Berry phase in the composite Fermi liquid

Abstract

We derive the definition of the Berry phase for the adiabatic transport of a composite fermion (CF) in a half-filled composite Fermi liquid (CFL). It is found to be different from that adopted in previous investigations by Geraedts et al. For the standard CFL wave function, we analytically show that the Berry curvature is uniformly distributed in the momentum space. For the Jain-Kamilla wave function, we numerically show that its Berry curvature has a continuous distribution inside the Fermi sea and vanishes outside. We conclude that the CF with respect to both the microscopic wave functions is not a massless Dirac particle.

Emergence of Dirac composite fermions: Dipole picture

“…As an attempt to determine the Berry phase and Berry curvature of CFs, Geraedts et al numerically calculate the matrix element of the density operator ρ−q = a exp(iq • r a ) between two Rezayi-Read states with different sets of wavevectors [40]. In Ref [43], we argue that their calculation could be regarded as a "firstprinciples" determination of the scattering matrix element from the microscopic wave function. It is then interesting to see how the scattering matrix element Eq.…”

“…These are exactly what are observed in Geraedts et al's work. The phase obtained from the scattering matrix element is in general not the Berry phase [43]. Geraedts et al interprets the lack of dependence of the cumulated phase on the radius of the circular path as a manifestation of the singular distribution of the Berry curvature in a massless Dirac cone.…”