Band structure calculations determine the allowed electron energy levels as a function of crystal momentum (k-vector) along high-symmetry paths in the Brillouin zone.
Calculation Procedure
- Self-consistent calculation: First, a standard DFT calculation on a uniform k-grid determines the converged charge density and potential
- Non-self-consistent calculation: The converged potential is then used to compute eigenvalues at k-points along the high-symmetry path, without updating the charge density
- Plotting: Eigenvalues are plotted as E(k) curves along the path
High-Symmetry Paths
The k-point path connects special points in the Brillouin zone. Standard paths are defined for each crystal system:
- Cubic (FCC): Gamma-X-W-K-Gamma-L-U-W-L-K
- Cubic (BCC): Gamma-H-N-Gamma-P-H
- Hexagonal: Gamma-M-K-Gamma-A-L-H-A
Spin-Orbit Coupling
For materials with heavy elements, spin-orbit coupling (SOC) can be included. This splits degenerate bands and can change the band gap significantly (important for Bi, Pb, Sn, Te compounds).
Accuracy Considerations
- Band dispersions (shapes) are generally reliable from GGA/PBE
- Absolute band gap values are underestimated
- For accurate gaps, HSE06 or GW calculations are needed but not available for all materials in the databases