Tunneling into fractional quantum Hall liquids

TL;DR

This paper investigates the non-ohmic tunneling characteristics into fractional quantum Hall liquids, explaining experimental discrepancies using chiral Tomonaga-Luttinger liquid theory and charge-neutral mode interactions.

Contribution

It provides a theoretical explanation for tunneling behavior in fractional quantum Hall liquids, accounting for charge-neutral mode interactions and their effect on tunneling exponents.

Findings

The correction to the tunneling exponent is proportional to the square root of the mode velocity ratio.

The correction reduces the tunneling exponent, potentially explaining experimental deviations.

The theory aligns with observed systematic discrepancies in tunneling exponents.

Abstract

Motivated by the recent experiment by Grayson et.al., we investigate a non-ohmic current-voltage characteristics for the tunneling into fractional quantum Hall liquids. We give a possible explanation for the experiment in terms of the chiral Tomonaga-Luttinger liquid theory. We study the interaction between the charge and neutral modes, and found that the leading order correction to the exponent $\alpha$ $(I\sim V^\alpha)$ is of the order of $\sqrt{\epsilon}$ $(\epsilon=v_n/v_c)$, which reduces the exponent $\alpha$. We suggest that it could explain the systematic discrepancy between the observed exponents and the exact $\alpha =1/\nu$ dependence.