Fermi Surface from VASP calculation

Fermi Surface

In condensed matter physics, the Fermi Surface is the surface of iso-energy in the reciprocal space, the energy of which is referred to as the Fermi energy or Fermi level. To visualize the Fermi surface, first you have to obtain the band energies in the reciprocal space. For example, one can sample the reciprocal space primitive cell using a uniform k-points grid and then use any ab initio code, e.g. VASP, to generate the band energies on these uniform grid points. With the band energies on the uniform grid, one can either plot the iso-surface with some coding or just use Xcrysden to do the plotting work.

Prerequisites

The following python library must be installed to run the script

• ase
• spglib
• scikit-image
• matplotlib [optional]
• mayavi [optional]

Steps to visualize the Fermi surface

1. Calculate the band energies using VASP.

Note that Gamma-centered KPOINTS is required.

Monkhorst-Pack
0
Gamma
21 21 21
 0  0  0

Moreover, there is no need to turn off the symmetry in the INCAR file. As is well-known, VASP utilize the symmetry to fold the k-points grid to symmetry-irreducible k-points in the BZ, which will significantly reduce the computation cost. The script use spglib to unfold the irreducible k-points in BZ to the uniform k-points grid.

2. Visualizing the Fermi surface

At this step, use the script fs.py to process the VASP output files.

usage: fs.py [-h] [-i EIGVENVAL] [--poscar POSCAR] [--kpoints KPOINTS]
             [--plot {xcrys,mpl,mayavi}] [--cell {uc,bz}] [--efermi EFERMI]
             [--symprec SYMPREC] [--kmesh KMESH KMESH KMESH]

optional arguments:
  -h, --help            show this help message and exit
  -i EIGVENVAL          Location of the EIGENVAL file. By default, the
                        KPOINTS/POSCAR are also read from the directory where


  --kpoints KPOINTS     location of VASP KPOINTS
  --plot {xcrys,mpl,mayavi}
                        Fermi surface plotting method

  --efermi EFERMI       the Fermi energy
  --symprec SYMPREC     the symmetry precision used in spglib
  --kmesh KMESH KMESH KMESH
                        the kmesh in the KPOINTS
  --interp NEW_KMESH NEW_KMESH NEW_KMESH
                        the new grid size

There are three different ways to visualize the Fermi surface:

• Using Xcrysden

First, you need to generate the bxsf file as input for xcrysden

fs.py -i EIGENVAL

then, launch xcrysden

xcrysden --bxsf ebands3d.bxsf

For example, below is the the Fermi surface of fcc Cu

• Using Matplotlib

fs.py --plot mpl

• Using Mayavi

  fs.py --plot mayavi               # Fermi Surface in Brillouin Zone
  fs.py --plot mayavi --cell uc     # Fermi Surface in primitive cell

  

You can also use vaspkit (tutorial) to generate KPOINTS with given k-spacing. Since the content in KPOINTS is quiet different, the script requires to input kmesh manually.

fs.py --kmesh 42 42 24 -i EIGENVAL
fs.py --kmesh 42 42 24 --interp 210 210 120 --plot mayavi --efermi 9.05973773

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This file was generated by Remarkable on Thursday, 27. February 2020 04:45PM