Transport and localization in periodic and disordered graphene superlattices

TL;DR

This paper investigates charge transport in one-dimensional graphene superlattices with periodic and disordered potentials, revealing anisotropic transport properties, delocalized states perpendicular to layers, and unique transmission features in p-n junction structures.

Contribution

It provides new insights into anisotropic transport, delocalization, and disorder effects in graphene superlattices, including the discovery of disorder-induced resonances and anomalous transmission properties.

Findings

Eigenstates are delocalized perpendicular to layers regardless of disorder.

Disorder can either suppress or enhance transmission depending on the system.

Graphene p-n junction superlattices exhibit narrow angular transmission spectra.

Abstract

We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Most remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. This transmission has anomalously narrow angular spectrum and, surprisingly, in some range of directions it is practically independent of the amplitude of fluctuations of the potential. Owing to these features, such samples could be used as building blocks in tunable electronic circuits. To better understand the physical implications of the results presented here, most of our results have been contrasted with those for analogous wave systems. Along with similarities, a number of quite surprising differences have been found.