Tunneling into the edge of a compressible Quantum Hall state

TL;DR

This paper develops a composite fermion theory to analyze tunneling into the edge of a compressible quantum Hall state, revealing non-ohmic conductance and a filling factor-dependent tunneling exponent.

Contribution

It introduces a new theoretical framework for tunneling in compressible quantum Hall states, connecting with existing chiral Luttinger liquid models at fractional fillings.

Findings

Tunneling conductance is non-ohmic due to slow relaxation effects.

The tunneling exponent varies continuously with filling factor nu.

Results agree with established theories at fractional quantum Hall states.

Abstract

We present a composite fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the tunneling electron. Universal results are obtained in the limit of a large number of channels involved in the relaxation. The tunneling exponent is found to be a continuous function of the filling factor nu, with a a slope that is discontinuous at nu=1/2 in the limit of vanishing bulk resistivity rho_xx. When nu corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen, and Kane, Fisher and Polchinski.