# 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 η^{A} agree with the expression η^{A} = ($$\hslash$$/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:

- 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}

}

DOI: 10.1103/PhysRevResearch.2.013139

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