Average and Second Moment of the Conductance of Randomly Coupled Chiral Channels

Abstract

We study the conductance of a spinless non-interacting electron system consisting of randomly coupled N R right-moving channels and N L left-moving channels. This system serves as a model of disordered quantum wires with unitary symmetry. We focus on the case of N R = 1 with an arbitrary N L . In this case, the dimensionless conductance g for the left-moving channels is by m ≡ N L -1 greater than the dimensionless conductance g ' for the right-moving channels due to the presence of m perfectly conducting channels. That is, g = g '+ m . Using a superspin approach, we obtain the average and second moment of g ' as a function of wire length L . The resulting asymptotic forms in the long- L regime are consistent with those obtained from the existing scaling theory.