Effective Mass

Compute carrier effective masses (m*/m₀) at the VBM and CBM by fitting a parabola to the band dispersion along each high-symmetry direction. Works from vasprun.xml alone — no extra input needed.

valyte effmass [options]

Workflow

Run valyte band kpt-gen to generate the line-mode KPOINTS, do a non-self-consistent band calculation, then point valyte effmass at the resulting vasprun.xml. You can also visualize the bands with valyte band using the same data.

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How it works

For each band extremum (VBM for holes, CBM for electrons), Valyte fits:

\[E(k) = \frac{\hbar^2 k^2}{2 m^*} + \text{const}\]

using a least-squares parabolic fit to a small window of k-points around the extremum. The effective mass is extracted from the quadratic coefficient:

\[\frac{m^*}{m_0} = \frac{\hbar^2}{2a \cdot m_0}\]

where \(a\) is the fitted coefficient in eV·Å².

A fit is produced for each high-symmetry direction in the band structure — so if the VBM sits at Γ and the path passes through Γ twice (e.g. Γ→X and Γ→Y), you get separate masses for each direction.

Non-parabolic bands

If the band is not well described by a parabola in the fitting window, a warning is printed. Narrow-gap semiconductors, d-bands, and bands with strong spin-orbit coupling are common cases where the parabolic approximation breaks down. See FAQ → Effective masses are unreasonably large for guidance.

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Options

Option	Default	Description
--vasprun	.	Path to vasprun.xml or directory containing it
--kpoints	auto-detected	Path to KPOINTS file for high-symmetry labels
--npoints	3	K-points on each side of extremum used for fitting
--band-index	auto	Manual 1-indexed band indices to fit
--tol	1e-3	Degeneracy tolerance in eV (for degenerate bands at extremum)
--plot	off	Save parabolic fit plot
-o, --output	valyte_effmass.png	Output plot filename (used with --plot)
--save-data	off	Save results to valyte_effmass.dat

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Usage

# Auto-detect VBM and CBM, print masses
valyte effmass

# Wider fitting window (more k-points → smoother fit)
valyte effmass --npoints 5

# Save parabolic fit figure
valyte effmass --plot -o effmass.png

# Export numerical results
valyte effmass --save-data

# Fit specific bands manually (1-indexed)
valyte effmass --band-index 42 43

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Output

Terminal

Effective mass
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  Band gap:     1.124 eV (indirect)
  VBM:          k = (0.000, 0.000, 0.000)  [Γ]    Band 42
  CBM:          k = (0.500, 0.000, 0.500)  [X]    Band 43

  Hole effective masses (VBM):
    Γ → X    :     m* =    0.284 m₀
    Γ → L    :     m* =    0.192 m₀
    Γ → K    :     m* =    0.231 m₀

  Electron effective masses (CBM):
    X → Γ    :     m* =    0.916 m₀
    X → U    :     m* =    0.191 m₀

Data file (--save-data)

valyte_effmass.dat — plain text with columns: Type, Band, Spin, Direction, m*/m₀.

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Requirements

• Line-mode band structure calculation (IBRION = -1, line-mode KPOINTS)
• vasprun.xml written with LWAVE = .FALSE. or LCHARG = .FALSE. is fine — projections are not required
• Self-consistent (SCF) calculations will raise an error — a k-path is needed

See FAQ → This does not appear to be a line-mode band calculation for troubleshooting.