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

TL;DR

This paper calculates the Hall viscosity of composite-fermion Fermi seas at various filling factors, showing they are finite and stable, but not topologically quantized, and relates findings to particle-hole symmetry and Dirac composite fermions.

Contribution

It provides the first direct numerical calculation of Hall viscosities for composite-fermion Fermi seas, revealing their finiteness and stability, and connects results to particle-hole symmetry and Dirac fermion models.

Findings

Hall viscosities are finite and stable with system size.

Hall viscosities are not topologically quantized across the entire parameter space.

Results are consistent with particle-hole symmetry and Dirac composite fermion theory.

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 $n\rightarrow \infty$ limit of the Jain $\nu=n/(nm\pm 1)$ states, whose Hall viscosities $(\pm n+m)\hbar \rho/4$ ($\rho$ is the two-dimensional density) approach $\pm \infty$ in the limit $n\rightarrow \infty$. 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.