Dynamics of hybrid junctions of Majorana wires

Abstract

We investigate the dynamics of hybrid junctions made of the topological superconductor (TS) and normal metal (N) wires. We consider an X-Y-Z configuration for the junctions where X, Y, Z = TS, N. We assume the wires X and Z are semi-infinite and in thermal equilibrium. We connect the wires X and Z through the short Y wire at some time and numerically study time evolution of the full device. For TS-N-TS devices, we find a persistent, oscillating electrical current at both junctions even in the absence of any phase, voltage, or thermal bias. The amplitude and period of the oscillating current depend on the initial conditions of the middle N wire indicating the absence of thermalization. This zero-bias current vanishes at long times for any of X and Z being an N wire or a TS wire near a topological phase transition. Using properties of different bound states within the superconducting gap, we develop a clear understanding of the oscillating currents.