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

by Moos van Caspel, Sergio Enrique Tapias Arze, Isaac PĂ©rez Castillo

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:

Ontology / Topics

See full Ontology or Topics database.

Lindblad master equations Periodically-driven (Floquet) systems Superconducting nanowires

Author comments upon resubmission

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.


Reports on this Submission

Anonymous Report 1 on 2019-1-29 Invited Report

Strengths

Completeness and clarity

Weaknesses

Free Lindbladian models

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

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