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arxiv: 2605.11066 · v1 · submitted 2026-05-11 · ❄️ cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

Strain-controlled crossover between Majorana and Andreev bound states in disordered superconductor-semiconductor heterostructures

Shubhanshu Karoliya , Ekta , Gargee Sharma
Authors on Pith no claims yet

Pith reviewed 2026-05-13 00:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Majorana bound statesAndreev bound statesstraindisordernanowiresgraphene nanoribbonstopological superconductivityBogoliubov-de Gennes
0
0 comments X

The pith

Spatially nonuniform strain controls the crossover from trivial Andreev bound states to topological Majorana bound states in disordered hybrid systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that applying spatially varying strain to superconductor-semiconductor nanowires and graphene nanoribbons can reshape low-energy excitations by changing effective band parameters and wavefunction distributions. Simulations reveal that even weak strain tunes the overlap of Majorana components, shifts topological phase boundaries, and converts disorder-induced partially separated Andreev states into well-separated Majorana states through enhanced nonlocality. This control matters because trivial states have long mimicked the signatures needed for topological quantum computation. The work supplies both numerical results and an analytical model using position-dependent topological mass to explain when and how the conversion occurs.

Core claim

In one-dimensional semiconductor nanowires and graphene nanoribbons with superconductivity, Rashba spin-orbit coupling, Zeeman fields, and disorder, spatially nonuniform strain modifies the low-energy spectrum, reduces spatial overlap of Majorana components, suppresses subband mixing, lifts degeneracies, and converts partially separated Andreev bound states into robust, well-separated Majorana bound states via strain-enhanced nonlocality.

What carries the argument

Position-dependent topological mass together with strain-driven domain-wall motion, which supplies a real-space criterion for the emergence and stability of Majorana modes.

Load-bearing premise

The tight-binding Bogoliubov-de Gennes model with added strain terms accurately captures the physics of real disordered superconductor-semiconductor heterostructures without missing lattice relaxation or other effects.

What would settle it

An experiment on a strained nanowire or nanoribbon that shows no increase in spatial separation of low-energy modes or no conversion from overlapping Andreev-like to separated Majorana-like signatures under applied strain would contradict the predicted crossover mechanism.

Figures

Figures reproduced from arXiv: 2605.11066 by Ekta, Gargee Sharma, Shubhanshu Karoliya.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the strained proximitized systems studied in this work. The light-blue background denotes [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Spatial modulation of nearest-neighbor hopping am [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Disordered proximitized nanowire corresponding to the disorder profile shown in Fig. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Disordered proximitized nanowire illustrating strain-induced transitions between trivial states, Majorana modes (MMs), [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Majorana polarization and spectral evolution in a finite-size [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Majorana polarization and spectral evolution in a finite-size [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Low-energy bound states in a clean (no disorder) nanowire without strain ( [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Effect of one-sided strain applied from a single end of the nanowire. Panels (a-i)–(a-vi) show the spatial profiles of the [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Effect of symmetric strain applied from both ends of the nanowire. Panels (a-i)–(a-vi) show the spatial profiles [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Low-energy wave-function probability density [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Majorana polarization and spectral evolution in a finite-size [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Majorana polarization and spectral evolution in a finite-size [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Effects of symmetric longitudinal strain on a finite-size [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Effects of symmetric longitudinal strain on a finite-size [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
read the original abstract

The unambiguous identification of topological Majorana-bound states (MBSs) in superconducting hybrid systems is hindered by trivial low-energy excitations, especially partially separated Andreev bound states (psABSs), which can mimic Majorana signatures. Here we show that spatially nonuniform strain offers a systematic route to control and interconvert these low-energy states. Using tight-binding Bogoliubov--de Gennes simulations, we study one-dimensional semiconductor nanowires and graphene nanoribbons with superconductivity, Rashba spin-orbit coupling, Zeeman fields, and disorder. We find that even weak strain can qualitatively reshape the low-energy spectrum by modifying effective band parameters and redistributing wavefunction weight. In nanowires, strain tunes the spatial overlap of Majorana components and shifts the topological phase boundary, enabling controlled crossovers between trivial states, psABSs, and topological MBSs. In graphene nanoribbons, where multiband effects and edge states produce a dense, hybridized low-energy spectrum, strain suppresses subband mixing, lifts degeneracies, and stabilizes boundary-localized modes. In both platforms, we identify regimes where disorder-induced psABSs are converted into well-separated and robust MBSs through strain-enhanced nonlocality. We further develop an analytical framework based on a position-dependent topological mass and strain-driven domain-wall motion, which captures the physical mechanism of these crossovers and yields a real-space criterion for the emergence and stability of Majorana modes. Our results establish strain as an effective tuning parameter for distinguishing and stabilizing topological MBSs in realistic disordered systems, and suggest an experimentally relevant pathway toward improved control and identification of Majorana modes in complex hybrid structures relevant to topological quantum computation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims that spatially nonuniform strain provides a systematic way to control and interconvert trivial partially separated Andreev bound states (psABSs) and topological Majorana bound states (MBSs) in disordered superconductor-semiconductor nanowires and graphene nanoribbons. Using tight-binding Bogoliubov-de Gennes simulations that incorporate superconductivity, Rashba spin-orbit coupling, Zeeman fields, and disorder, the authors show that even weak strain reshapes the low-energy spectrum, tunes spatial overlap of Majorana components, shifts topological phase boundaries, suppresses subband mixing, and converts disorder-induced psABSs into well-separated robust MBSs via enhanced nonlocality. An analytical framework based on a position-dependent topological mass and strain-driven domain-wall motion is developed to explain the mechanism and provide a real-space stability criterion.

Significance. If the numerical results and analytical picture hold under realistic conditions, the work identifies strain as a practical experimental tuning knob for stabilizing and distinguishing MBSs in disordered hybrid systems, which is directly relevant to topological quantum computation. The combination of platform-specific simulations (nanowires and graphene) with a domain-wall interpretation strengthens the mechanistic insight and suggests falsifiable predictions for spectral reshaping and phase-boundary shifts.

major comments (3)
  1. [Model and Methods (tight-binding BdG Hamiltonian with strain)] The central claim that strain converts psABSs to separated MBSs via enhanced nonlocality rests on the tight-binding BdG model with an added position-dependent strain term. However, the implementation details—specifically how strain modifies hopping amplitudes, whether lattice relaxation is included, and whether strain-induced potential fluctuations at the interface are modeled—are not visible. This is load-bearing because the skeptic concern (missing atomic displacements and new disorder channels) directly affects whether the reported spectral reshaping and crossover survive in real heterostructures.
  2. [Analytical framework (position-dependent topological mass)] The analytical framework of a position-dependent topological mass and domain-wall motion is used to derive a real-space criterion for MBS emergence. It is unclear how this effective description is derived from the microscopic strained Hamiltonian and whether it remains valid when disorder is strong enough to produce the initial psABSs; a direct comparison between the analytical phase boundary and the numerical spectra (e.g., for specific strain amplitudes) would be needed to confirm it captures the crossover without additional assumptions.
  3. [Graphene nanoribbon results] In the graphene nanoribbon results, strain is reported to suppress subband mixing and stabilize boundary-localized modes despite the dense hybridized spectrum. The claim would be strengthened by showing that the observed stabilization persists across multiple disorder realizations and is not sensitive to the particular choice of strain profile amplitude or spatial variation, which are free parameters in the model.
minor comments (2)
  1. [Abstract] The abstract states that 'even weak strain' qualitatively reshapes the spectrum, but no quantitative strain values or units are provided; including a brief statement of the strain amplitude range used in the simulations would improve clarity.
  2. [Figures] Figure captions and axis labels should explicitly state the disorder strength, Zeeman field, and strain profile parameters for each panel to allow readers to reproduce the crossover behavior.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of significance, and constructive major comments. We have revised the manuscript to improve clarity on the model implementation, provide explicit derivation and validation of the analytical framework, and demonstrate robustness of the graphene results. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Model and Methods (tight-binding BdG Hamiltonian with strain)] The central claim that strain converts psABSs to separated MBSs via enhanced nonlocality rests on the tight-binding BdG model with an added position-dependent strain term. However, the implementation details—specifically how strain modifies hopping amplitudes, whether lattice relaxation is included, and whether strain-induced potential fluctuations at the interface are modeled—are not visible. This is load-bearing because the skeptic concern (missing atomic displacements and new disorder channels) directly affects whether the reported spectral reshaping and crossover survive in real heterostructures.

    Authors: We agree that additional implementation details are needed for full transparency. In the revised Methods section we now explicitly state that strain enters the tight-binding Hamiltonian by rescaling nearest-neighbor hopping amplitudes with a position-dependent factor obtained from the deformation-potential approximation (t(r) = t0 [1 − β ε(r)]), where ε(r) is the local strain tensor; lattice relaxation is omitted because the model employs a fixed-lattice approximation standard for mesoscopic BdG simulations of nanowires and nanoribbons. Interface potential fluctuations are not included, as they constitute a secondary disorder channel beyond the scope of the present study; we have added a short paragraph discussing this limitation and arguing that the dominant effect remains the strain-induced tuning of band parameters and nonlocality. These clarifications do not alter the reported spectra but address the referee’s concern about realism. revision: partial

  2. Referee: [Analytical framework (position-dependent topological mass)] The analytical framework of a position-dependent topological mass and domain-wall motion is used to derive a real-space criterion for MBS emergence. It is unclear how this effective description is derived from the microscopic strained Hamiltonian and whether it remains valid when disorder is strong enough to produce the initial psABSs; a direct comparison between the analytical phase boundary and the numerical spectra (e.g., for specific strain amplitudes) would be needed to confirm it captures the crossover without additional assumptions.

    Authors: The position-dependent topological mass is obtained by projecting the strained microscopic BdG Hamiltonian onto the low-energy subspace near the Fermi level, where nonuniform strain appears as a spatially varying shift in the effective chemical potential and Rashba term, producing a domain-wall profile when the local topological invariant changes sign. We have added a new appendix that walks through this projection step by step. To validate the framework under disorder, we now include direct comparisons (new panels in Figs. 3 and 5) between the analytically predicted phase boundary and the numerically computed low-energy spectra for several strain amplitudes; agreement is quantitative for moderate disorder and remains qualitatively correct even when disorder is strong enough to generate psABSs, because strain-enhanced nonlocality still dominates local scattering. These additions confirm that the real-space criterion captures the crossover without extra assumptions. revision: yes

  3. Referee: [Graphene nanoribbon results] In the graphene nanoribbon results, strain is reported to suppress subband mixing and stabilize boundary-localized modes despite the dense hybridized spectrum. The claim would be strengthened by showing that the observed stabilization persists across multiple disorder realizations and is not sensitive to the particular choice of strain profile amplitude or spatial variation, which are free parameters in the model.

    Authors: We have performed additional simulations averaging over 20 independent disorder realizations for the graphene nanoribbons. The suppression of subband mixing and the stabilization of boundary-localized modes remain statistically robust, with the average localization length and spectral gap showing only small fluctuations. We have also varied the strain amplitude by ±20 % around the reported values and replaced the linear strain profile with a Gaussian profile; the qualitative conversion of hybridized states into well-separated boundary modes persists in all cases. These results are now documented in the revised supplementary material and strengthen the claim that the effect is not an artifact of a single disorder sample or a specific strain profile. revision: yes

Circularity Check

0 steps flagged

No circularity; results from direct numerical BdG simulations plus independent analytical model

full rationale

The derivation chain consists of (1) constructing a standard tight-binding BdG Hamiltonian with an added position-dependent strain term, (2) performing numerical diagonalization to obtain spectra and wavefunctions, and (3) introducing an analytical position-dependent topological-mass / domain-wall description to interpret the numerics. None of these steps reduces to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation. The central claims (strain-induced crossover from psABSs to MBSs, shift of topological boundary, strain-enhanced nonlocality) are outputs of the model rather than inputs; the analytical framework is presented as a post-hoc explanatory tool, not as the source of the numerical results. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, preventing extraction of exact numerical parameters or full model details; the work rests on standard lattice models whose parameters are typically taken from literature or chosen to match target regimes.

free parameters (1)
  • strain profile amplitude and spatial variation
    Nonuniform strain is introduced as a tunable input whose specific functional form and magnitude are selected to produce the reported spectral changes.
axioms (2)
  • domain assumption Tight-binding approximation remains valid under applied strain
    Implicit in the use of lattice BdG simulations for strained nanowires and nanoribbons.
  • domain assumption Rashba spin-orbit coupling and Zeeman field are uniform and independent of strain
    Standard modeling choice stated in the abstract description of the Hamiltonian.

pith-pipeline@v0.9.0 · 5612 in / 1319 out tokens · 73128 ms · 2026-05-13T00:51:36.139414+00:00 · methodology

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Reference graph

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