We consider a normal-superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times
of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from spliting of Cooper pairs at the interface and demonstrate a significant enhancement of the probability to detect two consecutive electrons in a short time interval. Finally, we discuss the electronic waiting time distribution in the more realistic situation of partial entanglement.
We study the spin and charge accumulation in junctions between a superconductor and a ferromagnet or a normal metal in the presence of a Zeeman magnetic field, when the junction is taken out of equilibrium by applying a voltage bias. We write down th
e most general form for the spin and charge current in such junctions, taking into account all spin-resolved possible tunneling processes. We make use of these forms to calculate the spin accumulation in NS junctions subjected to a DC bias, and to an AC bias, sinusoidal or rectangular. We observe that in the limit of negligeable changes on the superconducting gap, the NS dynamical conductance is insensitive to spin imbalance. Therefore to probe the spin accumulation in the superconductor, one needs to separate the injection and detection point, i. e. the electrical spin detection must be non-local. We address also the effect of the spin accumulation induced in the normal leads by driving a spin current and its effects on the detection of the spin accumulation in the superconductor. Finally, we investigate the out-of-equilibrium spin susceptibility of the SC, and we show that it deviates drastically from its equilibrium value.
We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Greens function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermi
ons. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor.
We study the effect of a finite proximity superconducting (SC) coherence length in SN and SNS junctions consisting of a semiconducting topological insulating wire whose ends are connected to either one or two s-wave superconductors. We find that such
systems behave exactly as SN and SNS junctions made from a single wire for which some regions are sitting on top of superconductors, the size of the topological SC region being determined by the SC coherence length. We also analyze the effect of a non-perfect transmission at the NS interface on the spatial extension of the Majorana fermions. Moreover, we study the effects of continuous phase gradients in both an open and closed (ring) SNS junction. We find that such phase gradients play an important role in the spatial localization of the Majorana fermions.
We study one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two SC finite-size leads. Using the Majorana Polarization order parameter (MP) introduced in Phys.
Rev. Lett. 108, 096802 (2012)(arxiv:1109.5697) we find that the extended Andreev bound states (ABS) of the normal part of the wire acquire a finite MP: for a finite-size SN junction the ABS spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with phase difference $pi$ transform into two zero-energy states carrying two Majorana fermions with the same MP. Given their extended character inside the whole normal link, and not only close to an interface, these Majorana-Andreev states can be directly detected in tunneling spectroscopy experiments.
We study the Josephson effect through a magnetic molecule with anisotropic properties. Performing calculations in the tunneling regime, we show that the exchange coupling between the electron spin on the molecule and the molecular spin can trigger a
transition from the $pi$ state to the 0 state, and we study how the spin anisotropy affects this transition. We show that the behavior of the critical current as a function of an external magnetic field can give access to valuable information about the spin anisotropy of the molecule.
We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branch
ing current and the noise crossed correlations in terms of single and two-particle Greens function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunneling, the antisymmetric case (the two levels have opposite energies with respect to the superconducting chemical potential) optimizes the Crossed Andreev Reflection (CAR) process while the symmetric case (the two levels have the same energies) favors the Elastic Cotunneling (EC) process. Switching on the direct tunneling tends to suppress the CAR process, leading to negative noise crossed correlations over the whole voltage range for large enough direct tunneling.
