Small band gap at K point in graphene DFT calculation (no SOC)

exciting
1

Hello everyone,

I have reproduced the DFT tutorial calculation for graphene. At the K point, without including spin–orbit coupling, I obtain a small gap.

The energies of the π and π* bands at the K point are:

π = 0.7479841447 × 10⁻³ Hartree
π* = 0.7481050960 × 10⁻³ Hartree

This corresponds to a small but non-zero gap, whereas graphene is expected to be gapless at the K point in the absence of SOC.

How can this unphysical gap be explained?

Any insights would be appreciated. Thank you.

2

Hi @sareh

The reason a gap shows up at the K point is due to interpolation of the k-space to include the K point. If you use the k-mesh provided in the tutorials (8x8x1), the K point is not captured. Try using a k-mesh with multiples of 3, e.g., 9x9x1 (as the K point sits at fractional coordinates 1/3, 2/3, 0).

To perfectly capture both the K and M points you could use a mesh like 12x12x1. Hope this helps!

Regards,

Kshitij