Comparison of tunneling rates of fractional charges and electrons across a quantum Hall strip

The fundamental mechanism of current dissipation in a Hall strip is investigated by searching for the fastest process of charge relaxation between the edges. The tunneling rate of the fractional charge across a nu = 1/3 Laughlin state of width Y on the cylinder is found to fit t(1/3) proportional to exp[-alpha Y-2/12 lambda(2)], where lambda is the Landau length, and alpha similar or equal to 1.0. This rate is exponentially larger than the electron tunneling rate, and can be interpreted by analogy to the tunneling of a vortex through a superfluid. Fractional charge tunneling dominates current relaxation. It determines the Aharonov-Bohm oscillation period, and the magnitude of quantum shot-noise.