Elevated Hall Responses as Indicators of Edge Reconstruction

TL;DR

This paper demonstrates that edge reconstruction in the quantum Hall state can cause significant deviations in electrical and thermal Hall conductances, serving as indicators of edge state modifications.

Contribution

It reveals how upstream charge and neutral modes lead to enhanced Hall conductance deviations, providing a diagnostic for edge reconstruction.

Findings

Electrical and thermal Hall conductances can exceed twice their unreconstructed values.

Upstream charge and neutral modes cause deviations from quantized conductance.

Edge reconstruction can be diagnosed via elevated Hall responses.

Abstract

We investigate edge reconstruction scenarios in the $\nu = 1$ quantum Hall state, focusing on configurations with upstream and downstream charge and neutral modes. Our analysis shows that the coexistence of upstream charge and neutral modes in a multi-terminal geometry can cause pronounced deviations from the expected quantized values of electrical ($e^2/h$) and thermal ($\pi^2 k_\text{B}^{2}T/3h$) Hall conductance dictated by bulk-boundary correspondence. In particular, we find that both electrical and thermal Hall conductances can be significantly enhanced -- exceeding twice their unreconstructed values -- offering a clear diagnostic of edge reconstruction.