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Title: 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.

Authors:
ORCiD logo; ORCiD logo; ORCiD logo
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. doi:10.1103/PhysRevResearch.2.013139.
Pu, Songyang, Fremling, Mikael, and Jain, J. K. Mon . "Hall viscosity of composite fermions". United States. doi: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 = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevResearch.2.013139

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Works referenced in this record:

Hydrodynamic Electron Flow and Hall Viscosity
journal, June 2017


Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982


New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
journal, August 1980


Hall Viscosity and Electromagnetic Response
journal, February 2012


Success and failure of the plasma analogy for Laughlin states on a torus
journal, November 2016


Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983


Transport Signatures of the Hall Viscosity
journal, November 2017


Hall viscosity of hierarchical quantum Hall states
journal, March 2014


Viscous transport and Hall viscosity in a two-dimensional electron system
journal, October 2018


Modular covariance properties of composite fermions on the torus
journal, February 2019


Quantized Hall Conductance in a Two-Dimensional Periodic Potential
journal, August 1982


Viscosity of the Electron Gas in Metals
journal, March 1958


Viscosity of Quantum Hall Fluids
journal, July 1995


Measuring Hall viscosity of graphene’s electron fluid
journal, February 2019


Theory of the fractional quantum Hall effect
journal, April 1990


Shift and spin vector: New topological quantum numbers for the Hall fluids
journal, August 1992


Berry phases for Landau Hamiltonians on deformed tori
journal, June 1995

  • Lévay, Péter
  • Journal of Mathematical Physics, Vol. 36, Issue 6
  • DOI: 10.1063/1.531066

Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians
journal, June 2013


Hall viscosity in the non-Abelian quantum Hall matrix model
journal, August 2018


Geometry of fractional quantum Hall fluids
journal, September 2014


Lorentz shear modulus of fractional quantum Hall states
journal, June 2009


Incompressible quantum Hall states
journal, October 1989


Composite fermions on a torus
journal, November 2017


Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids
journal, November 2017


Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
journal, September 1997


Entanglement Entropy of the ν = 1 / 2 Composite Fermion Non-Fermi Liquid State
journal, May 2015


Classification of Abelian quantum Hall states and matrix formulation of topological fluids
journal, July 1992


Odd viscosity in two-dimensional incompressible fluids
journal, September 2017


Lattice Monte Carlo for quantum Hall states on a torus
journal, March 2019


A modular-invariant modified Weierstrass sigma-function as a building block for lowest-Landau-level wavefunctions on the torus
journal, July 2018

  • Haldane, F. D. M.
  • Journal of Mathematical Physics, Vol. 59, Issue 7
  • DOI: 10.1063/1.5042618

Hall viscosity, orbital spin, and geometry: Paired superfluids and quantum Hall systems
journal, August 2011


Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
journal, December 2012


Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing
journal, August 2018


Topological orders and edge excitations in fractional quantum Hall states
journal, October 1995


Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989


Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
journal, October 2007


Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
journal, May 2018


Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons
journal, October 2016


Berry Phase and Model Wave Function in the Half-Filled Landau Level
journal, October 2018


Quantitative study of large composite-fermion systems
journal, February 1997


Shift and Spin Vector: New Topological Quantum Numbers for the Hall Fluids
journal, November 1992