Journal
PHYSICAL REVIEW LETTERS
Volume 111, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.111.037001
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Funding
- Dutch Science Foundation NWO/FOM
- ERC Advanced Investigator Grant
- EU network NanoCTM
- China Scholarship Council
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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 2 pi phase interval scales as root N, and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.
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