# Distinguishing Majorana Zero Modes from Impurity States through Time-Resolved Transport

## TL;DR

This paper demonstrates that time-resolved charge transport measurements can distinguish Majorana zero modes from impurity states in superconducting nanowires, revealing transient oscillations unique to Majoranas and highlighting the potential for topological quantum computing.

## Contribution

The study introduces a method using time-dependent Landauer-Büttiker theory to differentiate Majorana zero modes from trivial impurity states through transient transport signatures.

## Key findings

- Transient oscillations distinguish Majorana zero modes from impurity states.
- Quasi-Majorana states can produce similar zero-bias peaks as true Majoranas.
- Time-resolved transport provides a practical probe for topological quantum computing.

## Abstract

We study time-resolved charge transport in a superconducting nanowire using time-dependent Landauer-B{\"u}ttiker theory. We find that the steady-state Majorana zero-bias conductance peak emerges transiently accompanied by characteristic oscillations after a bias-voltage quench. These oscillations are absent for a trivial impurity state that otherwise shows a very similar steady-state signal as the Majorana zero mode. In addition, we find that Andreev bound states or quasi-Majorana states in the topologically trivial bulk phase can give rise to a zero-bias conductance peak, also retaining the transient properties of the Majorana zero mode. Our results imply that (1) time-resolved transport may be used as a probe to distinguish between the Majorana zero mode and interfacial impurity states; and (2) the quasi-Majorana states mimic the transient signatures of the topological Majorana zero modes, indicating of the possibility of utilizing also the quasi-Majorana states in topological quantum computing as anyons with non-Abelian braiding statistics.