Conductivity of disordered graphene at half filling

TL;DR

This paper investigates how different types of disorder affect electron transport in graphene at half filling, revealing conditions for localization, universal conductivity, and quantum critical behavior.

Contribution

It provides exact results for minimal conductivity under chiral disorder and develops an effective field theory for long-range disorder in graphene.

Findings

Localization is suppressed if disorder preserves chiral symmetry or valley decoupling.

Minimal conductivity of 4e^2/πh is obtained for chiral disorder.

Graphene exhibits quantum critical behavior with universal conductivity under certain disorder conditions.

Abstract

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity $4e^2/\pi h$ in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma model including a topological term with $\theta = \pi$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.