Two parameter flow of \sigma_{xx}(\omega) - \sigma_{xy}(\omega) for the graphene quantum Hall system in ac regime

TL;DR

This paper investigates the behavior of the conductivity tensor components in graphene quantum Hall systems under finite-frequency conditions, revealing that ac flow diagrams resemble dc flows and are influenced by a dynamical length scale.

Contribution

It introduces a numerical analysis of the two-parameter flow of conductivity in the ac regime and connects it with dynamical scaling theory, extending understanding of quantum Hall effects at finite frequencies.

Findings

Ac flow diagrams qualitatively resemble dc flow diagrams.

Dynamical length scale acts as a cutoff in the flow.

Large-frequency regime shows classical flow behavior.

Abstract

Flow diagram of $(\sigma_{xx}, \sigma_{xy})$ in finite-frequency ($\omega$) regime is numerically studied for graphene quantum Hall effect (QHE) system. The ac flow diagrams turn out to show qualitatively similar behavior as the dc flow diagrams, which can be understood that the dynamical length scale determined by the frequency poses a relevant cutoff for the renormalization flow. Then the two parameter flow is discussed in terms of the dynamical scaling theory. We also discuss the larger-$\omega$ regime which exhibits classical flows driven by the raw frequency $\omega$.