Edge States on a Quantum Hall Liquid--Solid Interface

TL;DR

This paper investigates how strong correlations at the interface between a quantum Hall liquid and an electron solid suppress the density of states, offering a potential experimental signature of mixed liquid-solid states in high magnetic fields.

Contribution

It demonstrates the impact of liquid-solid correlations on the density of states at the interface and provides a method to detect these states through tunneling experiments.

Findings

Correlation causes exponential suppression of the density of states.

Suppression coefficient depends on the regularity of the solid's electron distribution.

Probing this suppression can reveal liquid-solid mixture states in quantum dots.

Abstract

We study the edge--states excitations of a droplet of quantum Hall liquid embedded in an electron (Wigner) solid. The presence of strong correlations between the liquid and solid sectors in the ground state is shown to be reflected in the density of states $D(E)$, associated with the excitations of the liquid--solid interface. We find that the prominent effect of these correlations is a suppression of $D(E)$ with respect to its value ($D_0(E)$) in the absence of the Wigner solid environment: $D(E) \sim e^{-\alpha |E|}D_0(E)$. The coefficient $\alpha$ (which is shown to vanish for a perfectly regular distribution of electron sites in the solid), is evaluated for two different realizations of an irregular distribution. We conclude that probing this effect (e.g. in a tunneling experiment), can provide evidence for correlated liquid--solid mixture states in quantum dots, or disordered samples, in very strong magnetic fields.