Josephson junctions between topological and conventional superconductors

Topological superconductors host protected gapless modes at their boundaries. This leads to various robust phenomena when a topological superconductor is contacted to a topologically trivial lead, like the fractional ($4\pi$-periodic) Josephson effect or the zero-bias conductance peak in a tunneling NS-junction. Here we discuss phenomena arising in a Josephson contact between a topological and a trivial superconductor. The Josephson effect in this case has an asymmetric dependence on the order parameters involved, and the critical current is suppressed very strongly in a typical situation, so that the product $I_cR \ll e\Delta$ even in a short contact.