Dynamics of Andreev states in a diffusive NS ring
Prof. Hélène Bouchiat, Paris-Sud University, Orsay
A mesoscopic hybrid Normal/ Superconducting (NS) ring is characterized by a dense Andreev spectrum with a flux dependent minigap. We measure the linear response to a high frequency flux, in a wide frequency range, with a multimode superconducting resonator. We find that the current response contains, beside the well known dissipation-less Josephson contribution, a large dissipative component. At high frequency compared to the minigap and low temperature we find that the dissipation is due to transitions above the minigap. In contrast, at lower frequency there is range of temperature for which dissipation is caused predominantly by the relaxation of the Andreev states' population. This dissipative response, related via the fluctuation dissipation theorem to a non intuitive zero frequency thermal noise of supercurrent, is characterized by a phase dependence dominated by its second harmonic, as predicted long ago, but never yet observed before. We also present numerical simulations where 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 harmonics content, opposite to one another. Our findings are successfully compared to the results of experiments.