Quantum Boltzmann equation of composite fermions interacting with a gauge field

TL;DR

This paper derives a quantum Boltzmann equation for composite fermions near the $ u=1/2$ state, revealing non-quasiparticle behavior and unifying Fermi-liquid properties with experimental implications.

Contribution

It introduces a novel derivation of the QBE for composite fermions without assuming Landau quasiparticles, using a Green's function approach and generalized Fermi surface displacement.

Findings

No well-defined Landau quasiparticles due to gauge field fluctuations

Unified understanding of Fermi-liquid behaviors at $ u=1/2$

Explanation of energy gap singularities near $ u=1/2$

Abstract

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi surface displacement which corresponds to the local variation of the chemical potential in momentum space. {}From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at $\nu = 1/2$ (in the long wave length and the low frequency limits) and the singular behavior of the energy gap obtained from the finite temperature activation behavior of the compressibility near $\nu = 1/2$. Implications of these results to the recent experiments are also discussed.