Effects of Induced Flux on Andreev Levels in a Quantum Point Contact Embedded in Superconducting Ring

We investigate the effects of flux induced by persistent current on the states of Andreev levels in a quantum point contact (QPC) embedded in a superconducting ring. The Andreev levels correspond to the bound states in the QPC created by multiple reflection at the boundaries. We self-consistently calculate the eigenstates and persistent current of such a system with different external fluxes threaded through the ring by using a tight-binding model with Bogoliubov-de Gennes potential. We show that the induced flux can significantly change the dependence of the Andreev levels and the persistent current on the external flux if the inductance of the system is large. By solving the time-dependent Schrödinger equation we obtain the dynamical behaviour of Andreev states in the presence of flux oscillations in the equivalent LC circuit.