Anomalous Josephson Effect in Topological Insulator-Based Josephson Trijunction

We studied anomalous Josephson effect (AJE) in Josephson trijunctions fabricated on Bi${}_2$Se${}_3$, and found that the AJE in T-shaped trijunctions significantly alters the Majorana phase diagram of the trijunctions, when an in-plane magnetic field is applied parallel to two of the three single junctions. Such a phenomenon in topological insulator-based Josephson trijunction provides unambiguous evidence for the existence of AJE in the system, and might provide an additional knob for controlling the Majorana bound states in the Fu-Kane scheme of topological quantum computation.