Effective tunnel conductance and effective ac conductivity of randomly strained graphene

TL;DR

This paper investigates how high ripples in graphene induce pseudo-magnetic fields, leading to local Landau levels whose effects persist in the macroscopic properties, notably affecting the density of states and ac conductivity.

Contribution

It introduces a model for the effective electronic properties of highly rippled graphene considering local Landau quantization and averaging over ripple distributions.

Findings

Average DOS shows an inflection point at the first Landau level energy.

Effective ac conductivity exhibits a maximum at the first Landau level frequency.

Landau quantization effects survive the averaging process despite ripples.

Abstract

We consider a single-layer graphene with high ripples, so that the pseudo-magnetic fields due to these ripples are strong. If the magnetic length corresponding to a typical pseudo-magnetic field is smaller than the ripple size, the resulting Landau levels are local. Then the effective properties of the macroscopic sample can be calculated by averaging the local properties over the distribution of ripples. We find that this averaging does not wash out the Landau quantization completely. Average density of states (DOS) contains a feature (inflection point) at energy corresponding to the first Landau level in a {\em typical} field. Moreover, the frequency dependence of the ac conductivity %while the average ac conductivity contains a maximum at a frequency corresponding to the first Landau level in a typical field. This nontrivial behavior of the effective characteristics of randomly strained graphene is a consequence of non-equidistance of the Landau levels in the Dirac spectrum.