Random-matrix theory of thermal conduction in superconducting quantum dots

J. P. Dahlhaus; B. Béri; C. W. J. Beenakker

doi:10.1103/PhysRevB.82.014536

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Random-matrix theory of thermal conduction in superconducting quantum dots

J. P. Dahlhaus, B. Béri, C. W. J. Beenakker

DOI 10.1103/PhysRevB.82.014536 · Physical Review B

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Abstract

We calculate the probability distribution of the transmission eigenvalues Tn 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 symmetries) give rise to four circular ensembles of scattering matrices. We determine P({Tn}) for each ensemble, characterized by two symmetry indices β and γ. For a single d-fold degenerate transmission channel we thus obtain the distribution P(g)∝g−1+β/2(1−g)γ/2 of the thermal conductance g (in units of dπ2kB2T0/6h at low temperatures T0). We show how this single-channel limit can be reached using a topological insulator or superconductor, without running into the problem of fermion doubling.