Sharp and Smooth Boundaries of Quantum Hall Liquids

TL;DR

This paper investigates the transition from sharp to smooth edges in Quantum Hall Liquids, revealing a reconstruction process influenced by interactions and confining potentials, with observable consequences in tunneling experiments.

Contribution

It demonstrates that edge reconstruction occurs due to a balance of Hartree and exchange interactions, and describes the resulting gapless excitations within a Hartree-Fock framework.

Findings

Edge transition occurs at a critical confining potential.

Reconstructed edges exhibit new gapless excitation branches.

Transition is observable in resonant tunneling experiments.

Abstract

We study the transition between sharp and smooth density distributions at the edges of Quantum Hall Liquids in the presence of interactions. We find that, for strong confining potentials, the edge of a $\nu=1$ liquid is described by the $Z_F=1$ Fermi Liquid theory, even in the presence of interactions, a consequence of the chiral nature of the system. When the edge confining potential is decreased beyond a point, the edge undergoes a reconstruction and electrons start to deposit a distance $\sim 2$ magnetic lengths away from the initial QH Liquid. Within the Hartree-Fock approximation, a new pair of branches of gapless edge excitations is generated after the transition. We show that the transition is controlled by the balance between a long-ranged repulsive Hartree term and a short-ranged attractive exchange term. Such transition also occurs for Quantum Dots in the Quantum Hall Regime, and should be observable in resonant tunneling experiments. Electron tunneling into the reconstructed edge is also discussed.