Tunneling into fractional quantum Hall liquids

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 $α$ $(I\sim V^α)$ is of the order of $\sqrtε$ $(ε=v_n/v_c)$, which reduces the exponent $α$. We suggest that it could explain the systematic discrepancy between the observed exponents and the exact $α=1/ν$ dependence.