# Transport in a disordered $\nu=2/3$ fractional quantum Hall junction

## TL;DR

This paper studies electric and thermal transport in a disordered $
u=2/3$ fractional quantum Hall junction, revealing how conductances evolve with system size and interaction strength, including mesoscopic fluctuations and fixed point behaviors.

## Contribution

It provides a detailed analysis of transport properties in a $
u=2/3$ quantum Hall junction under different interaction regimes and disorder strengths, extending to experimental device configurations.

## Key findings

- Small system size conductances are close to quantized values.
- Large system size conductances show universal scaling behaviors.
- Mesoscopic fluctuations occur at intermediate system sizes.

## Abstract

Electric and thermal transport properties of a $\nu=2/3$ fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, $G$ and $G^Q$, 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 $e^2/h$) and $G^Q$ to 2 (in units of $\pi T / 6 \hbar$) 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 $G^Q$ showing the Ohmic scaling, $G^Q\propto 1/L$, 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 $G^Q=1$. The analysis is extended also to a device with floating 1/3 mode, as studied in a recent experiment [A. Grivnin et al, Phys. Rev. Lett. 113, 266803 (2014)].