Random-matrix theory of thermal conduction in superconducting quantum dots

TL;DR

This paper derives the probability distribution of transmission eigenvalues for thermal conductance in chaotic superconducting quantum dots across all symmetry classes, revealing how topological insulators or superconductors can achieve single-channel limits.

Contribution

It provides the first comprehensive calculation of transmission eigenvalue distributions for all symmetry classes in superconducting quantum dots, linking topological properties to thermal conductance.

Findings

Derived P({T_n}) for four symmetry classes characterized by nd mma.

Obtained the distribution P(g) for a single degenerate channel, showing its dependence on symmetry indices.

Showed how topological insulators or superconductors can realize single-channel thermal conductance without fermion doubling issues.

Abstract

We calculate the probability distribution of the transmission eigenvalues T_n of Bogoliubov quasiparticles at the Fermi level in an ensemble of chaotic Andreev quantum dots. The four Altland-Zirnbauer symmetry classes (determined by the presence or absence of time-reversal and spin-rotation symmetry) give rise to four circular ensembles of scattering matrices. We determine P({T_n}) for each ensemble, characterized by two symmetry indices \beta and \gamma . For a single d-fold degenerate transmission channel we thus obtain the distribution P(g) ~ g^{-1+\beta /2}(1-g)^{\gamma /2} of the thermal conductance g (in units of d \pi ^2 k_B^2 T_0/6h at low temperatures T_0). We show how this single-channel limit can be reached using a topological insulator or superconductor, without running into the problem of fermion doubling.