# Dynamical signatures of topological order in the driven-dissipative Kitaev chain

### Submission summary

 As Contributors: Sergio Enrique Tapias Arze · Moos van Caspel Arxiv Link: https://arxiv.org/abs/1812.02126v2 Date accepted: 2019-02-04 Date submitted: 2019-01-28 Submitted by: van Caspel, Moos Submitted to: SciPost Physics Domain(s): Theoretical Subject area: Condensed Matter Physics - Theory

### Abstract

We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator $\hat{\mathcal{L}}$ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -- localized eigenmodes of $\hat{\mathcal{L}}$. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.

###### Current status:
Publication decision taken: accept

We would like to thank both referees for their comments. In the present revised version of the manuscript we have tried to accommodate their comments as best as we could.

### List of changes

- We have retracted the final sentence of the abstract.
- We have added a sentence just before the last paragraph of section 3.1, explaining why we focus on only one of the rapidity bands.
- We have added several lines to the conclusion of our paper, in order to more clearly relate our definitions and our results to the existing literature.
- We have added multiple references at the start of section 3, as kindly suggested by the referees.
- At the start of section 4.3, we have changed the chemical potential of the time-averaged Hamiltonian, relaxing the assumption that $t_1 = t_2$.
- We have amended various typographical errors.

### Submission & Refereeing History

Resubmission 1812.02126v2 (28 January 2019)
Submission 1812.02126v1 (6 December 2018)

## Invited Reports on this Submission

Toggle invited reports view

### Strengths

Completeness and clarity

### Report

After reading the second version of the manuscript, we recommend the publication of the article

• validity: good
• significance: good
• originality: good
• clarity: good
• formatting: good
• grammar: good