Gauge Theory of Composite Fermions: Particle-Flux Separation in Quantum Hall Systems

Abstract

Fractionalization phenomenon of electrons in quantum Hall states is studied in terms of U(1) gauge theory. We focus on the Chern-Simons(CS) fermion description of the quantum Hall effect(QHE) at the filling factor $ν=p/(2pq\pm 1)$, and show that the successful composite-fermions(CF) theory of Jain acquires a solid theoretical basis, which we call particle-flux separation(PFS). PFS can be studied efficiently by a gauge theory and characterized as a deconfinement phenomenon in the corresponding gauge dynamics. The PFS takes place at low temperatures, $T \leq T_{\rm PFS}$, where each electron or CS fermion splinters off into two quasiparticles, a fermionic chargeon and a bosonic fluxon. The chargeon is nothing but Jain's CF, and the fluxon carries $2q$ units of CS fluxes. At sufficiently low temperatures $T \leq T_{\rm BC} (< T_{\rm PFS})$, fluxons Bose-condense uniformly and (partly) cancel the external magnetic field, producing the correlation holes. This partial cancellation validates the mean-field theory in Jain's CF approach. FQHE takes place at $T < T_{\rm BC}$ as a joint effect of (i) integer QHE of chargeons under the residual field $ΔB$ and (ii) Bose condensation of fluxons. We calculate the phase-transition temperature $T_{\rm PFS}$ and the CF mass. PFS is a counterpart of the charge-spin separation in the t-J model of high-$T_{\rm c}$ cuprates in which each electron dissociates into holon and spinon. Quasiexcitations and resistivity in the PFS state are also studied. The resistivity is just the sum of contributions of chargeons and fluxons, and $ρ_{xx}$ changes its behavior at $T = T_{\rm PFS}$, reflecting the change of quasiparticles from chargeons and fluxons at $T < T_{\rm PFS}$ to electrons at $T_{\rm PFS} < T$.