Quantum-classical correspondence in the wavefunctions of Andreev billiards

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the limitations of a widely used retracing approximation. We show that the mixed classical dynamics gives rise to a wealth of wavefunction phenomena, including periodic orbit scarring and localization of the wavefunction onto other classical phase space objects such as intermittent regions and quantized tori.