# Berry phase of the composite Fermi-liquid

## TL;DR

This paper defines and analyzes the Berry phase of composite fermions in a half-filled composite Fermi-liquid, revealing differences from previous definitions and showing the Berry curvature distribution for different wave functions, challenging the Dirac particle picture.

## Contribution

It introduces a new definition of the Berry phase for composite fermions and compares the Berry curvature distribution for different wave functions.

## Key findings

- Berry curvature is uniformly distributed in momentum space for the standard wave function.
- Berry curvature has a continuous distribution inside the Fermi sea for the Jain-Kamilla wave function.
- Composite fermions are not massless Dirac particles based on Berry curvature analysis.

## 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.