Lorentz shear modulus of fractional quantum Hall states

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 ν = 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.