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 = ( /4)Sρ, where ρ is the density and S = 2p ± n is the "shift" in the spherical geometry. We discuss the role of modular invariance of the wave functions, of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for ν = n 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.

Bardeen-Cooper-Schrieffer pairing of composite fermions

“…Eq. 51 has been derived for the Laughlin state, Pfaffian state, and Jain states by various approaches [54,72,[74][75][76][77][78]. It has also been numerically confirmed for the Laughlin and Pfaffian states in Ref.…”

“…The wave functions that satisfy this property are said to be modular covariant [54,60,61]. The modified JK projection for Jain states and CFFSs have been shown to be modu-lar covariant [43,54,61]. In Appendix C, we show the CF-BCS-paired wave function in Eq.…”

“…[75] and for the Jain states in Refs. [54,60]. The Hall viscosity is computed through the Berry curvature in the τ space, which captures the adiabatic change of gapped state with the shear deformation of the torus:…”

“…k i < k j for i < j. The single particle orbitals in the LLL can be written as [54] ψ(z,z) = N e The basis |k 1 , k 2 , .., k N are automatically eigenstates oft i (L) [here we only consider ν = 1/2, for which GCD(N, N φ )= N ] as we choose the primary axis along the x direction:…”

Quantum Hall effective action for the anisotropic Dirac semimetal

“…To shed light on the generic low-energy properties of such quantum Hall states, we construct an effective action for systems with a semi-Dirac phase. Our construction contributes to the quest of understanding Hall viscosities; nondissipative transport coefficients that emerge in the context of topological order [21][22][23][24][25][26][27], fluid dynamics [28][29][30][31][32][33][34][35][36][37][38][39][40], or active matter [41][42][43][44][45][46]. Initially thought of as an elusive transport property, Hall viscosity has been experimentally identified in both hard [47] and soft [48] condensed matter experiments.…”