Nonzero temperature transport near fractional quantum Hall critical points

Abstract

In an earlier work, Damle and the author (Phys. Rev. B in press; cond-mat/9705206) demonstrated the central role played by incoherent, inelastic processes in transport near two-dimensional quantum critical points. This paper extends these results to the case of a quantum transition in an anyon gas between a fractional quantized Hall state and an insulator, induced by varying the strength of an external periodic potential. We use the quantum field theory for this transition introduced by Chen, Fisher and Wu (Phys. Rev. B 48, 13749 (1993)). The longitudinal and Hall conductivities at the critical point are both $e^2/ h$ times non-trivial, fully universal functions of $\hbar \omega / k_B T$ ($\omega$ is the measuring frequency). These functions are computed using a combination of perturbation theory on the Kubo formula, and the solution of a quantum Boltzmann equation for the anyonic quasiparticles and quasiholes. The results include the values of the d.c. conductivities ($\hbar \omega /k_B T \to 0$); earlier work had been restricted strictly to T=0, and had therefore computed only the high frequency a.c. conductivities with $\hbar \omega / k_B T \to \infty$.