Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

We consider the effect of spin-orbit coupling on the low-energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor) using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: in zero magnetic field, (i) the narrowing of the distribution of the excitation gap and (ii) the appearance of oscillations in the average density of states and, in strong magnetic field, (iii) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.

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