Lorentz shear modulus of a two-dimensional electron gas at high magnetic field

TL;DR

This paper calculates the Lorentz shear modulus of a 2D electron gas in high magnetic fields exactly, revealing its dependence on electron density and magnetic field orientation, and refines understanding of collective mode dispersion in fractional quantum Hall liquids.

Contribution

It provides an exact calculation of the Lorentz shear modulus in the lowest Landau level, enhancing theoretical understanding of electron gases under strong magnetic fields.

Findings

Lorentz shear modulus is ± ħ n / 4 in high magnetic fields

Refined dispersion calculations for fractional quantum Hall liquids

Sign of shear modulus depends on magnetic field orientation

Abstract

We show that the Lorentz shear modulus -- one of the three elastic moduli of a homogeneous electron gas in a magnetic field -- can be calculated exactly in the limit of high magnetic field (i.e. in the lowest Landau level). Its value is $\pm \hbar n/4$, where $n$ is the two-dimensional electron density and the sign is determined by the orientation of the magnetic field. We use this result to refine our previous calculations of the dispersion of the collective modes of fractional quantum Hall liquids.