Andreev Bound States Formation and Quasiparticle Trapping in Quench Dynamics Revealed by Time-Dependent Counting Statistics.

We analyze the quantum quench dynamics in the formation of a phase-biased superconducting nanojunction. We find that in the absence of an external relaxation mechanism and for very general conditions the system gets trapped in a metastable state, corresponding to a nonequilibrium population of the Andreev bound states. The use of the time-dependent full counting statistics analysis allows us to extract information on the asymptotic population of even and odd many-body states, demonstrating that a universal behavior, dependent only on the Andreev state energy, is reached in the quantum point contact limit.

The Andreev states of a superconducting quantum dot: mean field versus exact numerical results.

We analyze the spectral density of a single level quantum dot coupled to superconducting leads focusing on the Andreev states appearing within the superconducting gap. We use two complementary approaches: the numerical renormalization group and the Hartree-Fock approximation. Our results show the existence of up to four bound states within the gap when the ground state is a spin doublet (π phase).

Even-odd effect in Andreev transport through a carbon nanotube quantum dot.

We have measured the current (I)-voltage (V) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance dI/dV due to the Kondo resonance is observed in the normal state, this feature around zero-bias voltage is absent in the superconducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the dI/dV subgap structure caused by Andreev reflection.

Dynamical coulomb blockade of multiple Andreev reflections.

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as n2 with n = Int(2delta/eV), where V is the bias voltage and delta is the superconducting gap, as it would correspond to the occurrence of shots of charge ne. For higher transmission the blockade is reduced because of both the Pauli principle and the elastic renormalization of the MAR probability, and for certain voltage regions it may even become an anti-blockade; i.

Nonequilibrium dynamics of Andreev states in the Kondo regime.

The transport properties of a quantum dot coupled to superconducting leads are analyzed. It is shown that the quasiparticle current in the Kondo regime is determined by the nonequilibrium dynamics of subgap states (Andreev states) under an applied voltage. The current at low bias is suppressed exponentially for decreasing Kondo temperature in agreement with recent experiments.