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

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 (2017)2469-995010.1103/PhysRevB.96.195302] 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 π in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)2160-330810.1103/PhysRevX.5.031027], 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 π Berry phase and the exact particle-hole symmetry in the lowest Landau level.