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 = ($$\hslash$$/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 = $$n\over{2pn+1}$$ 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.
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1599495
- Alternate Identifier(s):
- OSTI ID: 1606394
- Grant/Contract Number:
- SC0005042
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 1; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Hall viscosity; composite fermions; fractional quantum Hall effect
Citation Formats
Pu, Songyang, Fremling, Mikael, and Jain, J. K. Hall viscosity of composite fermions. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.013139.
Pu, Songyang, Fremling, Mikael, & Jain, J. K. Hall viscosity of composite fermions. United States. https://doi.org/10.1103/PhysRevResearch.2.013139
Pu, Songyang, Fremling, Mikael, and Jain, J. K. Mon .
"Hall viscosity of composite fermions". United States. https://doi.org/10.1103/PhysRevResearch.2.013139.
@article{osti_1599495,
title = {Hall viscosity of composite fermions},
author = {Pu, Songyang and Fremling, Mikael and Jain, J. K.},
abstractNote = {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 = ($\hslash$/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 = $n\over{2pn+1}$ 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.},
doi = {10.1103/PhysRevResearch.2.013139},
journal = {Physical Review Research},
number = 1,
volume = 2,
place = {United States},
year = {Mon Feb 10 00:00:00 EST 2020},
month = {Mon Feb 10 00:00:00 EST 2020}
}
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