Multiple Andreev reflections as a transport problem in energy space

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the th...

We derive the full counting statistics of charge transfer through a voltage biased superconducting junction. We find that for measurement times much longer than the inverse Josephson frequency, the counting statistics describes a correlated transfer of quanta of multiple electron charges, each quantum associated with the transfer of a single quasiparticle. An expression for the the counting statistics in terms of the quasiparticle scattering amplitudes is derived.

We develop a new theoretical approach for modelling a wide range of semiconductor-superconductor structures with arbitrary potential barriers and a spatially-dependent superconducting order parameter. We demonstrate asymmetry in the conductance spectrum as a result of a Schottky barrier shape. We further show that Andreev reflection process can be significantly enhanced through resonant tunneling with appropriate barrier configuration, which can incorporate the Schottky barri...

Despite several theoretical approaches describing multiple Andreev reflections (MAR) effect in superconductor-normal metal-superconductor (SNS) junction are elaborated, the problem of comprehensive and adequate description of MAR is highly actual. In particular, a broadening parameter $\Gamma$ is still unaccounted at all, whereas a ballistic condition (the mean free path for inelastic scattering $l$ to the barrier width $d$ ratio) is considered only in the framework of K\"{u}...

We theoretically study coherent multiple Andreev reflections in a biased three-terminal Josephson junction. We demonstrate that the direct current flowing through the junction consists of supercurrent components when the bias voltages are commensurate. This dissipationless current depends on the phase in the superconducting leads and stems from the Cooper pair transfer processes induced by non-local Andreev reflections of the quasiparticles originating from the superconductin...

We study the spectrum of Andreev bound states and Josephson currents across a junction of $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries and develop a scattering matrix based formalism which allows us to address transport across such junctions. For $N \ge 3$, it is well known that Berry curvature terms contribute to the Josephson currents; we chart out situations where such terms can have relatively large effects. For a system of three $s$- or th...

A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal metal-superconductor (SNS) interferometers. We consider a Y-shape normal electron beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phase. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, $I(V,\phi)$. MAR in interferometers incorporates...

The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get an insight into formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.

We present a consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogoliubov-de Gennes quantum mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage biased junctions are considered. Elastic quasiparticle scattering by the junction determines equilibrium Josephson current. We discuss the origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport. In contrast,...

We report new measurements on sup-gap energy structure originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high transparency superconducting contacts of Al deposited on highly diffusive and surface d-doped n++-GaAs. For samples with a normal GaAs region of active length 0.3um the Josephson effect with a maximal supercurrent Ic=3mA at T=237mK was observed. The sub-gap structure was observed as a ser...