Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Phys Rev Lett. 2013 Jul 19;111(3):037001. doi: 10.1103/PhysRevLett.111.037001. Epub 2013 Jul 17.
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 2π phase interval scales as √[N], and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.
约瑟夫森结的位相相关束缚态（安德烈夫能级）如果超导基态在偶数和奇数费米子宇称之间发生转变，就可能在费米能级处交叉。在没有时间反演和自旋旋转对称的情况下，这种能级交叉是拓扑保护的，无论超导本身是否具有拓扑平庸性。我们通过将安德烈夫能级交叉与随机非厄米矩阵的实特征值相关联，发展了一种 N 模式量子点约瑟夫森结中这些拓扑转变的统计理论。在 2π 相位间隔内的拓扑转变数量按 N 的平方根缩放，它们的间隔分布是随机矩阵理论的威格纳和泊松分布的混合。
