified_wf.append(old_wf)
49 | return modified_wf
50 |
51 |
52 | def _gen_k_loop_bz(self, k_along, k_start, k_num=50):
53 | """
54 | Generate a closed k loop for wilson_loop function
55 |
56 | """
57 | step = np.array([0 for _ in range(self.dim)],dtype=float)
58 | step[k_along] = 1/(k_num-1)
59 | # self._back_to_bz(k_start)
60 | k_grids = [copy.deepcopy(k_start)]
61 | for i in range(k_num-1):
62 | k_start += step
63 | # print(k_start)
64 | # self._back_to_bz(k_start)
65 | # print(k_start)
66 | temp = copy.deepcopy(k_start)
67 | k_grids.append(temp)
68 | return np.array(k_grids)
69 |
70 |
71 | def gen_BZ_wfs(self, k_along, k_start, k_num=60):
72 | """
73 | Generate the phonon eigenvectors along a closed line over the whole brillioun zone.
74 |
75 | Parameters
76 | ----------
77 | k_along : int
78 | the direction of the line
79 | k_start : list of float
80 | the starting (and the ending) point of the line
81 | k_num : int, optional
82 | total number of kpoints on the line
83 | The default is 60
84 | Returns
85 | -------
86 | an array of eigenvectors along the line
87 | """
88 | k_start = np.array(k_start, dtype=float)
89 | k_grids = self._gen_k_loop_bz(k_along, k_start, k_num)
90 | self.k_grids = k_grids
91 | all_wfs = []
92 | for kpt in k_grids:
93 | modified_wf = self._wfs_at_kpt(kpt)
94 | all_wfs.append(modified_wf)
95 | return np.array(all_wfs)
96 |
97 |
98 | def gen_circle_wfs(self, center, dirc=2, z=0, r=0.05, k_num=60):
99 | """
100 | Generate the eigenvectors along a circle.
101 |
102 | Parameters
103 | ----------
104 | center : list, [float, float]
105 | two floats that specify the coordinates of the center
106 | dirc : int, optional
107 | the direction that is normal to the circle
108 | The default is 2
109 | z : float, optional
110 | the third coordinate that defines the plane of the circle; for example,
111 | if the dirc=0 and z=0.5, the wfs are generated on x=0.5 plane.
112 | The default is 0.0
113 | r : float, optional
114 | the radius of the circle
115 | The default is 0.05
116 | k_num : int, optional
117 | total number of kpoints on the line
118 | The default is 60
119 | Returns
120 | -------
121 | an array of eigenvectors on the circle
122 | """
123 |
124 | kpts = []
125 | wfs = []
126 | for i in range(k_num):
127 | theta = 2 * np.pi * i / k_num
128 | x = center[0] + r * np.cos(theta)
129 | y = center[1] + r * np.sin(theta)
130 |
131 | if self.dim == 2:
132 | kpt = np.array([x,y,0])
133 | else:
134 | if dirc == 0:
135 | kpt = np.array([z,x,y])
136 | elif dirc == 1:
137 | kpt = np.array([y,z,x])
138 | elif dirc == 2:
139 | kpt = np.array([x,y,z])
140 | else:
141 | raise Exception("dirc must be 0, 1 or 2 if dim of the model is 3")
142 | # kpt = np.dot(kpt, np.linalg.inv(self.model.structure.k_lat))
143 | kpts.append(kpt)
144 | wfs.append(self._wfs_at_kpt(kpt))
145 | # make sure the last wf is equal to the first one
146 | kpts.append(kpts[0])
147 | wfs.append(wfs[0])
148 | return np.array(kpts), np.array(wfs)
149 |
150 |
151 | def _gen_orbit_wfs(self, center, r, theta, dirc, k_num=60):
152 | """
153 | Generate an orbit around for a given center
154 | """
155 | wfs = []
156 | for i in range(k_num+1):
157 | phi = 2 * np.pi * i / k_num
158 | x = center[0] + r * np.sin(theta) * np.cos(phi)
159 | y = center[1] + r * np.sin(theta) * np.sin(phi)
160 | z = center[2] + r * np.cos(theta)
161 | if dirc == 0:
162 | kpt = np.array([y,z,x])
163 | elif dirc == 1:
164 | kpt = np.array([z,x,y])
165 | elif dirc == 2:
166 | kpt = np.array([x,y,z])
167 | else:
168 | raise Exception("dirc must be 0, 1 or 2")
169 | # print(kpt)
170 | wfs.append(self._wfs_at_kpt(kpt))
171 | return np.array(wfs)
172 |
173 |
174 | @staticmethod
175 | def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.001, index=None):
176 | # find the gauge for continous berry connections
177 | # print(np.abs(vector))
178 | vector = np.array(vector)
179 | if index == None:
180 | index = np.argmax(np.abs(vector))
181 | print('index: ', index)
182 | angle = np.angle(vector[index])
183 | vector = vector*np.exp(-1j*angle)
184 | return vector
185 |
186 |
187 | @staticmethod
188 | def find_vector_with_fixed_gauge_by_minimizing_real_part(vector, index):
189 | # find the gauge for continous berry connections
190 | def func(theta):
191 | res = np.cos(theta) * vector.real - np.sin(theta) * vector.imag
192 | return np.linalg.norm(res)
193 |
194 | min_real = float('inf')
195 | # minimizer_kwargs = dict(method="L-BFGS-B", bounds=[(0, 2*np.pi)], tol=1e-12)
196 | for start_point in np.arange(0, 2*3.14, 0.5):
197 | # argmin_theta = basinhopping(func, start_point, minimizer_kwargs=minimizer_kwargs, stepwise_factor=0.1).x[0]
198 | argmin_theta = minimize(func, start_point, method='COBYLA' , bounds=[(0, 2*np.pi)], tol=1e-30, options={'maxiter':100}).x[0]
199 | # print(argmin_theta, func(argmin_theta))
200 | if func(argmin_theta) < min_real:
201 | globalmin_theta = argmin_theta
202 | min_real = func(argmin_theta)
203 | # print(min_real)
204 |
205 | vector = vector * np.exp(1j * globalmin_theta)
206 | # set one component positive
207 | if vector[index].real < 0:
208 | vector *= -1
209 | return vector
210 |
211 |
212 | def connection(self, k, band, index=None, delta=1e-9, precision=0.0001):
213 | """
214 | Calculate Berry Connection
215 | """
216 | # print(k)
217 | dy_mt = self.model._make_dynamical_matrix(k)
218 | eigenvalue, eigenvector = np.linalg.eigh(dy_mt)
219 | vector = eigenvector[:, np.argsort(np.real(eigenvalue))[band]]
220 | # vector = eigenvector[:, band]
221 | # print('vector_org',vector)
222 | print(abs(vector))
223 | vector = self.find_vector_with_fixed_gauge_by_making_one_component_real(vector, index=index)
224 | # vector = self.find_vector_with_fixed_gauge_by_minimizing_real_part(vector, index)
225 | # print('vector',vector)
226 | # vector = self.find_vector_with_the_same_gauge(d_vector, vector)
227 |
228 | k = np.dot(k, self.model.structure.k_lat)
229 | A = []
230 | for d in range(self.model.dim):
231 | dk = copy.deepcopy(k)
232 | dk[d] = dk[d] + delta
233 | dk = np.dot(dk, np.linalg.inv(self.model.structure.k_lat))
234 | # print(dk)
235 | dmt = self.model._make_dynamical_matrix(dk)
236 | d_eigenvalue, d_eigenvector = np.linalg.eigh(dmt)
237 | d_vector = d_eigenvector[:, np.argsort(np.real(d_eigenvalue))[band]]
238 | # d_vector = d_eigenvector[:, band]
239 | # print('d_vector_org',d_vector)
240 | d_vector = self.find_vector_with_fixed_gauge_by_making_one_component_real(d_vector, index=index)
241 | # d_vector = self.find_vector_with_fixed_gauge_by_minimizing_real_part(d_vector, index)
242 | # d_vector = self.find_vector_with_the_same_gauge(d_vector, vector)
243 | # print('d_vector',d_vector)
244 | # print('d_vector-vector', d_vector-vector)
245 | # if d == 0:
246 | # print('d_vector', d_vector)
247 | # print('d_vector-vector', d_vector-vector)
248 | A.append(1j * np.dot(vector.transpose().conj(), d_vector-vector)/delta)
249 | # print(' ')
250 | # print('---------------')
251 | return A
252 |
253 |
254 | @staticmethod
255 | def wilson_loop(band_indices, all_wfs,):
256 | """
257 | Compute the berry phase of a given set of eigenvectors, the first eigenvector
258 | must be equal to the last eigenvector
259 |
260 | Parameters
261 | ----------
262 | band_indices : list of ints
263 | list of band indices for which the wilson loop is calculated.
264 | all_wfs : ndarray of complex
265 | an array of eigenvectors around a closed path.
266 |
267 | Returns
268 | -------
269 | berry phase calculated with wilson loop method
270 | """
271 |
272 | if isinstance(band_indices, int):
273 | band_indices = [band_indices]
274 | num_bands = len(band_indices)
275 | k_num = len(all_wfs)
276 | prod = np.identity(num_bands, dtype=complex)
277 | det = 1
278 | #iterate over all kpoints on the loop
279 | for i in range(k_num-1):
280 | #container for overlap matrix
281 | ovlp = np.zeros([num_bands,num_bands],dtype=complex)
282 | #iterate over all bands for overlap matrix
283 | for j in range(num_bands):
284 | for k in range(num_bands):
285 | wf_1 = all_wfs[i][band_indices[j]]
286 | wf_2 = all_wfs[i+1][band_indices[k]]
287 | ovlp[j,k] = np.dot(wf_1.conjugate(),wf_2)
288 | # det *= np.linalg.det(ovlp)
289 | # print(np.linalg.det(ovlp),det)
290 | # phase = -np.imag(np.log(det)) / np.pi
291 | # calculate determinant for each overlap matrix and then multiply?
292 | # multiply all overlap matrices
293 | prod = np.dot(prod,ovlp)
294 | # print(prod)
295 | # compute the determinant
296 | det = np.linalg.det(prod)
297 | # the flux for this small plaquette
298 | phase = (-1.0)*np.angle(det, deg=False)/np.pi
299 | return phase
300 |
301 |
302 | def wcc_evol_sphere(self, band_indices, center, r=0.001, dirc=2, num=60,):
303 | """
304 | Generate a sphere and plot the evolution of wannier centers around that sphere,
305 | for 3d only. The sphere is sliced into multiple orbitals. Wilson loop
306 | method is applied to calculate the wannier center on each orbit.
307 |
308 | Parameters
309 | ----------
310 | band_indices : list of int
311 | list of band indices on which the wannier centers are calculated.
312 | center : list, [float, float, float]
313 | three floats that specify the coordinates of the sphere center
314 | r : float, optional
315 | the radius of the sphere
316 | The default is 0.001
317 | dirc : int, optional
318 | the direction along which theta evolves; in other words, the orbitals
319 | are perpendicular to those orbitals
320 | The default is 2
321 | num : int, optional
322 | number of slices and number of k points on the loop
323 | The default is 60
324 |
325 | Returns
326 | -------
327 | berry phase calculated with wilson loop method
328 | """
329 |
330 | if isinstance(band_indices, int):
331 | band_indices = [[band_indices]]
332 | if isinstance(band_indices[0],int):
333 | band_indices = [band_indices]
334 | print("calculating wcc charge center evolution around {}...".format(center))
335 | polar_angles = []
336 | all_wccs = [[] for _ in range(len(band_indices))]
337 | for i in range(num+1):
338 | theta = np.pi * i / num
339 | polar_angles.append(theta/np.pi)
340 | wfs = self._gen_orbit_wfs(center, r, theta, dirc, k_num=num)
341 | for j in range(len(band_indices)):
342 | w = self.wilson_loop(band_indices[j], wfs)
343 | all_wccs[j].append(w)
344 | # self.polar_angles = polar_angles
345 | # self.wccs = wccs
346 | for i, wccs in enumerate(all_wccs):
347 | plt.figure()
348 | plt.scatter(polar_angles, wccs)
349 | plt.ylim(-1, 1)
350 | plt.xlim(0, 1)
351 | plt.title("band {}".format(str(band_indices[i])))
352 | # return polar_angles, all_wccs
353 |
354 |
355 | def berry_curvature(self, kpt, band_indices, delta=1e-9):
356 | """
357 | Compute the berry curvature for one or more bands on a given k point,
358 | using Kubo formulation.
359 | Works for 2d and 3d cases.
360 |
361 | Parameters
362 | ----------
363 | kpt : list of floats
364 | the coordinates of the kpoint; the length must be equal to self.dim
365 | band_indices : list of ints
366 | list of band indices on which the berry curvature is calculated.
367 | delta : float, optional
368 | a small distance between two points for differentiating the Hamiltonian.
369 | The default is 1e-9
370 |
371 | Returns
372 | -------
373 | a 3/1-component vector for 3-d/2-d models
374 | """
375 |
376 | assert len(kpt) == self.dim, ("wrong dimension of kpt")
377 | # build a wilson loop adjacent to the point
378 | d, freqs, eig_vecs =\
379 | self.model.solve_dynamical_matrix_kpath([kpt],
380 | k_num=1)
381 | num_deg = len(band_indices)
382 | num_bands = len(freqs[0])
383 | f0 = [freqs[0][i] for i in band_indices]
384 | wfs = [eig_vecs[0][:,i] for i in band_indices]
385 |
386 | if self.dim == 2:
387 | # total = np.array(0+0j)
388 | kxp = kpt + np.array([delta,0])
389 | kyp = kpt + np.array([0,delta])
390 | d_x, _, _ = self.model.solve_dynamical_matrix_kpath([kxp],
391 | k_num=1,)
392 | d_y, _, _ = self.model.solve_dynamical_matrix_kpath([kyp],
393 | k_num=1,)
394 | delta_x = (d_x - d)/delta
395 | delta_y = (d_y - d)/delta
396 | # build the berry curvature matrix B_ij
397 | total = np.zeros((num_deg, num_deg),dtype=complex)
398 | for i in range(num_deg):
399 | for j in range(num_deg):
400 | fi, fj = f0[i], f0[j]
401 | wfi, wfj = wfs[i], wfs[j]
402 | # iterate over all bands
403 | for m in range(num_bands):
404 | if m in band_indices:
405 | continue
406 | wfm = np.array(eig_vecs[0][:,m])
407 | fm = freqs[0][m]
408 | if abs(fi - fm) < 1e-11:
409 | raise Exception("band {} and {} are degenerate"\
410 | .format(i, m))
411 | if abs(fj - fm) < 1e-11:
412 | raise Exception("band {} and {} are degenerate"\
413 | .format(j, m))
414 | prod1, prod2 = np.zeros(2, dtype=complex), np.zeros(2, dtype=complex)
415 | prod1[0] = np.dot(wfi.conjugate(),np.dot(delta_x, wfm))
416 | prod1[1] = np.dot(wfi.conjugate(),np.dot(delta_y, wfm))
417 | prod2[0] = np.dot(wfm.conjugate(),np.dot(delta_x, wfj))
418 | prod2[1] = np.dot(wfm.conjugate(),np.dot(delta_y, wfj))
419 | # total[i][j] += np.cross(prod1, prod2) / (fi-fm) / (fj-fm)
420 | total[i][j] += np.cross(prod1, prod2) / (fi-fm) / (fj-fm)
421 | elif self.dim == 3:
422 | # total = np.zeros(3, dtype=complex)
423 | kxp = kpt + np.array([delta,0,0])
424 | kyp = kpt + np.array([0,delta,0])
425 | kzp = kpt + np.array([0,0,delta])
426 | d_x, _, _ = self.model.solve_dynamical_matrix_kpath([kxp],
427 | k_num=1,)
428 | d_y, _, _ = self.model.solve_dynamical_matrix_kpath([kyp],
429 | k_num=1,)
430 | d_z, _, _ = self.model.solve_dynamical_matrix_kpath([kzp],
431 | k_num=1,)
432 | delta_x = (d_x - d)/delta
433 | delta_y = (d_y - d)/delta
434 | delta_z = (d_z - d)/delta
435 |
436 | # build the berry curvature matrix B_ij
437 | total = np.zeros((num_deg, num_deg, 3),dtype=complex)
438 | for i in range(num_deg):
439 | for j in range(num_deg):
440 | fi, fj = f0[i], f0[j]
441 | wfi, wfj = wfs[i], wfs[j]
442 | # iterate over all bands
443 | for m in range(num_bands):
444 | if m in band_indices:
445 | continue
446 | wfm = np.array(eig_vecs[0][:,m])
447 | fm = freqs[0][m]
448 | if abs(fi - fm) < 1e-22:
449 | warnings.warn("band {} and {} are likely to be degenerate at {}"\
450 | .format(band_indices[i], m, kpt))
451 | if abs(fj - fm) < 1e-22:
452 | warnings.warn("band {} and {} are likely to be degenerate at {}"\
453 | .format(band_indices[j], m, kpt))
454 | prod1, prod2 = np.zeros(3, dtype=complex), np.zeros(3, dtype=complex)
455 | prod1[0] = np.dot(wfi.conjugate(),np.dot(delta_x, wfm))
456 | prod1[1] = np.dot(wfi.conjugate(),np.dot(delta_y, wfm))
457 | prod1[2] = np.dot(wfi.conjugate(),np.dot(delta_z, wfm))
458 | prod2[0] = np.dot(wfm.conjugate(),np.dot(delta_x, wfj))
459 | prod2[1] = np.dot(wfm.conjugate(),np.dot(delta_y, wfj))
460 | prod2[2] = np.dot(wfm.conjugate(),np.dot(delta_z, wfj))
461 | total[i][j] += np.cross(prod1, prod2) / (fi-fm) / (fj-fm)
462 | else:
463 | raise Exception("To calculate berry curvatures, the dimension must\
464 | be 2 or 3")
465 | return np.real(1j * np.trace(total))
466 |
467 |
468 | @staticmethod
469 | def _make_k_grid(xy_range, num):
470 | """
471 | make a 2d k_grid for berry_curvature_proj and berry_curvature_2d method
472 | """
473 | interval = xy_range/num
474 | a = np.arange(-xy_range, xy_range+interval, interval)
475 | kx,ky = np.meshgrid(a,a)
476 | return kx, ky
477 |
478 |
479 | # @staticmethod
480 | # def _log_scale(x):
481 | # # scale the vector logarithmically
482 | # return np.sign(x)*np.log10(1+np.abs(x))
483 |
484 |
485 | # @staticmethod
486 | # def _normalization(x, y):
487 | # return x/np.sqrt(x**2 + y**2), y/np.sqrt(x**2 + y**2)
488 |
489 |
490 | def berry_curvature_proj(self,
491 | band_indices,
492 | dirc,
493 | kz,
494 | center=[0,0],
495 | xy_range=0.5,
496 | num=10,):
497 |
498 | """
499 | plot 3d berry curvature for one or more bands projected on a 2D plane,
500 | "dirc" is normal to the plane, "center" specify the center of the map;
501 | "kz" determines the position of the plane on "dirc" axis. for example:
502 | dirc=2, kz=0.5, center=[0,0], the berry curvature is plotted on xy
503 | plane with kz=0.5 around [0,0,0.5] point.
504 |
505 | Parameters
506 | ----------
507 | band_indices : list of ints
508 | list of band indices on which the berry curvature is calculated.
509 | dirc : int
510 | the direction that is normal to the plane on which the berry curvatures
511 | are projected.
512 | kz : float
513 | the third coordinate that defines the plane of the circle; for example,
514 | if the dirc=0 and z=0.5, the berry curvatures will be plotted on x=0.5 plane.
515 | center : list, [float, float], optional
516 | coordinate of the point around which the berry curvatures are plotted;
517 | specify only two component on the plane; the third coordinate is specified by kz.
518 | xy_range : float
519 | the range of the grid, i.e., the plot spans [center[0]-xy_range,
520 | center[0]+xy_range] and [center[1]-xy_range, center[1]+xy_range]
521 | The default is 0.5
522 | num : int, optional
523 | number of points sampled on the plane is given by num * num
524 | The default is 10
525 |
526 | """
527 |
528 | print("start plotting the berry curvature field map...")
529 | if isinstance(band_indices, int):
530 | band_indices = [band_indices]
531 | # # a1 = np.arange(-xy_range[0], -interval/2, interval)
532 | # # a2 = np.arange(interval/2, xy_range[0], interval)
533 | # # a = np.hstack((a1,a2))
534 | # interval_0, interval_1 = xy_range[0]/num, xy_range[1]/num
535 | # a = np.arange(-xy_range[0], xy_range[0], interval_0)
536 | # # b1 = np.arange(-xy_range[1], -interval/2, interval)
537 | # # b2 = np.arange(interval/2, xy_range[1], interval)
538 | # # b = np.hstack((b1,b2))
539 | # b = np.arange(-xy_range[1], xy_range[1], interval_1)
540 | # kx,ky = np.meshgrid(a,b)
541 | kx, ky = self._make_k_grid(xy_range, num)
542 | kx0, ky0 = center[0], center[1]
543 | #the x and y component of berry curvature
544 | # for group in band_indices:
545 |
546 | u = np.zeros((len(kx), len(kx[0])), dtype=float)
547 | v = np.zeros((len(kx), len(kx[0])), dtype=float)
548 | plt.figure()
549 | for i in range(len(kx)):
550 | for j in range(len(kx[0])):
551 | if dirc == 0:
552 | kpt = np.array([kz,kx0+kx[i][j],ky0+ky[i][j]])
553 | berry_curv = self.berry_curvature(kpt, band_indices)
554 | norm = np.sqrt(berry_curv[1]**2 + berry_curv[2]**2)
555 | if norm == 0:
556 | u[i][j] = None
557 | v[i][j] = None
558 | else:
559 | u[i][j] = berry_curv[1]/norm
560 | v[i][j] = berry_curv[2]/norm
561 | elif dirc == 1:
562 | kpt = np.array([ky0+ky[i][j],kz,kx0+kx[i][j]])
563 | berry_curv = self.berry_curvature(kpt, band_indices)
564 | norm = np.sqrt(berry_curv[2]**2 + berry_curv[0]**2)
565 | if norm == 0:
566 | u[i][j] = None
567 | v[i][j] = None
568 | else:
569 | u[i][j] = berry_curv[2]/norm
570 | v[i][j] = berry_curv[0]/norm
571 | elif dirc == 2:
572 | kpt = np.array([kx0+kx[i][j],ky0+ky[i][j],kz])
573 | berry_curv = self.berry_curvature(kpt, band_indices)
574 | norm = np.sqrt(berry_curv[0]**2 + berry_curv[1]**2)
575 | # print(norm)
576 | if norm == 0:
577 | u[i][j] = None
578 | v[i][j] = None
579 | else:
580 | u[i][j] = berry_curv[0]/norm
581 | v[i][j] = berry_curv[1]/norm
582 | else:
583 | raise Exception("dirc must be 0, 1 or 2")
584 | # plt.quiver(kx,ky,self._log_scale(u),self._log_scale(v), scale_units='xy')
585 | # print(u, v)
586 | plt.quiver(kx+kx0, ky+ky0, u, v, scale_units='xy')
587 | plt.title("band {}".format(str(band_indices)))
588 |
--------------------------------------------------------------------------------
/topophonon/units.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Fri Aug 19 15:18:17 2022
4 |
5 | @author: zhuhe
6 | """
7 |
8 | masses_dict = {'H' : 1.008,'HE' : 4.003, 'LI' : 6.941, 'BE' : 9.012,\
9 | 'B' : 10.811, 'C' : 12.011, 'N' : 14.007, 'O' : 15.999,\
10 | 'F' : 18.998, 'NE' : 20.180, 'NA' : 22.990, 'MG' : 24.305,\
11 | 'AL' : 26.982, 'SI' : 28.086, 'P' : 30.974, 'S' : 32.066,\
12 | 'CL' : 35.453, 'AR' : 39.948, 'K' : 39.098, 'CA' : 40.078,\
13 | 'SC' : 44.956, 'TI' : 47.867, 'V' : 50.942, 'CR' : 51.996,\
14 | 'MN' : 54.938, 'FE' : 55.845, 'CO' : 58.933, 'NI' : 58.693,\
15 | 'CU' : 63.546, 'ZN' : 65.38, 'GA' : 69.723, 'GE' : 72.631,\
16 | 'AS' : 74.922, 'SE' : 78.971, 'BR' : 79.904, 'KR' : 84.798,\
17 | 'RB' : 84.468, 'SR' : 87.62, 'Y' : 88.906, 'ZR' : 91.224,\
18 | 'NB' : 92.906, 'MO' : 95.95, 'TC' : 98.907, 'RU' : 101.07,\
19 | 'RH' : 102.906, 'PD' : 106.42, 'AG' : 107.868, 'CD' : 112.414,\
20 | 'IN' : 114.818, 'SN' : 118.711, 'SB' : 121.760, 'TE' : 126.7,\
21 | 'I' : 126.904, 'XE' : 131.294, 'CS' : 132.905, 'BA' : 137.328,\
22 | 'LA' : 138.905, 'CE' : 140.116, 'PR' : 140.908, 'ND' : 144.243,\
23 | 'PM' : 144.913, 'SM' : 150.36, 'EU' : 151.964, 'GD' : 157.25,\
24 | 'TB' : 158.925, 'DY': 162.500, 'HO' : 164.930, 'ER' : 167.259,\
25 | 'TM' : 168.934, 'YB' : 173.055, 'LU' : 174.967, 'HF' : 178.49,\
26 | 'TA' : 180.948, 'W' : 183.84, 'RE' : 186.207, 'OS' : 190.23,\
27 | 'IR' : 192.217, 'PT' : 195.085, 'AU' : 196.967, 'HG' : 200.592,\
28 | 'TL' : 204.383, 'PB' : 207.2, 'BI' : 208.980, 'PO' : 208.982,\
29 | 'AT' : 209.987, 'RN' : 222.081, 'FR' : 223.020, 'RA' : 226.025,\
30 | 'AC' : 227.028, 'TH' : 232.038, 'PA' : 231.036, 'U' : 238.029,\
31 | 'NP' : 237, 'PU' : 244, 'AM' : 243, 'CM' : 247, 'BK' : 247,\
32 | 'CT' : 251, 'ES' : 252, 'FM' : 257, 'MD' : 258, 'NO' : 259,\
33 | 'LR' : 262, 'RF' : 261, 'DB' : 262, 'SG' : 266, 'BH' : 264,\
34 | 'HS' : 269, 'MT' : 268, 'DS' : 271, 'RG' : 272, 'CN' : 285,\
35 | 'NH' : 284, 'FL' : 289, 'MC' : 288, 'LV' : 292, 'TS' : 294,\
36 | 'OG' : 294}
37 |
38 | # convert VASP default frequency unit to THz
39 | VASP2THZ = 15.633302
40 |
41 | unit_dict = {"thz" : 1,
42 | "cm-1" : 33.356,
43 | "cm^-1" : 33.356,
44 | "ev" : 4.136 * 1e-3,
45 | "mev" : 4.136
46 | }
47 |
48 | HBARCGS = 1.0546 * 10 ** (-27) # in cm^2 * g / s
49 | HBAR = 6.5821 * 10 ** (-16) # in eV * s
50 | KB = 8.6173 * 10 ** (-5) # in eV / K
51 |
52 | MOLE = 6.022 * 10 ** 23
53 |
54 | ATOMS = ['H', 'HE', 'LI', 'BE', 'B', 'C', 'N', 'O', 'F', 'NE', 'NA', 'Mg', 'AL',\
55 | 'Si', 'P', 'S', 'CL', 'AR', 'K', 'CA', 'SC', 'TI', 'V', 'CR', 'MN', 'FE',\
56 | 'CO', 'NI', 'CU', 'ZN', 'Ga', 'Ge', 'As', 'SE', 'BR', 'KR', 'RB', 'SR',\
57 | 'Y', 'ZR', 'NB', 'MO', 'TC', 'RU', 'RH', 'PD', 'AG', 'CD', 'IN', 'SN',\
58 | 'SB', 'TE', 'I', 'XE', 'CS', 'BA', 'LA', 'CE', 'PR', 'ND', 'PM', 'SM',\
59 | 'EU', 'GD', 'TB', 'DY', 'HO', 'ER', 'TM', 'YB', 'LU', 'HF', 'TA', 'W',\
60 | 'RE', 'OS', 'IR', 'PT', 'AU', 'HG', 'TL', 'PB', 'BI', 'PO', 'AT', 'RN',\
61 | 'FR', 'RA', 'AC', 'TH', 'PA', 'U', 'NP', 'PU', 'AM', 'CM', 'BK', 'CT',\
62 | 'ES', 'FM', 'MD', 'NO', 'LR', 'RF', 'DB', 'SG', 'BH', 'HS', 'MT', 'DS',\
63 | 'RG', 'CN', 'NH', 'FL', 'MC', 'LV', 'TS', 'OG']
64 |
65 | SCATTER_PAR_A = {'H' : 1.008,'HE' : 4.003, 'LI' : 6.941, 'BE' : 9.012,\
66 | 'B' : [0.945, 1.312, 0.419, 0.116],\
67 | 'C' : [0.731, 1.195, 0.456, 0.125], 'N' : 14.007, 'O' : 15.999,\
68 | 'F' : 18.998, 'NE' : 20.180, 'NA' : 22.990,\
69 | 'Mg' : [2.268, 1.803, 0.839, 0.289],\
70 | 'AL' : 26.982, 'Si' : [2.129, 2.533, 0.835, 0.322], 'P' : 30.974, 'S' : 32.066,\
71 | 'CL' : 35.453, 'AR' : 39.948, 'K' : 39.098, 'CA' : 40.078,\
72 | 'SC' : 44.956, 'TI' : 47.867, 'V' : 50.942, 'CR' : 51.996,\
73 | 'MN' : 54.938, 'FE' : 55.845, 'CO' : 58.933, 'NI' : 58.693,\
74 | 'CU' : 63.546, 'ZN' : 65.38, 'Ga' : [2.321, 2.486, 1.688, 0.599], 'Ge' : [2.447, 2.702, 1.616, 0.601],\
75 | 'As' : [2.399, 2.790, 1.529, 0.594], 'SE' : 78.971, 'BR' : 79.904, 'KR' : 84.798,\
76 | 'RB' : 84.468, 'SR' : 87.62, 'Y' : 88.906, 'ZR' : 91.224,\
77 | 'NB' : 92.906, 'MO' : 95.95, 'TC' : 98.907, 'RU' : 101.07,\
78 | 'RH' : 102.906, 'PD' : 106.42, 'AG' : 107.868, 'CD' : 112.414,\
79 | 'IN' : 114.818, 'SN' : 118.711, 'SB' : 121.760, 'TE' : 126.7,\
80 | 'I' : 126.904, 'XE' : 131.294, 'CS' : 132.905, 'BA' : 137.328,\
81 | 'LA' : 138.905, 'CE' : 140.116, 'PR' : 140.908, 'ND' : 144.243,\
82 | 'PM' : 144.913, 'SM' : 150.36, 'EU' : 151.964, 'GD' : 157.25,\
83 | 'TB' : 158.925, 'DY': 162.500, 'HO' : 164.930, 'ER' : 167.259,\
84 | 'TM' : 168.934, 'YB' : 173.055, 'LU' : 174.967, 'HF' : 178.49,\
85 | 'TA' : 180.948, 'W' : 183.84, 'RE' : 186.207, 'OS' : 190.23,\
86 | 'IR' : 192.217, 'PT' : 195.085, 'AU' : 196.967, 'HG' : 200.592,\
87 | 'TL' : 204.383, 'PB' : 207.2, 'BI' : 208.980, 'PO' : 208.982,\
88 | 'AT' : 209.987, 'RN' : 222.081, 'FR' : 223.020, 'RA' : 226.025,\
89 | 'AC' : 227.028, 'TH' : 232.038, 'PA' : 231.036, 'U' : 238.029,\
90 | 'NP' : 237, 'PU' : 244, 'AM' : 243, 'CM' : 247, 'BK' : 247,\
91 | 'CT' : 251, 'ES' : 252, 'FM' : 257, 'MD' : 258, 'NO' : 259,\
92 | 'LR' : 262, 'RF' : 261, 'DB' : 262, 'SG' : 266, 'BH' : 264,\
93 | 'HS' : 269, 'MT' : 268, 'DS' : 271, 'RG' : 272, 'CN' : 285,\
94 | 'NH' : 284, 'FL' : 289, 'MC' : 288, 'LV' : 292, 'TS' : 294,\
95 | 'OG' : 294}
96 |
97 | SCATTER_PAR_B = {'H' : 1.008,'HE' : 4.003, 'LI' : 6.941, 'BE' : 9.012,\
98 | 'B' : [46.444, 14.178, 3.223, 0.377],\
99 | 'C' : [36.995, 11.297, 2.814, 0.346], 'N' : 14.007, 'O' : 15.999,\
100 | 'F' : 18.998, 'NE' : 20.180, 'NA' : 22.990,\
101 | 'Mg' : [73.76, 20.175, 3.013, 0.405],\
102 | 'AL' : 26.982, 'Si' : [57.78, 16.48, 2.880, 0.386], 'P' : 30.974, 'S' : 32.066,\
103 | 'CL' : 35.453, 'AR' : 39.948, 'K' : 39.098, 'CA' : 40.078,\
104 | 'SC' : 44.956, 'TI' : 47.867, 'V' : 50.942, 'CR' : 51.996,\
105 | 'MN' : 54.938, 'FE' : 55.845, 'CO' : 58.933, 'NI' : 58.693,\
106 | 'CU' : 63.546, 'ZN' : 65.38, 'Ga' : [65.602, 15.458, 2.581, 0.351], 'Ge' : [55.89, 14.39, 2.45, 0.342],\
107 | 'As' : [45.718, 12.817, 2.280, 0.328], 'SE' : 78.971, 'BR' : 79.904, 'KR' : 84.798,\
108 | 'RB' : 84.468, 'SR' : 87.62, 'Y' : 88.906, 'ZR' : 91.224,\
109 | 'NB' : 92.906, 'MO' : 95.95, 'TC' : 98.907, 'RU' : 101.07,\
110 | 'RH' : 102.906, 'PD' : 106.42, 'AG' : 107.868, 'CD' : 112.414,\
111 | 'IN' : 114.818, 'SN' : 118.711, 'SB' : 121.760, 'TE' : 126.7,\
112 | 'I' : 126.904, 'XE' : 131.294, 'CS' : 132.905, 'BA' : 137.328,\
113 | 'LA' : 138.905, 'CE' : 140.116, 'PR' : 140.908, 'ND' : 144.243,\
114 | 'PM' : 144.913, 'SM' : 150.36, 'EU' : 151.964, 'GD' : 157.25,\
115 | 'TB' : 158.925, 'DY': 162.500, 'HO' : 164.930, 'ER' : 167.259,\
116 | 'TM' : 168.934, 'YB' : 173.055, 'LU' : 174.967, 'HF' : 178.49,\
117 | 'TA' : 180.948, 'W' : 183.84, 'RE' : 186.207, 'OS' : 190.23,\
118 | 'IR' : 192.217, 'PT' : 195.085, 'AU' : 196.967, 'HG' : 200.592,\
119 | 'TL' : 204.383, 'PB' : 207.2, 'BI' : 208.980, 'PO' : 208.982,\
120 | 'AT' : 209.987, 'RN' : 222.081, 'FR' : 223.020, 'RA' : 226.025,\
121 | 'AC' : 227.028, 'TH' : 232.038, 'PA' : 231.036, 'U' : 238.029,\
122 | 'NP' : 237, 'PU' : 244, 'AM' : 243, 'CM' : 247, 'BK' : 247,\
123 | 'CT' : 251, 'ES' : 252, 'FM' : 257, 'MD' : 258, 'NO' : 259,\
124 | 'LR' : 262, 'RF' : 261, 'DB' : 262, 'SG' : 266, 'BH' : 264,\
125 | 'HS' : 269, 'MT' : 268, 'DS' : 271, 'RG' : 272, 'CN' : 285,\
126 | 'NH' : 284, 'FL' : 289, 'MC' : 288, 'LV' : 292, 'TS' : 294,\
127 | 'OG' : 294}
128 |
129 | SCATTER_PAR_C = {'H' : 1.008,'HE' : 4.003, 'LI' : 6.941, 'BE' : 9.012,\
130 | 'B' : -0.1932, 'C' : 12.011, 'N' : 14.007, 'O' : 15.999,\
131 | 'F' : 18.998, 'NE' : 20.180, 'NA' : 22.990, 'Mg' : 0.8584,\
132 | 'AL' : 26.982, 'Si' : 12.011, 'P' : 30.974, 'S' : 32.066,\
133 | 'CL' : 35.453, 'AR' : 39.948, 'K' : 39.098, 'CA' : 40.078,\
134 | 'SC' : 44.956, 'TI' : 47.867, 'V' : 50.942, 'CR' : 51.996,\
135 | 'MN' : 54.938, 'FE' : 55.845, 'CO' : 58.933, 'NI' : 58.693,\
136 | 'CU' : 63.546, 'ZN' : 65.38, 'GA' : 69.723, 'GE' : 72.631,\
137 | 'AS' : 74.922, 'SE' : 78.971, 'BR' : 79.904, 'KR' : 84.798,\
138 | 'RB' : 84.468, 'SR' : 87.62, 'Y' : 88.906, 'ZR' : 91.224,\
139 | 'NB' : 92.906, 'MO' : 95.95, 'TC' : 98.907, 'RU' : 101.07,\
140 | 'RH' : 102.906, 'PD' : 106.42, 'AG' : 107.868, 'CD' : 112.414,\
141 | 'IN' : 114.818, 'SN' : 118.711, 'SB' : 121.760, 'TE' : 126.7,\
142 | 'I' : 126.904, 'XE' : 131.294, 'CS' : 132.905, 'BA' : 137.328,\
143 | 'LA' : 138.905, 'CE' : 140.116, 'PR' : 140.908, 'ND' : 144.243,\
144 | 'PM' : 144.913, 'SM' : 150.36, 'EU' : 151.964, 'GD' : 157.25,\
145 | 'TB' : 158.925, 'DY': 162.500, 'HO' : 164.930, 'ER' : 167.259,\
146 | 'TM' : 168.934, 'YB' : 173.055, 'LU' : 174.967, 'HF' : 178.49,\
147 | 'TA' : 180.948, 'W' : 183.84, 'RE' : 186.207, 'OS' : 190.23,\
148 | 'IR' : 192.217, 'PT' : 195.085, 'AU' : 196.967, 'HG' : 200.592,\
149 | 'TL' : 204.383, 'PB' : 207.2, 'BI' : 208.980, 'PO' : 208.982,\
150 | 'AT' : 209.987, 'RN' : 222.081, 'FR' : 223.020, 'RA' : 226.025,\
151 | 'AC' : 227.028, 'TH' : 232.038, 'PA' : 231.036, 'U' : 238.029,\
152 | 'NP' : 237, 'PU' : 244, 'AM' : 243, 'CM' : 247, 'BK' : 247,\
153 | 'CT' : 251, 'ES' : 252, 'FM' : 257, 'MD' : 258, 'NO' : 259,\
154 | 'LR' : 262, 'RF' : 261, 'DB' : 262, 'SG' : 266, 'BH' : 264,\
155 | 'HS' : 269, 'MT' : 268, 'DS' : 271, 'RG' : 272, 'CN' : 285,\
156 | 'NH' : 284, 'FL' : 289, 'MC' : 288, 'LV' : 292, 'TS' : 294,\
157 | 'OG' : 294}
158 |
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/topophonon/utils.py:
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1 | # -*- coding: utf-8*-
2 | """
3 | Created on Fri Jun 30 14:02:07 2023
4 |
5 | @author: zhuhe
6 | """
7 |
8 | # Some help functions
9 |
10 |
11 | import numpy as np
12 |
13 | from typing import List, Union
14 |
15 |
16 | def _direct_to_cartesian(coord: np.ndarray,
17 | lat: np.ndarray) -> np.ndarray :
18 | """
19 | convert a direct coordinate to a cartesian coordinate
20 |
21 | """
22 | return np.dot(coord, lat)
23 |
24 |
25 | def _cartesian_to_direct(coord: np.ndarray,
26 | lat: np.ndarray) -> np.ndarray :
27 | """
28 | convert a cartesian coordinate to a direct coordinate
29 |
30 | """
31 | return np.dot(coord, np.linalg.inv(lat))
32 |
33 |
34 | def _convert_pair_to_str(index_prm_1: int,
35 | index_prm_2: int,
36 | lattice_vec: Union[List[int], np.ndarray]
37 | ) -> str:
38 | """
39 | hash the atomic a pair by converting the information to a string
40 |
41 | """
42 | temp = str(index_prm_1) + str(index_prm_2)
43 | for x in lattice_vec:
44 | temp += str(int(x))
45 | return temp
46 |
47 |
48 | def _cartesian_to_direct(coord: np.ndarray,
49 | lat: np.ndarray):
50 | """
51 | convert a cartesian coordinate to a direct coordinate
52 |
53 | """
54 | return np.dot(coord, np.linalg.inv(lat))
55 |
56 |
57 | def _modify_freq(eig_vals: np.ndarray):
58 | """
59 | convert the imaginary numbers to negative numbers
60 |
61 | """
62 | for j, eig_val in enumerate(eig_vals):
63 | if eig_val >= 0:
64 | eig_vals[j] = np.sqrt(eig_val)
65 | else:
66 | eig_vals[j] = -np.sqrt(-eig_val)
67 |
68 |
69 | def _set_ylabel(unit: str) -> str:
70 | """
71 | determine the ylabel of the plot based on unit specified
72 |
73 | """
74 |
75 | if isinstance(unit, str):
76 | return "Frequency ({})".format(unit)
77 | return "Frequency"
78 |
79 |
80 | def _coth(x: float) -> float:
81 | return (np.exp(2*x) + 1) / (np.exp(2*x) - 1)
82 |
83 |
84 | def _make_k_grid(xy_range,
85 | num):
86 | """
87 | make a 2d k_grid; num points along each axis, between [-xy_range, xr_range]
88 | """
89 | interval = xy_range/num
90 | a = np.arange(-xy_range, xy_range+interval, interval)
91 | kx,ky = np.meshgrid(a,a)
92 | return kx, ky
93 |
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