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Phase-sensitive transport at a normal metal-superconductor interface close to a Josephson junction

Phase- and voltage bias-sensitive quasiparticle transport at a double $NIS_1IS_2$ interface is considered. The barriers $I$ range from tunnel to transparent, and the intermediate region $S_1$ has a width comparable to the superconducting coherence length. A phase difference $φ$ is applied to the Josephson junction $S_1IS_2$. The normal and Andreev reflections at the $NIS_1$ interface become $φ$-sensitive, and transport is governed by interferences within the narrow $S_1$ region, both in the normal and anomalous channels. The subgap conductance is separately (energy $E$)- and (phase $φ$)- symmetric. Above the superconducting gap, the conductance is in general not symmetric even if $(E,φ)$ is changed in $(-E,-φ)$, but the symmetry is restored by averaging Fermi oscillations. The Tomasch oscillations are amplified by the phase difference. The subgap conductance exhibits a resonant structure at the energy of the Andreev bound states (ABS) of the $S_1IS_2$ junction, providing a side-spectroscopy of such states. Depending on the relative transparencies of the junctions, the resonance can increase or reduce the conductance, and it can even vanish for $φ=π$, featuring total reflection of quasiparticles at $NS_1$ by the ABS at $S_1S_2$.