Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons

Abstract

The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at $\nu =1/m$, where $m$ is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the $1/m$ composite-fermion Fermi seas as the $n\to \infty$ limit of the Jain $\nu =n/(nm\pm 1)$ states, whose Hall viscosities $(\pm n+m)\hslash \rho /4$ ($\rho$ is the two-dimensional density) approach $\pm \infty$ in the limit $n\to \infty$. A direct calculation shows that the Hall viscosities of the composite-fermion Fermi sea states are finite, and also relatively stable with system size variation, although they are not topologically quantized in the entire $\tau$ space. I find that the $\nu =1/2$ composite-fermion Fermi sea wave function for a square torus yields a Hall viscosity that is expected from particle-hole symmetry and is also consistent with the orbital spin of $1/2$ for Dirac composite fermions. I compare my numerical results with some theoretical conjectures.

10 pages, 2 figures

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Cited by in corpus (7)

• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Observable signatures of Hall viscosity in lowest Landau level superfluids
• Composite anyons on a torus
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions