Detecting topological superconductivity with φ0 Josephson junctions

The recent experimental discovery of φ0 Josephson junctions by Szombati et al. [Nat. Phys. 12, 568 (2016)1745-247310.1038/nphys3742], characterized by a finite phase offset in the supercurrent, requires the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we show that a quantum dot φ0 Josephson junction can serve as a qualitative indicator for topological superconductivity: microscopically, we find that the phase shift in a junction of s-wave superconductors is due to the spin-orbit induced mixing of singly occupied states on the quantum dot, while for a topological superconductor junction it is due to singlet-triplet mixing. Because of this important difference, when the spin-orbit vector of the quantum dot and the external Zeeman field are orthogonal, the s-wave superconductors form a π Josephson junction, while the topological superconductors have a finite offset φ0 by which topological superconductivity can be distinguished from conventional superconductivity. Our prediction can be immediately tested in nanowire systems currently used for Majorana fermion experiments and thus offers a realistic approach for detecting topological bound states.