Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry

TL;DR

This paper uses a random-matrix approach to analyze electron transport in disordered wires with symplectic symmetry, revealing even-odd differences in conductance behavior, especially in long-wire regimes, due to perfectly conducting channels.

Contribution

It derives the DMPK equation for both even and odd channel cases, highlighting the distinct conductance decay behaviors caused by symplectic symmetry and perfectly conducting channels.

Findings

Weak-antilocalization correction is similar for even and odd channels in short wires.

Variance of conductance is independent of even or odd number of channels.

In long wires, even channels decay to zero conductance, while odd channels remain perfectly conducting.

Abstract

The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been believed that Anderson localization inevitably arises in ordinary disordered wires. A counterexample is recently found in the systems with symplectic symmetry, where one perfectly conducting channel is present even in the long-wire limit when the number of conducting channels is odd. This indicates that the odd-channel case is essentially different from the ordinary even-channel case. To study such differences, we derive the DMPK equation for transmission eigenvalues for both the even- and odd- channel cases. The behavior of dimensionless conductance is investigated on the basis of the resulting equation. In the short-wire regime, we find that the weak-antilocalization correction to the conductance in the odd-channel case is equivalent to that in the even-channel case. We also find that the variance does not depend on whether the number of channels is even or odd. In the long-wire regime, it is shown that the dimensionless conductance in the even-channel case decays exponentially as <g_even> --> 0 with increasing system length, while <g_odd> --> 1 in the odd-channel case. We evaluate the decay length for the even- and odd-channel cases and find a clear even-odd difference. These results indicate that the perfectly conducting channel induces clear even-odd differences in the long-wire regime.