Quasiparticle trapping, Andreev level population dynamics, and charge imbalance in superconducting weak links

We present a comprehensive theoretical framework for the Andreev bound state population dynamics in superconducting weak links. Contrary to previous works, our approach takes into account the generated nonequilibrium distribution of the continuum quasiparticle states in a self-consistent way. As application of our theory, we show that the coupling of the superconducting contact to environmental phase fluctuations induces a charge imbalance of the continuum quasiparticle population. This imbalance is due to the breaking of the left-right symmetry in the rates connecting continuum quasiparticles and the Andreev bound state system, and causes a quasiparticle current on top of the Josephson current in a ring geometry. We evaluate the phase dependence of the quasiparticle current for realistic choices of the model parameters. Our theory also allows one to analyze the quantum coherent evolution of the system from an arbitrary initial state.

Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots

We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(varphi), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference varphi. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(varphi=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find the onset behavior I_apropto {rm sgn}(B) in the presence of interactions, suggesting the incipient spontaneous breakdown of time-reversal symmetry. We also provide conditions for realizing spatially separated (but topologically unprotected) Majorana bound states in this system, which have a clear signature in the 2pi-periodic current-phase relation.

Josephson-current induced conformational switching of a molecular quantum dot

We discuss the behavior of a two-level system coupled to a quantum dot contacted by superconducting source/drain electrodes, representing a simple model for the conformational degree of freedom of a molecular dot or a break junction. The Josephson current is shown to induce conformational changes, including a complete reversal. For small bias voltage, periodic conformational motions induced by Landau-Zener transitions between Andreev states are predicted.