TY - JOUR

T1 - Hall viscosity of composite fermions

AU - Pu, Songyang

AU - Fremling, Mikael

AU - Jain, J. K.

N1 - Publisher Copyright:
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevResearch.2.013139

DO - 10.1103/PhysRevResearch.2.013139

M3 - Article

AN - SCOPUS:85090891413

VL - 2

JO - Physical Review Research

JF - Physical Review Research

SN - 2643-1564

IS - 1

M1 - 013139

ER -