Transport in a disordered [formula omitted] fractional quantum Hall junction

Abstract

Electric and thermal transport properties of a ν=2∕3 fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, G and GQ, with system size L and temperature T. This is done both for the case of strong interaction between the 1 and 1/ 3 modes (when the low-temperature physics of the interacting segment of the device is controlled by the vicinity of the strong-disorder Kane–Fisher–Polchinski fixed point) and for relatively weak interaction, for which the disorder is irrelevant at T=0 in the renormalization-group sense. The transport properties in both cases are similar in several respects. In particular, G(L) is close to 4/3 (in units of e2∕h) and GQ to 2 (in units of πT∕6ħ) for small L, independently of the interaction strength. For large L the system is in an incoherent regime, with G given by 2/3 and GQ showing the Ohmic scaling, GQ∝1∕L, again for any interaction strength. The hallmark of the strong-disorder fixed point is the emergence of an intermediate range of L, in which the electric conductance shows strong mesoscopic fluctuations and the thermal conductance is GQ=1. The analysis is extended also to a device with floating 1/3 mode, as studied in a recent experiment (Grivnin et al. 2014).