Hall Viscosity of Composite Fermions

Abstract

Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form ν = n/(2pn ± 1), where n and p are integers, from the explicit wave functions for these states. The calculated Hall viscosities ηA agree with the expression ηA = ( ¯h/4)Sρ, where ρ is the density and S = 2p ± n is the “shift” in the spherical geometry. We discuss the role of modular covariance of the wave functions, projection of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for ν = n 2pn+1 may be derived analytically from the microscopic wave functions, provided that the overall normalization factor satisfies a certain behavior in the thermodynamic limit. This derivation should be applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction