Fractional Conductances of Wires: The S-Matrix Approach

Quasi-one-dimensional systems with multiple conduction channels are essential for describing a range of physical phenomena. In this paper, we analyse transport in wires where electrons are subject to arbitrary number of strong multi-particle backscattering terms. We present an exact calculation of the system’s scattering matrix and derive a formula for the two-terminal conductance. We find the conductance is reduced from its ideal value by a term corresponding to the projection of current fields onto the subspace of integer-valued vectors characterising the gapped channels created by the perturbations. Applying this result, we establish the minimal model required to reproduce the recently observed, yet unexplained, fractional conductance plateaus with even denominators.