Inter edge Tunneling in Quantum Hall Line Junctions

TL;DR

This paper models tunneling in quantum Hall line junctions as coupled chiral Luttinger liquids, explaining experimental zero-bias conductance peaks and their dependence on filling factor, interactions, and temperature.

Contribution

It introduces a theoretical framework for understanding tunneling features in quantum Hall systems using coupled Luttinger liquids, accounting for interaction effects and spin considerations.

Findings

Zero-bias conductance peak magnitude is proportional to the Luttinger parameter K.

The zero-bias peak appears abruptly near certain filling factors and diminishes with temperature.

Spin effects can cause reappearance of the zero-bias peak at higher filling factors.

Abstract

We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors $\nu\sim1$ the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter $K$, leading to the appearance of a zero-bias differential conductance peak of magnitude $G_t=Ke^2/h$ at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value $ \nu^* \gtrsim 1$, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage $V$, the crossover scale $T_K$, and the temperature $T$. The low height of the zero bias peak $\sim 0.1e^2/h$ observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for $\nu \gtrsim 2$ can be explained as an effect caused by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a small polarization near $\nu\sim2$. We also predict that as the temperature is lowered $\nu^*$ should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for $\nu \gtrsim 2$.