A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

TL;DR

This paper proves that in time reversal symmetric systems with half-integer spins, the transmission eigenvalues of the scattering matrix come in pairs, based solely on the antisymmetry of the matrix.

Contribution

It provides a general proof of Kramers degeneracy of transmission eigenvalues applicable to systems with any number of modes, emphasizing antisymmetry due to time reversal symmetry.

Findings

Transmission eigenvalues come in pairs in such systems

Proof applies to both even and odd number of modes

Relies on antisymmetry of the scattering matrix

Abstract

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.