Novel electric field effects on Landau levels in Graphene

TL;DR

This paper investigates how a uniform electric field influences the Landau level spectrum in graphene, revealing a critical electric field where levels collapse, potentially causing breakdown of quantum Hall states.

Contribution

It provides an exact analytical and numerical analysis of electric field effects on graphene's Landau levels, introducing a physical interpretation based on 'graphene relativity' and boost operations.

Findings

Landau levels collapse at a critical electric field E_c(B).

Electric fields cause local collapse at nanoscopic scales.

Potential breakdown of quantum Hall states in graphene due to high Hall currents.

Abstract

A single graphene layer exhibits an anomalous Landau level spectrum. A massless Dirac like low energy electronic spectrum underlies this anomaly. We study, analytically and numerically, the effect of a uniform electric field $(E)$ on the anomalous Landau levels. We solve the problem exactly within the Dirac cone approximation and find an interesting scaling of the spectrum, leading to the collapse of the Landau levels at a critical $E_c(B)$, for a given magnetic field $B$. We offer a physical interpretation of our result, which uses `graphene relativity' and the boost operation. Electric fields, non-uniform at nanoscopic ($\sim l_c$, magnetic) length scales, produce local collapse at $E < E_c$. We expect an anomalous breakdown of quantum Hall states in real graphene, induced by large Hall currents.