Static and dynamic properties of crystalline phases of two-dimensional electrons in a strong magnetic field

TL;DR

This paper investigates the elastic and phase properties of two-dimensional electron crystals in high magnetic fields, revealing non-monotonic shear moduli behavior and effects of screening and finite thickness on phase stability.

Contribution

It provides a detailed analysis of the elastic properties of electron crystals, including the impact of screening and finite thickness, using a Hartree-Fock approach.

Findings

Shear moduli show non-monotonic dependence on filling factor.

Screening and finite thickness significantly alter phase diagrams.

Implications for microwave resonance experiments are discussed.

Abstract

We study the cohesive energy and elastic properties as well as normal modes of the Wigner and bubble crystals of the two-dimensional electron system (2DES) in higher Landau levels. Using a simple Hartree-Fock approach, we show that the shear moduli ($c_{66}$'s) of these electronic crystals show a non-monotonic behavior as a function of the partial filling factor $\nu^*$ at any given Landau level, with $c_{66}$ increasing for small values of $\nu^*$, before reaching a maximum at some intermediate filling factor $\nu^*_m$, and monotonically decreasing for $\nu^*>\nu^*_m$. We also go beyond previous treatments, and study how the phase diagram and elastic properties of electron solids are changed by the effects of screening by electrons in lower Landau levels, and by a finite thickness of the experimental sample. The implications of these results on microwave resonance experiments are briefly discussed.