Hall viscosity of composite fermions

Songyang Pu, Mikael Fremling, J. K. Jain

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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=(ℏ/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=n2pn+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.

Original languageEnglish (US)
Article number013139
JournalPhysical Review Research
Issue number1
StatePublished - Feb 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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