Asymptotic Behavior of the Conductance in Disordered Wires with Perfectly Conducting Channels

Abstract

We study the conductance of disordered wires with unitary symmetry focusing on the case in which m perfectly conducting channels are present due to the channel-number imbalance between two-propagating directions. Using the exact solution of the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation for transmission eigenvalues, we obtain the average and second moment of the conductance in the long-wire regime. For comparison, we employ the three-edge Chalker–Coddington model as the simplest example of channel-number-imbalanced systems with m = 1, and obtain the average and second moment of the conductance by using a supersymmetry approach. We show that the result for the Chalker–Coddington model is identical to that obtained from the DMPK equation.