Wigner crystalization about $\nu$=3

TL;DR

This paper reports the observation of a resonance in the conductivity near integer filling factor ν=3, interpreted as evidence of a pinned Wigner crystal phase whose properties depend on electron density and filling factor.

Contribution

It provides experimental evidence of a Wigner crystal formation near ν=3 through frequency-dependent conductivity measurements, extending understanding of electron solid phases in quantum Hall regimes.

Findings

Resonance frequency varies with filling factor and electron density.

Resonance interpreted as a pinned Wigner crystal phase.

Comparison with similar measurements at ν=1 and 2.

Abstract

We measure a resonance in the frequency dependence of the real diagonal conductivity, Re[$\sigma_{xx}$], near integer filling factor, $\nu=3$. This resonance depends strongly on $\nu$, with peak frequency $f_{pk} \approx 1.7$ GHz at $\nu=3.04$ or 2.92 close to integer $\nu$, but $f_{pk} \approx$ 600 MHz at $\nu=3.19$ or 2.82, the extremes of where the resonance is visible. The dependence of $f_{pk}$ upon $n^*$, the density of electrons in the partially filled level, is discussed and compared with similar measurments by Chen {\it et al.}\cite{yong} about $\nu=1$ and 2. We interpret the resonance as due to a pinned Wigner crystal phase with density $n^*$ about the $\nu=3$ state.