Lorentz shear modulus of fractional quantum Hall states

TL;DR

This paper establishes a relationship between the Lorentz shear modulus and the bulk modulus in fractional quantum Hall states, providing explicit calculations for Laughlin states and confirming recent theoretical results.

Contribution

It introduces a novel correspondence linking the Lorentz shear modulus to classical particle systems and computes this modulus for Laughlin states at specific filling factors.

Findings

Lorentz shear modulus is proportional to the bulk modulus in the thermodynamic limit.

Calculated Lorentz shear modulus for Laughlin states at filling factor 1/m.

Results agree with recent theoretical predictions by Read.

Abstract

We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit. Making use of this correspondence we calculate the Lorentz shear modulus of Laughlin's fractional quantum Hall states at filling factor $\nu=1/m$ ($m$ an odd integer) and find that it is equal to $\pm \hbar mn/4$, where $n$ is the density of particles and the sign depends on the direction of magnetic field. This is in agreement with the recent result obtained by Read in arXiv:0805.2507 and corrects our previous result published in Phys. Rev. B {\bf 76}, 161305 (R) (2007).