Anti-localization of graphene under substrate electric field

TL;DR

This paper provides a criterion for understanding how substrate electric fields influence the localization properties of graphene, highlighting the role of spin-orbit interactions and internal degrees of freedom in determining anti-localization effects.

Contribution

It introduces a simple criterion linking internal degrees of freedom and external electric fields to graphene's localization behavior, emphasizing the impact of Rashba spin-orbit interaction.

Findings

Perpendicular electric fields induce anti-localization in graphene.

Internal degrees of freedom determine localization properties.

Rashba spin-orbit interaction is enhanced by substrate electric fields.

Abstract

A simple criterion is provided how the (anti-)localization properties of graphene are determined in the presence of inter-valley scattering, Kane-Mele topological mass term, and Rashba spin-orbit interaction (SOI). A set of (pseudo) time-reversal operations show that the number of effective internal degrees of freedom, such as spin and pseudo-spins distinguishing the sublattice and the valley, is the crucial parameter for localization. It is predicted that perpendicular electric field due to gate voltage of the substrate drives the system to anti-localization by enhancing the Rashba SOI.