Wigner-Poisson Statistics of Topological Transitions in a Josephson Junction

被引：34

作者：

Beenakker, C. W. J. ^{[1
]}

Edge, J. M. ^{[1
]}

Dahlhaus, J. P. ^{[1
]}

Pikulin, D. I. ^{[1
]}

Mi, Shuo ^{[1
]}

Wimmer, M. ^{[1
]}

机构：

[1] Leiden Univ, Inst Lorentz, NL-2300 RA Leiden, Netherlands

来源：

PHYSICAL REVIEW LETTERS | 2013年 / 111卷 / 03期

关键词：

CIRCULAR LAW; REAL MATRICES; SUPERCONDUCTORS; EIGENVALUES; INSULATORS; SYSTEMS;

D O I：

10.1103/PhysRevLett.111.037001

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：5

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