Phase-dependent Andreev spectrum in a diffusive SNS junction: Static and dynamic current response

摘要

A long phase coherent normal (N) wire between superconductors (S) is characterized by a dense phase-dependent Andreev spectrum. We investigate the current response of Andreev states of an NS ring to a time-dependent Aharonov Bohm flux superimposed to a dc one. The ring is modeled with a tight-binding Hamiltonian including a superconducting region with a BCS coupling between electron and hole states, in contact with a normal region with on-site disorder. Both dc and ac currents are determined from the computed eigenstates and energies using a Kubo formula approach. Beside the well-known Josephson current, we identify different contributions to the ac response: a low-frequency one related to the dynamics of the thermal occupations of the Andreev states and a higher-frequency one related to microwave induced transitions between levels. Both are characterized by phase dependencies with a high-harmonic content, opposite to one another. Our findings are successfully compared to the results of recent experiments.