Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing

Abstract

We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $\pi$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple model wherein we determine the variational ground state as a function of Landau level mixing within the space spanned by two basis functions: the lowest-Landau-level projected and the unprojected composite-fermion Fermi sea wave functions. We evaluate Berry phase for a path around the Fermi circle within this model following a recent prescription, and find that it rotates rapidly as a function of Landau level mixing. We also consider the effect of a particle-hole symmetry breaking three-body interaction on the Berry phase while confining the Hilbert space to the lowest Landau level. Our study deepens the connection between the $\pi$ Berry phase and the exact particle-hole symmetry in the lowest Landau level.

13 pages, 6 figures

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• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Foundations and Applications of Quantum Kinetic Theory
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Hall Viscosity of Composite Fermions
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Berry phase of the composite Fermi-liquid
• On the modular covariance properties of composite fermions on the torus
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Fractional Quantum Hall States on CP2 Space