Random-matrix theory of thermal conduction in superconducting quantum dots

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.