Bragg resonances for tunneling between edges of a 2D Quantum Hall system

TL;DR

This paper develops a theoretical model for tunneling in 2D Quantum Hall systems, showing how Bragg resonances arise from umklapp scattering on a Wigner crystal at the edges, matching recent experimental observations.

Contribution

It introduces a novel theory linking Bragg resonances in tunneling to Wigner crystal formation and umklapp scattering in Quantum Hall edge states.

Findings

Resonant tunneling conductivity varies with incompressible strip width.

Bragg conditions lead to quantized momentum transfer and resonances.

The model explains experimental tunneling resonance patterns.

Abstract

A theory is presented for tunneling between compressible regions on the sides of a narrow incompressible Quantum Hall strip. Assuming that electron interactions lead to formation of a Wigner crystal on the edges of the compressible regions, we consider the situation when the non-conservation of electron momentum required for transport is provided, in the absence of disorder, by umklapp scattering on the crystal. The momentum given to the crystal is quantized due to the Bragg condition, which leads to resonances in tunneling conductivity as a function of the incompressible strip width, similar to those reported recently by N. Zhitenev, M. Brodsky, R. Ashoori, and M. Melloch.