Conductance of Disordered Wires with Symplectic Symmetry: Comparison between Odd- and Even-Channel Cases

TL;DR

This paper investigates how the conductance of disordered wires with symplectic symmetry differs between odd- and even-channel cases, revealing the absence of localization in odd-channel wires and faster conductance decay in even-channel wires.

Contribution

The study provides numerical evidence showing the contrasting conductance behaviors in odd- and even-channel disordered wires with symplectic symmetry, supporting existing analytic theories.

Findings

Odd-channel wires maintain high conductance with increasing length.

Even-channel wires exhibit exponential decay of conductance due to localization.

Decay rate of conductance is faster in odd-channel cases.

Abstract

The conductance of disordered wires with symplectic symmetry is studied by numerical simulations on the basis of a tight-binding model on a square lattice consisting of M lattice sites in the transverse direction. If the potential range of scatterers is much larger than the lattice constant, the number N of conducting channels becomes odd (even) when M is odd (even). The average dimensionless conductance g is calculated as a function of system length L. It is shown that when N is odd, the conductance behaves as g --> 1 with increasing L. This indicates the absence of Anderson localization. In the even-channel case, the ordinary localization behavior arises and g decays exponentially with increasing L. It is also shown that the decay of g is much faster in the odd-channel case than in the even-channel case. These numerical results are in qualitative agreement with existing analytic theories.