We present a theoretical study of electronic transport in a hybrid junction consisting of an excitonic insulator sandwiched between a normal and a superconducting electrode. The normal region is described as a two-band semimetal and the superconducti
ng lead as a two-band superconductor. In the excitonic insulator region, the coupling between carriers in the two bands leads to an excitonic condensate and a gap $Gamma$ in the quasiparticle spectrum. We identify four different scattering processes at both interfaces. Two types of normal reflection, intra- and inter-band; and two different Andreev reflections, one retro-reflective within the same band and one specular-reflective between the two bands. We calculate the differential conductance of the structure and show the existence of a minimum at voltages of the order of the excitonic gap. Our findings are useful towards the detection of the excitonic condensate and provide a plausible explanation of recent transport experiments on HgTe quantum wells and InAs/GaSb bilayer systems.
The Andreev bound states and charge transport in a Josephson junction between two superconductors with intrinsic exchange fields are studied. We find that for a parallel configuration of the exchange fields in the superconductors the discrete spectru
m consists of two pairs of spin-split states. The Josephson current in this case is mainly carried by bound states. In contrast, for the antiparallel configuration we find that there is no spin-splitting of the bound states and that for phase differences smaller than certain critical value there are no bound states at all. Hence the supercurrent is only carried by states in the continuous part of the spectrum. Our predictions can be tested by performing a tunneling spectroscopy of a weak link between two spin-split superconductors.
