Crossovers between superconducting symmetry classes
V. A. Koziy, M. A. Skvortsov
L.D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
Moscow Institute of Physics and Technology, 141700 Moscow, Russia
We study the average density of states in a small metallic grain
coupled to two superconductors with the phase difference π,
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
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
σ-model we derive the exact expressions for the average density
of states in the crossovers between the symmetry classes A-C and CI-C.