Crossovers between superconducting symmetry classes

Details Crossovers between superconducting symmetry classes Crossovers between superconducting symmetry classes

2011-06-20

arxiv.org/abs/1106.3863v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages

Scientific paper

We study the average density of states in a small metallic grain coupled to two superconductors with the phase difference $\pi$, in a magnetic field. The spectrum of the low-energy excitations in the grain is described by the random matrix theory whose symmetry depends on the magnetic field strength and coupling to the superconductors. In the limiting cases, a pure superconducting symmetry class is realized. For intermediate magnetic fields or couplings to the superconductors, the system experiences a crossover between different symmetry classes. With the help of the supersymmetric sigma-model we derive the exact expressions for the average density of states in the crossovers between the symmetry classes A-C and CI-C.

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