Minimal conductivity of rippled graphene with topological disorder

TL;DR

This paper investigates how topological defects and curvature in graphene influence its electrical conductivity, revealing a diffusive regime with minimal conductivity inversely related to defect density.

Contribution

It introduces a model linking topological disorder in rippled graphene to Dirac fermions in a random magnetic field and variable Fermi velocity, highlighting unique long-range correlated disorder effects.

Findings

Minimal conductivity is inversely proportional to topological defect density.

Curvature-induced disorder leads to diffusive transport behavior.

The model captures the impact of topological defects on electronic properties.

Abstract

We study the transport properties of a neutral graphene sheet with curved regions induced or stabilized by topological defects. The proposed model gives rise to Dirac fermions in a random magnetic field and in the random space dependent Fermi velocity induced by the curvature. This last term leads to singular long range correlated disorder with special characteristics. The Drude minimal conductivity at zero energy is found to be inversely proportional to the density of topological disorder, a signature of diffusive behavior.