Hall viscosity of the composite-fermion Fermi seas for fermions and bosons

Pu, Songyang

doi:10.1103/physrevb.102.165101

Cited by 8 publications

(4 citation statements)

References 50 publications

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“…In the limit δ k F → 0, which is the CF-Fermi sea, we obtain the same Hall viscosity as that reported in Ref. [43]. When δ k F increases, the Hall viscosity changes.…”

Section: Hall Viscosity Of Paired Bcs Wave Functionsupporting

confidence: 88%

“…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.…”

Section: Construction Of Bcs Wave Function For Composite Fermionsmentioning

confidence: 99%

“…In torus geometry, the analogous wave function satisfying the periodic boundary conditions is given by [37,38,43]:…”

Section: Composite Fermions On a Torusmentioning

confidence: 99%

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Bardeen-Cooper-Schrieffer pairing of composite fermions

Sharma¹,

Pu²,

Jain³

2020

Preprint

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Topological pairing of composite fermions has led to remarkable ideas, such as excitations obeying non-Abelian braid statistics and topological quantum computation. We construct a p-wave paired Bardeen-Cooper-Schrieffer (BCS) wave function for composite fermions in the torus geometry, which is a convenient geometry for formulating momentum space pairing as well as for revealing the underlying composite-fermion Fermi sea. Following the standard BCS approach, we minimize the Coulomb interaction energy at half filling in the lowest and the second Landau levels, which correspond to filling factors ν = 1/2 and ν = 5/2 in GaAs quantum wells, by optimizing two variational parameters that are analogous to the gap and the Debye cut-off energy of the BCS theory. Our results show no evidence for pairing at ν = 1/2 but a clear evidence for pairing at ν = 5/2. To a good approximation, the highest overlap between the exact Coulomb ground state at ν = 5/2 and the BCS state is obtained for parameters that minimize the energy of the latter, thereby providing support for the physics of composite-fermion pairing as the mechanism for the 5/2 fractional quantum Hall effect. We discuss the issue of modular covariance of the composite-fermion BCS wave function, and calculate its Hall viscosity and pair correlation function. By similar methods, we look for but do not find an instability to s-wave pairing for a spin-singlet composite-fermion Fermi sea at half-filled lowest Landau level in a system where the Zeeman splitting has been set to zero. t(Lτ )e z 2 −|z| 2 4 2 = e z 2 −|z| 2 4 2

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“…In the limit δ k F → 0, which is the CF-Fermi sea, we obtain the same Hall viscosity as that reported in Ref. [43]. When δ k F increases, the Hall viscosity changes.…”

Section: Hall Viscosity Of Paired Bcs Wave Functionsupporting

confidence: 88%

Section: Construction Of Bcs Wave Function For Composite Fermionsmentioning

confidence: 99%

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Bardeen-Cooper-Schrieffer pairing of composite fermions

Sharma¹,

Pu²,

Jain³

2020

Preprint

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“…7 is an eigenstate of t CM (L 2 /N φ ), the more familiar Laughlin wave functions in Ref. [58] and other literature are chosen to be the eigenstates of t CM (L 1 /N φ ). If one defines the periodic properties Eq.…”

Section: Multi-component Anyon Wave Functions and Ground State Degene...mentioning

confidence: 99%

Composite anyons on a torus

Pu,

Jain

2021

Preprint

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An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Finally, we obtain from these wave functions, both analytically and numerically, various topological quantities, such the ground state degeneracy, the Chern number and the Hall viscosity.

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Origin of the ν=1/2 fractional quantum Hall effect in wide quantum wells

Zhao

Faugno

et al. 2021

Phys. Rev. B

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Hall viscosity of the composite-fermion Fermi seas for fermions and bosons

Cited by 8 publications

References 50 publications

Bardeen-Cooper-Schrieffer pairing of composite fermions

Bardeen-Cooper-Schrieffer pairing of composite fermions

Composite anyons on a torus

Origin of the ν=1/2 fractional quantum Hall effect in wide quantum wells

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