Elevated Hall Responses as Indicators of Edge Reconstruction

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 ($e^2\mathrm{/}h$) and thermal (${\pi }^2{k}_{\text{B}}^{2}T\mathrm{/}3h$) 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.