SciPost Submission Page
Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
by M. S. Shustin, S. V. Aksenov, I. S. Burmistrov
Submission summary
| Authors (as registered SciPost users): | Igor Burmistrov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2508.11242v1 (pdf) |
| Date submitted: | Aug. 18, 2025, 8:56 a.m. |
| Submitted by: | Igor Burmistrov |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The search for conditions supporting degenerate steady states in nonequilibrium topological superconductors is important for advancing dissipative quantum engineering, a field that has attracted significant research attention over the past decade. In this study, we address this problem by investigating topological superconductors hosting unpaired Majorana modes under the influence of environmental dissipative fields. Within the Gorini-Kossakowski-Sudarshan-Lindblad framework and the third quantization formalism, we establish a correspondence between equilibrium Majorana zero modes and non-equilibrium kinetic zero modes. We further derive a simple algebraic relation between the numbers of these excitations expressed in terms of hybridization between the single-particle wavefunctions and linear dissipative fields. Based on these findings, we propose a practical recipes how to stabilize degenerate steady states in topological superconductors through controlled dissipation engineering. To demonstrate their applicability, we implement our general framework in the BDI-class Kitaev chain with long-range hopping and pairing terms -- a system known to host a robust edge-localized Majorana modes.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1) Establishes a novel algebraic relation between equilibrium Majorana zero modes and dissipative kinetic zero modes. 2) Provides a transparent symmetry-based framework via GKSL + third quantization. 3) Demonstrates concepts concretely on a generalized BDI-class Kitaev chain with numerics. 4) Addresses a timely question of dissipative engineering of topological steady states.
Weaknesses
1) Algebraic relation not stated with full rigor; assumptions remain not fully clear. 2) Robustness to realistic perturbations, i.e., interactions, disorder, non-Markovianity insufficiently addressed. 3) Limited comparison to prior no-go theorems and related results.
Report
This is applied to a generalized Kitaev chain (class BDI with long-range couplings), and the authors illustrate how appropriate Lindblad operators can stabilize steady-state degeneracies.
The work is timely and relevant, and the analytic–numerical combination is a strength. The algebraic relation is useful to both theorists and experimentalists interested in dissipative state engineering. However, several aspects require clarification and strengthening before the results can be fully appreciated and trusted.
First, the algebraic counting relation could be stated with greater rigor: its assumptions, scope, and precise conditions of validity should be formulated explicitly (ideally as a theorem with proof in an appendix).
Second, robustness issues are only lightly touched upon. Since realistic systems inevitably involve interactions, disorder, and non-Markovian baths, the authors should analyze or at least discuss stability under such perturbations.
Third, the connection to prior literature, particularly “no-go” results on dissipative topology, should be sharpened: the manuscript must explicitly delineate how the present approach circumvents or complements those limitations.
In summary, this is a promising and novel contribution which could merit publication in SciPost Physics after minor revision. With clearer formulation of the central relation and an expanded discussion of robustness, prior work, and experimental feasibility, the manuscript would reach a greater level of clarity and reliability, which would support publication in SciPost Physics.
Requested changes
1) Formulate the counting relation precisely (theorem-style, with explicit assumptions). 2) Discuss robustness to perturbations (disorder, interactions, non-Markovian effects). 3) Sharpen the discussion of prior no-go results and clearly position the present work.
Recommendation
Ask for minor revision