Edge reconstructions in fractional quantum Hall systems

TL;DR

This paper provides a microscopic analysis of edge state reconstructions in fractional quantum Hall systems, revealing that edges at ν=1/3 can reconstruct under certain conditions, while higher filling factors remain stable.

Contribution

It offers a detailed microscopic calculation of edge states across various filling factors, highlighting the conditions for edge reconstruction and stability.

Findings

Edge at ν=1/3 undergoes reconstruction as background potential softens.

Edges at ν=2/5 and 3/7 are stable against reconstruction.

Edge state properties depend on temperature, interactions, and confining potential.

Abstract

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are present. We present a {\it microscopic} calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at $\nu=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as $\nu=2/5, 3/7$, are robust against reconstruction. We present the results for the dependence of the edge states on various system parameters such as temperature, functional form and range of electron-electron interactions, and the confining potential. Our results have implications for the tunneling experiments into the edge of a fractional quantum Hall system.