Conductivity tensor of striped quantum Hall phases

TL;DR

This paper analyzes the transport properties of striped quantum Hall phases, revealing a semicircle law for the conductivity tensor that applies broadly, including in the presence of topological defects, and explains experimental resistivity product rules.

Contribution

It establishes a general semicircle law for the conductivity tensor in striped quantum Hall phases, regardless of defects or phase type, extending previous theoretical results.

Findings

The macroscopic conductivity tensor follows a semicircle law.

The semicircle law holds for both smectic and nematic phases.

The results explain experimental resistivity product rules.

Abstract

We study the transport properties of pinned striped quantum Hall phases. We show that under quite general assumptions, the macroscopic conductivity tensor satisfies a semicircle law. In particular, this result is valid for both smectic and nematic stripe phases, independent of the presence of topological defects such as dislocations and grain boundaries. As a special case, our results explain the experimental validity of a product rule for the dissipative part of the resistivity tensor, which was previously derived by MacDonald and Fisher for a perfect stripe structure.