Quantum criticality and minimal conductivity in graphene with long-range disorder

TL;DR

This paper investigates the quantum critical behavior of graphene's conductivity under long-range disorder, revealing a universal conductivity at criticality and transitions akin to quantum Hall effects.

Contribution

It derives an effective field theory for graphene with potential disorder, showing the system's quantum criticality and universal conductivity, and explores symmetry-breaking effects.

Findings

Graphene exhibits a quantum critical point with universal conductivity near $e^2/h$.

Breaking time-reversal symmetry shifts the system to a different symmetry class with quantum Hall transition characteristics.

The effective field theory includes a topological term indicating non-trivial quantum critical behavior.

Abstract

We consider the conductivity $\sigma_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, 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 $\sigma_{xx}$ acquires the value characteristic for the quantum Hall transition.