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effective mass fitting improve #44

Merged
merged 10 commits into from
Jan 14, 2024
55 changes: 55 additions & 0 deletions docs/examples/example_mgo.md
Original file line number Diff line number Diff line change
Expand Up @@ -108,3 +108,58 @@ Unfolded MgO band structure with atomic projections plotted separately.
There are _many_ customisation options available for the plotting functions in `easyunfold`. See `easyunfold plot -h` or
`easyunfold unfold plot-projections -h` for more details!
:::


The command `easyunfold unfold effective-mass` can be used to find the effective masses of the unfolded band structure.

The example output is shown below:

```
Loaded data from easyunfold.json
Band extrema data:
Kpoint index Kind Sub-kpoint index Band indices
-------------- ------ ------------------ --------------
0 cbm 0 16
47 cbm 0 16
0 vbm 0 15
47 vbm 0 15

Electron effective masses:
index Kind Effective mass Band index from to
------- ------ ---------------- ------------ ------------------------ -------------------
0 m_e 0.373553 16 [0.0, 0.0, 0.0] (\Gamma) [0.5, 0.5, 0.5] (L)
1 m_e 0.367203 16 [0.0, 0.0, 0.0] (\Gamma) [0.5, 0.0, 0.5] (X)

Hole effective masses:
index Kind Effective mass Band index from to
------- ------ ---------------- ------------ ------------------------ -------------------
0 m_h -3.44604 15 [0.0, 0.0, 0.0] (\Gamma) [0.5, 0.5, 0.5] (L)
1 m_h -2.13525 15 [0.0, 0.0, 0.0] (\Gamma) [0.5, 0.0, 0.5] (X)
Unfolded band structure can be ambiguous, please cross-check with the spectral function plot.
```

If detected band extrema are not consistent with the band structure, one should adjust the `--intensity-tol` and `--extrema-detect-tol`.
Increasing the value of `--intensity-tol` will filter away bands with very small spectral weights.
On the other hand, increasing `--extrema-detect-tol` will increase the energy window with respect
to the VBM or CBM to assign extrema points.
One can also inspect if the detected bands makes sense by using the `--plot` option.
A Jupyter Notebook example can be found [here](../../examples/MgO/effective-mass.ipynb).


```{figure} ../../examples/MgO/unfold-effective-mass.png
:width: 800 px
:alt: Effective bands extracted

Extracted bands at CBM and VBM for an unfolded MgO band structure.
```


:::{warning}
Make sure the band extrema data tabulated is correct and consistent before using any of the reported values.
The results can unreliable for systems with little or no band gaps and those with complex unfolded band structures.
:::


:::{tip}
For complex systems where the detection is difficult, one can manually pass the kpoint and the band indices using the `--manual-extrema` option.
:::
2 changes: 1 addition & 1 deletion docs/index.md
Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ package.
For the methodology of supercell band unfolding, see
[here](https://link.aps.org/doi/10.1103/PhysRevB.85.085201).

### Example Outputs
## Example Outputs
| [Cs₂(Sn/Ti)Br₆ Vacancy-Ordered Perovskite Alloys](https://doi.org/10.1021/acs.jpcc.3c05204) | Oxygen Vacancy (*V*ₒ⁰) in MgO |
|:-------------------------------------------------------------------------------------------:|:---------------------------------------------------------------------------:|
| <img src="img/CSTB_easyunfold.gif" height="400"/> | <img src="../examples/MgO/unfold_project_MgO_v_O_0_tall.png" height="400"/> |
Expand Down
35 changes: 35 additions & 0 deletions docs/theory.md
Original file line number Diff line number Diff line change
Expand Up @@ -74,5 +74,40 @@ cell, followed by a reduction using the symmetry of the supercell. The spectral
is then a weighted combination of that set of $\vec{k_s^\prime}$ points that are inequivalent under the
symmetry of the supercell.


## Cell and Transformation Matrix convention

The cell matrix may be consisted of column or row lattice vectors. In this package we use the **row vector**
convention as commonly found in many post-processing tools and DFT codes. The cell matrix is defined as:

$$
\mathbf{C} = \begin{pmatrix}
x_a & y_a & z_a \\
x_b & y_b & z_b \\
x_c & y_c & z_c
\end{pmatrix}
$$

where $x_a$, $y_a$, $z_a$ are components of the lattice vector $\mathbf{a}$.

The cell matrix of the supercell $\mathbf{C_s}$ is obtained by (left) multiplying the original unit cell $\mathbf{C_u}$ by the transformation matrix $\mathbf{M}$:


$$
\mathbf{C_{s}} = \mathbf{M} \, \mathbf{C_u}
$$

:::{note}
Sometimes the cell matrix is defined by **column** vectors of the lattice parameters, e.g. $\mathbf{C_u^c} = \mathbf{C_u^T}$, and the relationship becomes:
$$
\mathbf{C_u^c} = \mathbf{C_u^T} \, \mathbf{M^T}
$$

Hence, when the column vector convention is used, the transformation matrix is the **transpose** of that used by the row convention.

One example of code using the column vector convention is [Phonopy](https://phonopy.github.io/phonopy/setting-tags.html#dim).
:::


[^1]: Popescu, V.; Zunger, A. Effective Band Structure of Random Alloys. Phys. Rev. Lett. 2010, 104 (23), 236403. https://doi.org/10.1103/PhysRevLett.104.236403.
[^2]: Popescu, V.; Zunger, A. Extracting $E$ versus $\vec{k}$ Effective Band Structure from Supercell Calculations on Alloys and Impurities. Phys. Rev. B 2012, 85 (8), 085201. https://doi.org/10.1103/PhysRevB.85.085201.
50 changes: 33 additions & 17 deletions easyunfold/cli.py
Original file line number Diff line number Diff line change
Expand Up @@ -51,17 +51,22 @@ def easyunfold():
@click.option('--matrix',
'-m',
help='Transformation matrix, in the form "x y z" for a diagonal matrix, '
'or "x1 y1 z1, x2 y2 z2, x3 y3 z3" for a 3x3 matrix. Automatically guessed if not '
'or "x1 y1 z1 x2 y2 z2 x3 y3 z3" for a 3x3 matrix. Automatically guessed if not '
'provided.')
@click.option('--symprec', help='Tolerance for determining the symmetry', type=float, default=1e-5, show_default=True)
@click.option('--out-file', '-o', default='easyunfold.json', help='Name of the output file')
@click.option('--no-expand', help='Do not expand the kpoints by symmetry', default=False, is_flag=True)
@click.option('--nk-per-split', help='Number of band structure kpoints per split.', type=int)
@click.option('--separate-folders/--no-separate-folders',
help='Whether to use separate folders for each split.',
default=False,
show_default=True)
@click.option('--scf-kpoints',
help='File (IBZKPT) to provide SCF kpoints for self-consistent calculations. Needed for hybrid functional calculations.',
type=click.Path(exists=True, dir_okay=False))
@click.option('--yes', '-y', is_flag=True, default=False, help='Skip and confirmation.', hidden=True) # hide help
def generate(pc_file, code, sc_file, matrix, kpoints, time_reversal, out_file, no_expand, symprec, nk_per_split, scf_kpoints, yes):
def generate(pc_file, code, sc_file, matrix, kpoints, time_reversal, out_file, no_expand, symprec, nk_per_split, scf_kpoints, yes,
separate_folders):
"""
Generate the kpoints for performing supercell calculations.

Expand Down Expand Up @@ -107,6 +112,7 @@ def generate(pc_file, code, sc_file, matrix, kpoints, time_reversal, out_file, n
else:
tmp = supercell.cell @ np.linalg.inv(primitive.cell)
transform_matrix = np.rint(tmp)
transform_matrix[transform_matrix == 0] = 0
if not np.allclose(tmp, transform_matrix, rtol=2e-2): # 2% mismatch tolerance
if np.allclose(transform_matrix @ primitive.cell, supercell.cell, rtol=5e-2): # 2-5% mismatch
click.echo(_quantitative_inaccuracy_warning)
Expand Down Expand Up @@ -154,6 +160,7 @@ def generate(pc_file, code, sc_file, matrix, kpoints, time_reversal, out_file, n
out_kpt_name,
nk_per_split=nk_per_split,
scf_kpoints_and_weights=scf_kpoints_and_weights,
use_separate_folders=separate_folders,
source=sc_file,
)

Expand Down Expand Up @@ -267,19 +274,17 @@ def wrapper(*args, **kwargs):
@click.option('--spin', type=int, default=0, help='Index of the spin channel.', show_default=True)
@click.option('--npoints', type=int, default=3, help='Number of kpoints used for fitting from the extrema.', show_default=True)
@click.option('--extrema-detect-tol', type=float, default=0.01, help='Tolerance for band extrema detection.', show_default=True)
@click.option('--degeneracy-detect-tol',
type=float,
default=0.01,
help='Tolerance for band degeneracy detection at extrema.',
show_default=True)
@click.option('--nocc', type=int, help='DEV: Use this band as the extrema at all kpoints.')
@click.option('--plot', is_flag=True, default=False)
@click.option('--plot-fit', is_flag=True, default=False, help='Generate plots of the band edge and parabolic fits.')
@click.option('--fit-label', help='Which branch to use for plot fitting. e.g. electrons:0', default='electrons:0', show_default=True)
@click.option('--band-filter', default=None, type=int, help='Only displace information for this band.')
@click.option('--out-file', '-o', default='unfold-effective-mass.png', help='Name of the output file.', show_default=True)
def unfold_effective_mass(ctx, intensity_threshold, spin, band_filter, npoints, extrema_detect_tol, degeneracy_detect_tol, nocc, plot,
plot_fit, fit_label, out_file):
@click.option('--emin', type=float, default=-5., help='Minimum energy in eV relative to the reference.', show_default=True)
@click.option('--emax', type=float, default=5., help='Maximum energy in eV relative to the reference.', show_default=True)
@click.option('--manual-extrema', help='Manually specify the extrema to use for fitting, in the form "mode,k_index,band_index"')
def unfold_effective_mass(ctx, intensity_threshold, spin, band_filter, npoints, extrema_detect_tol, nocc, plot, plot_fit, fit_label,
out_file, emin, emax, manual_extrema):
"""
Compute and print effective masses by tracing the unfolded weights.

Expand All @@ -293,7 +298,7 @@ def unfold_effective_mass(ctx, intensity_threshold, spin, band_filter, npoints,
from easyunfold.unfold import UnfoldKSet
from tabulate import tabulate
unfoldset: UnfoldKSet = ctx.obj['obj']
efm = EffectiveMass(unfoldset, intensity_tol=intensity_threshold, extrema_tol=extrema_detect_tol, degeneracy_tol=degeneracy_detect_tol)
efm = EffectiveMass(unfoldset, intensity_tol=intensity_threshold, extrema_tol=extrema_detect_tol)

click.echo('Band extrema data:')
table = []
Expand All @@ -306,12 +311,20 @@ def unfold_effective_mass(ctx, intensity_threshold, spin, band_filter, npoints,

if nocc:
efm.set_nocc(nocc)
output = efm.get_effective_masses(ispin=spin, npoints=npoints)
if manual_extrema is None:
output = efm.get_effective_masses(ispin=spin, npoints=npoints)
else:
mode, ik, ib = manual_extrema.split(',')
ik = int(ik)
ib = int(ib)
click.echo(f'Using manually passed kpoint and band: {ik},{ib}')
output = efm.get_effective_masses(ispin=spin, npoints=npoints, mode=mode, iks=[ik], iband=[[ib]])

# Filter by band if requested
if band_filter is not None:
for carrier in ['electrons', 'holes']:
output[carrier] = [entry for entry in output[carrier] if entry['band_index'] == band_filter]
if carrier in output:
output[carrier] = [entry for entry in output[carrier] if entry['band_index'] == band_filter]

## Print data
def print_data(entries, tag='me'):
Expand All @@ -332,19 +345,22 @@ def print_data(entries, tag='me'):
click.echo(tabulate(table, headers=['index', 'Kind', 'Effective mass', 'Band index', 'from', 'to']))

click.echo('Electron effective masses:')
print_data(output['electrons'], 'm_e')
print_data(output.get('electrons', []), 'm_e')
print('')
click.echo('Hole effective masses:')
print_data(output['holes'], 'm_h')
print_data(output.get('holes', []), 'm_h')

click.echo('Unfolded band structure can be ambiguous, please cross-check with the spectral function plot.')
if not plot:
click.echo(
'NOTE: Unfolded band structure can be ambiguous.'
'You may want to run the command with `--plot` and check if the detected bands are consistent with the spectral function.')

if plot:
from easyunfold.plotting import UnfoldPlotter
plotter = UnfoldPlotter(unfoldset)
click.echo('Generating spectral function plot for visualising detected branches...')
click.echo('Generating spectral function plot for visualising detected band branches...')
engs, sf = unfoldset.get_spectral_function()
plotter.plot_effective_mass(efm, engs, sf, effective_mass_data=output, save=out_file)
plotter.plot_effective_mass(efm, engs, sf, effective_mass_data=output, save=out_file, ylim=(emin, emax))

elif plot_fit:
from easyunfold.plotting import UnfoldPlotter
Expand Down
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