Fermi Velocity calculation

[soumadip_banerjee]

Dear VASP Community,

I am studying a two-dimensional material whose electronic band structure shows a possible Dirac cone near the Fermi level. I would like to calculate the Fermi velocity, (v_F), associated with the bands forming the Dirac cone.

Could you please advise on the recommended procedure for calculating the Fermi velocity from a VASP band-structure calculation?

[martin.schlipf]

The Fermi velocity is simply the derivative of the band structure near the Dirac point with respect to the distance in reciprocal space v_F = (1/ħ)·∂E/∂k. The main challenge is to get the units correct. I would suggest that you try this on a simple system where you know the Fermi velocity of the effective mass at the PBE level and try to reproduce that. This avoids making a annoying unit conversion error on the real material.

The other points to consider are related to physics and methods:

• Make sure to use a dense mesh near the Dirac point (usually explicit k-points list is best), this is even more important if the Dirac point is not at a high-symmetry point
• Keep in mind that the linear slope is the first order approximation and only valid near the Dirac point. If you extend to slope fit to far from the Dirac point, the curvature of the bands will taint your result.
• Band edges can be very sensitive to small changes. This includes the xc functional choice, the lattice constant, the inclusion of SOC, numerical cutoffs used, ... If precise values are required you may need to go beyond local DFT.
• If your system is not cubic, v_F will typically have different values along different directions, i.e., the Dirac cone will have an elliptic cross section instead of a circle.