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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 2pi phase interval scales as sqrt(N) and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.
We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanish
We study theoretically the electrical current and low-frequency noise for a linear Josephson junction structure on a topological insulator, in which the superconductor forms a closed ring and currents are injected from normal regions inside and outsi
Experiments on planar Josephson junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensi
The ac Josephson effect in a ferromagnetic Josephson junction, which is composed of two superconductors separated by a ferromagnetic metal (FM), is studied by a tunneling Hamiltonian and Greens function method. We obtain two types of superconducting