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 π 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 Landaulevel 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. arXiv:1805.09237v3 [cond-mat.str-el]

Thirty Years of Composite Fermions and Beyond

“…7 shows the exact spectrum at ν = 1/2 in the torus geometry, along with the CF energies for the lowest energy states in several momentum sectors. 79 Higher bands are often not clearly identifiable in the exact spectra, presumably because of the broadening induced by the residual interaction between composite fermions. Interestingly, more and more bands become visible as we we go to higher CF fillings.…”

Berry phase in the composite Fermi liquid

“…In this case, the phase carried by the prefactor cannot be easily distinguished from the Berry phase to be determined. One encounters such a situation when studying the effect of the Landau level mixing [25]. In the study, Pu et al adopt the wave function , and V 1 > 0 (V 1 < 0) for particles (holes).…”

“…From Eq. 25, the prefactor contributes a phase 0 (π ) for each step of transporting a particle (hole) [25]. On the other hand, for the projected wave function k , V 2 dominates, and the prefactor contributes a phase ±π/2.…”

Fractional Quantum Hall States on CP2 Space

“…In contrast to the two-dimension, high dimension may support membrane-like excitations 31,32 . It may also be possible to extend this work to other quantum Hall states including the paired states 45 and gapless states [46][47][48][49][50][51] . A thorough mathematical understanding of quasi-hole wavefunctions besides Section.…”