Role of the trigonal warping on the minimal conductivity of bilayer graphene

TL;DR

This paper calculates the zero-energy minimal conductivity of bilayer graphene considering trigonal warping, revealing it is unaffected by warping strength and significantly larger than in single-layer graphene.

Contribution

It demonstrates that trigonal warping increases minimal conductivity in bilayer graphene and that this effect is independent of warping strength.

Findings

Conductivity is three times larger with trigonal warping.

Conductivity is six times larger than in single-layer graphene.

Trigonal warping's effect cannot be neglected at zero energy.

Abstract

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is three times as large as that without trigonal warping, and six times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.