Which tunnel faster across a quantum Hall strip: fractional charges or electrons?

TL;DR

This paper numerically compares the tunneling rates of fractional charges and electrons across a quantum Hall strip, finding fractional charges tunnel significantly faster, with implications for quantum measurement and interference experiments.

Contribution

It provides a numerical analysis showing fractional charges tunnel exponentially faster than electrons, offering new insights into quantum Hall edge physics.

Findings

Fractional charge tunneling rate is exponentially larger than electron tunneling rate.

Tunneling decay fits an exponential function with respect to strip width.

Results have implications for quantum interference and shot noise measurements.

Abstract

The tunneling rate of fractional charge across a Laughlin state on the cylinder is computed numerically. The decay with strip width Y is fitted to exp[- a (Y/ l)**2/12] where l is the Landau length, and a is approximately 1.0. This rate is exponentially LARGER than the electron tunneling rate and can be interpreted by analogy to a superfluid vortex tunneling problem. Experimental implications include the ``law of corresponding states'', periodicity of Aharonov-Bohm resistance oscillations and charge measurements by quantum shot noise.