Elevated Hall Responses as Indicators of Edge Reconstruction

Abstract

We investigate edge reconstruction scenarios in the $\hat{I}½=1$ 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 ($\ddot{I}{€}^2{k}_{\text{B}}^{2}T/3h$) 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.

12 pages, 4 figures; investigation of excess shot noise is included to provide a deeper insight into the role of upstream neutral modes and equilibration processes; version accepted for publication in Physical Review B