Dynamical matrix of two-dimensional electron crystals

TL;DR

This paper develops a method to compute the dynamical matrix of two-dimensional electron crystals in magnetic fields using the density response function within the GRPA, bridging microscopic calculations with elasticity theory.

Contribution

It introduces a novel approach to derive the dynamical matrix from the density response function in the context of 2D electron crystals under magnetic fields.

Findings

The method accurately reproduces elastic properties of electron crystals.

Comparison shows good agreement between GRPA-based and elasticity theory calculations.

The approach provides a microscopic foundation for understanding crystal dynamics.

Abstract

In a quantizing magnetic field, the two-dimensional electron (2DEG) gas has a rich phase diagram with broken translational symmetry phases such as Wigner, bubble, and stripe crystals. In this paper, we derive a method to get the dynamical matrix of these crystals from a calculation of the density response function performed in the Generalized Random Phase Approximation (GRPA). We discuss the validity of our method by comparing the dynamical matrix calculated from the GRPA with that obtained from standard elasticity theory with the elastic coefficients obtained from a calculation of the deformation energy of the crystal.