Fermi Surface

Method Decision Guide

Need Fermi surface analysis?
  |
  +--> 3D bulk metal?
  |      YES --> 3d-fermi-surface/
  |
  +--> 2D or layered material (single kz slice)?
  |      YES --> 2d-fermi-surface/
  |
  +--> Need orbital character on the Fermi surface?
         YES --> projected-fermi-surface/

Common Prerequisites

• Metallic system: Fermi surfaces only exist for metals (bands crossing the Fermi level). For semiconductors/insulators, use constant-energy contour analysis instead.
• Well-converged SCF: A standard SCF on a coarse k-grid to obtain the charge density and Fermi energy.
• Dense k-mesh NSCF: A non-self-consistent calculation on a very dense uniform k-grid (typically 30x30x30 or denser for 3D, 60x60x1 or denser for 2D).
• QE executables: pw.x, pp.x, projwfc.x (Quantum ESPRESSO 7.5).
• Python packages: numpy, scipy (for interpolation and marching cubes), matplotlib (for 2D/3D plotting), pymatgen, ase.
• MACE limitation: MACE cannot compute Fermi surfaces. It is a force field with no electronic degrees of freedom. Use it only for structure pre-relaxation.

Important Notes

• Fermi surface quality depends critically on k-mesh density. Undersampled meshes produce jagged or incomplete surfaces.
• For QE, use occupations = 'smearing' with small degauss (0.005-0.01 Ry) for the SCF step. The NSCF step should also use smearing (not tetrahedra) to obtain eigenvalues on every k-point.
• Spin-polarized metals have separate Fermi surfaces for majority and minority spin channels. Set nspin = 2 and analyze each spin independently.
• The Fermi energy from SCF may differ slightly from the NSCF Fermi energy due to k-mesh differences. Use the NSCF Fermi energy for surface extraction.