Edge reconstruction in the fractional quantum Hall regime

TL;DR

This paper investigates how electron interactions and confining potentials cause edge reconstruction in fractional quantum Hall systems, affecting observable properties like microwave conductivity and tunneling spectra, with numerical and experimental relevance.

Contribution

It provides numerical evidence of edge reconstruction considering realistic effects such as layer thickness and Landau level mixing, linking these to experimental measurements.

Findings

Edge reconstruction leads to additional nonchiral edge modes.

Enhanced microwave conductivity observed at low temperatures.

Edge reconstruction impacts the electron spectral function.

Abstract

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single electron spectral function at the edge.