# Dynamics of hybrid junctions of Majorana wires

## TL;DR

This study explores the non-equilibrium dynamics of hybrid topological superconductor-normal metal junctions, revealing persistent oscillating currents and their dependence on initial conditions and topological phases.

## Contribution

It provides a detailed numerical analysis of time-evolution in TS-N-TS junctions, uncovering persistent currents and their relation to bound states and topological properties.

## Key findings

- Persistent, oscillating currents occur at zero bias in TS-N-TS junctions.
- Oscillation amplitude and period depend on initial conditions of the N wire.
- Zero-bias current disappears when one wire is normal or near a topological transition.

## 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 being 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 device, we find a persistent, oscillating electrical current at both junctions even when there is no thermal or voltage bias, and the TS wires are identical. 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 a long time 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.