Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

TL;DR

This paper derives an analytical expression for the minimal conductivity in bilayer graphene, showing its dependence on band structure topology and symmetry breaking mechanisms, confirmed by two independent methods.

Contribution

It introduces a general formula for minimal conductivity in two-band systems and applies it to bilayer graphene with symmetry breaking, revealing topological effects.

Findings

Minimal conductivity varies with the complex parameter w.

Good agreement between Kubo and Landauer calculations.

Conductivity is highly sensitive to band topology and electrode orientation.

Abstract

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter $w$ related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on Landauer approach and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter $w$ and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low energy band structure.