Multiple Andreev reflections as a transport problem in energy space

We study coherent multiple Andreev reflections in quantum SNS junctions of finite length and arbitrary transparency. The presence of superconducting bound states in these junctions gives rise to great enhancement of the subgap current. The effect is most pronounced in low-transparency junctions, $D\ll1$, and in the interval of applied voltage $\Delta/2<eV<\Delta$, where the amplitude of the current structures is proportional to the first power of the junction transparency $D$...

We investigate theoretically charge transport in hybrid multiterminal junctions with superconducting leads kept at different voltages. It is found that multiple Andreev reflections involving several superconducting leads give rise to rich subharmonic gap structures in the current-voltage characteristics. The structures are evidenced numerically in junctions in the incoherent regime.

We investigate the properties of subharmonic gap structure (SGS) in superconducting quantum contacts with normal-electron resonances. We find two distinct new features of the SGS in resonant junctions which distinguish them from non-resonant point contacts: (i) The odd-order structures on the current-voltage characteristics of resonant junctions are strongly enhanced and have pronounced peaks, while the even-order structures are suppressed, in the case of a normal electron re...

We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)-superconductor junctions with low-transparency interfaces. Assuming strong thermalization in the weak link we calculate the current-voltage dependence $I(V)$. At intermediate temperatures, $E_\mathrm{Th}\ll T\ll\Delta$, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferromagnetic junction. We find that t...

We analyze the influence of the structure within a SNS junction on the multiple Andreev resonances in the subgap I-V characteristics. Coherent interference processes and incoherent propagation in the normal region are considered. The detailed geometry of the normal region where the voltage drops in superconducting contacts can lead to observable effects in the conductance at low voltages.

Particle transport across Josephson junctions is commonly described using a simplifying approximation (often called the Andreev approximation), which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections, with no normal reflections, occur at interfaces. While this approximation is appropriate for superconductors with high carrier density (for which the chemical potential vastly exceeds the pairing gap), it breaks down for low-carrier-density su...

The analysis in the present paper is based on the most known concept introduced by the brilliant physicist Alexander Andreev: Andreev bound states in a normal metal sandwiched between two superconductors. The paper presents results of direct calculations of {\em ab initio} expressions for the currents in a long ballistic SNS junction. The expressions are expanded in $1/L$ ($L$ is the thickness of the normal layer). The main contribution $\propto 1/L$ to the current agrees wit...

We have generalized the scattering-matrix theory of multiple Andreev reflections in mesoscopic Josephson junctions to the multi-mode case, and applied it to short superconductor/normal metal/superconductor junctions with diffusive electron transport. Both the dc and ac current-voltage characteristics are analyzed for a wide range of bias voltages $V$. For voltages smaller than the supeconducting gap the dc differential conductance of the junction diverges as $1/\sqrt{V}$.

We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function.

A general formula for the current through a disordered normal--superconducting junction is derived, which is valid at finite temperature and includes the full voltage dependence. The result depends on a multichannel scattering matrix, which describes elastic scattering in the normal region, and accounts for the Andreev scattering at the NS interface. The symmetry of the current with respect to sign reversal in the subgap regime is discussed. The Andreev approximation is used ...