Random gauge field effects on the conductivity of graphene sheets with disordered ripples

TL;DR

This paper investigates how disordered ripples and external magnetic fields influence the electrical conductivity of graphene, revealing anisotropic effects and offering methods to quantify pseudo-magnetic fields.

Contribution

It introduces a comprehensive analysis of ripple-induced pseudo-magnetic fields and their impact on graphene conductivity, including the effects of external in-plane magnetic fields.

Findings

Disordered ripples induce anisotropic conductivity in graphene.

External in-plane magnetic fields can be mapped to effective random magnetic fields.

The interplay between mechanisms allows quantification of pseudo-magnetic field strength.

Abstract

We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field $B_\parallel$. Due to the irregular local curvature found at graphene sheets deposited over a substrate, $B_\parallel$ can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudo magnetic fields originated from deformations and strain. We find that the competition between these mechanisms gives rise to a strong anisotropy in the conductivity tensor. This result provides a new strategy to quantitatively infer the strength of pseudo-magnetic fields in rippled graphene flakes.