Averaged Conductance of the Three-Edge Chalker–Coddington Model

Abstract

To study electron transport in disordered wires with the channel-number imbalance between two propagating directions, we consider the three-edge Chalker–Coddington model consisting of one right-moving and two left-moving edge channels of length L coupled by random tunneling. Since the imbalance makes one left-moving channel being perfectly conducting, the dimensionless conductances g and g′ for the left-moving and right-moving channels, respectively, differ from each other and satisfy g=g′+1. Using a supersymmetry approach, we obtain the asymptotic form of the ensemble average ⟨g⟩−1=⟨g′⟩ which decays exponentially with increasing L. It is shown that the corresponding decay length is four times shorter than that for the two-edge case. This result is in quantitative agreement with the existing random-matrix theory.