Anomalous Josephson coupling through Majorana fermions in Time-Reversal Invariant Topological Superconductor

From QCLab

Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. These Majorana fermions will come in doublets when there is time-reversal symmetry in the topological superconductor. As long as the time-reversal symmetry is preserved, the two Majorana fermions of the doublet does not combine into one complex fermions as the coupling between them are forbidden. In all physical dimensions, this property leads to an anomalous Josephson coupling between topological and trivial superconductors where a nonzero phase difference is preferred. This non-trivial Josephson coupling lead to a parity dependent SQUID current-phase relation and a Zeeman field tuning of the periodicity in the Fraunhofer diffraction pattern. Therefore the detection of such effects will verify whether a superconductor is topological or not.

  • Ref: S B Chung, J Horowitz, X-L Qi, PRB (2013) 88, 214514