Wigner-Poisson statistics of topological transitions in a Josephson junction

Abstract

The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level, if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topological transitions in an N-mode quantum-dot Josephson junction, by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topological transitions in a 2pi phase interval scales as sqrt(N) and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.

12 pages, 15 figures; v2 to appear in PRL, with appendix in the supplementary material

References in corpus (6)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
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• Revealing topological superconductivity in extended quantum spin Hall Josephson junctions
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• Low-temperature environments for quantum computation and quantum simulation
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
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• Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix
• Zero-dimensional topologically nontrivial state in a superconducting quantum dot
• Higher-order topological superconductors characterized by Fermi level crossings
• Pseudo-symmetric random matrices: semi-Poisson and sub-Wigner statistics
• Full tomography of topological Andreev bands in graphene Josephson junctions
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