Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field

TL;DR

This study investigates the correlation lengths of Wigner crystal order in a two-dimensional electron system under high magnetic fields, revealing a linear relationship influenced by magnetic compression of electron wavefunctions.

Contribution

It provides the first systematic measurement of Wigner crystal correlation lengths across various densities and magnetic fields, highlighting the linear dependence on filling factor.

Findings

Correlation length L increases linearly with filling factor at low bc

Resonance peak frequency f_pk varies with magnetic field and density

Electron wavefunction compression affects electron-impurity interactions

Abstract

The insulator terminating the fractional quantum Hall series at low Landau level filling \nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. Systematically studying the resonance in a high quality sample for carrier densities, n, between 1.8 and 5.7 x 10^{10} cm^-2, we find maxima in resonance peak frequency, f_pk, vs magnetic field, B. L, the domain size, or correlation length of Wigner crystalline order, is calculated from f_pk. For each n, L vs \nu tends at low \nu toward a straight line with intercept; the linear fit is accurate over as much as a factor of 5 range of \nu. We interpret the striking linear behavior as due to B compressing the electron wavefunctions, to alter the effective electron-impurity interaction.