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arxiv: 2510.26894 · v2 · submitted 2025-10-30 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Proximity-induced superconductivity and emerging topological phases in altermagnet-based heterostructures

Ohidul Alam , Amartya Pal , Paramita Dutta , Arijit Saha This is my paper

Pith reviewed 2026-05-18 03:14 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords altermagnetproximity-induced superconductivitytopological superconductivityRashba spin-orbit couplingheterostructurestopological phasesedge modes
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0 comments X

The pith

Adding Rashba spin-orbit coupling to altermagnet-superconductor heterostructures induces both weak and strong topological superconducting phases with edge modes.

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

The paper develops a model for a two-dimensional d-wave altermagnet layer placed next to a three-dimensional s-wave superconductor. Integrating out the superconductor produces an effective description of induced pairing in the altermagnet, initially limited to even-parity singlet and triplet components. Inserting a Rashba spin-orbit coupling layer adds the odd-parity triplet pairings needed for topology. Band-structure analysis then shows the system enters weak topological phases marked by a winding number and strong topological phases marked by a Chern number, each supporting localized edge modes. This matters to a reader because it outlines a concrete route to topological superconductivity in a platform that carries no net magnetization.

Core claim

In a d-wave altermagnet proximitized to an s-wave superconductor, the proximity effect first induces even-parity singlet and triplet pairing amplitudes. Introducing Rashba spin-orbit coupling generates odd-parity triplet components. The resulting effective two-dimensional system then realizes both weak topological superconducting phases characterized by a winding number and strong topological superconducting phases characterized by a Chern number, each hosting edge-localized modes.

What carries the argument

Effective Green's function derived from the self-energy after integrating out the superconductor, combined with Rashba spin-orbit coupling to enable odd-parity triplet pairing and computation of winding and Chern numbers.

If this is right

  • Odd-parity triplet pairing amplitudes become accessible in the altermagnet layer once Rashba coupling is present.
  • The heterostructure supports both weak and strong topological phases in the same two-dimensional platform.
  • Edge-localized modes appear whose protection is tied to the winding number or Chern number.
  • The setup functions as a versatile platform for engineering topological superconductivity without net magnetization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Varying the strength of the Rashba coupling or the altermagnet exchange field could map out a phase diagram separating the weak and strong topological regions.
  • Similar proximity setups with other altermagnet symmetries might produce higher-order topological states or Majorana corner modes.
  • Experimental signatures could include quantized conductance plateaus or specific spin-polarized currents along the sample edges.

Load-bearing premise

The effective Hamiltonian and Green's function obtained by integrating out the superconducting degrees of freedom accurately describe the proximity-induced pairing amplitudes and band topology in the altermagnet layer without significant higher-order corrections or unaccounted interface effects.

What would settle it

Transport or tunneling spectroscopy that finds no zero-energy edge states and measures trivial values of both the winding number and Chern number when Rashba strength is increased would show the topological phases do not emerge.

Figures

Figures reproduced from arXiv: 2510.26894 by Amartya Pal, Arijit Saha, Ohidul Alam, Paramita Dutta.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of our heterostructure com [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The total DOS [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. In panels (a) and (b), we display the real and imagi [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Momentum-resolved pairing amplitudes are depicted in the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Numerical ED results for the DOS of the AM layer is [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Panels (a)–(d) demonstrate the frequency depen [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Panels (a)–(c) exhibit the edge spectra employing [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Panel (a) shows the energy-resolved LDOS for MEMs [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Panel (a) shows the winding number [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Singlet component [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

We present a theoretical framework for investigating superconducting proximity effect in altermagnet (AM)-superconductor (SC) heterostructures. In general, AMs, characterized by vanishing net magnetization but spin-split electronic spectra, provide a promising platform for realizing unconventional magnetic phases. We consider a two-dimensional $d$-wave AM proximity coupled to a three dimensional ordinary $s$-wave SC. By integrating out the superconducting degrees of freedom, we derive an effective Hamiltonian that describes the proximity-induced modifications in the AM layer in the form of a self-energy. We then derive an effective Green's function to obtain the proximity-induced pairing amplitudes in the AM layer and classify the induced pairing amplitudes according to their parity, frequency, and spin. We find the presence of even-parity singlet and triplet pairing amplitudes in the AM layer. To achieve the odd-parity triplet components, important to realize topological superconductivity, we introduce a layer of Rashba spin-orbit coupling (RSOC) in the heterostructure. We analyse the band topology of this proximity-induced AM-RSOC layer and demonstrate the emergence of both weak and strong topological superconducting phases with edge-localized modes, characterized by winding number and Chern number. These findings highlight the role of AM-SC hybrid setup as a versatile platform for realizing odd-parity triplet pairings and engineering topological superconductivity in two-dimension.

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

1 major / 2 minor

Summary. The paper develops a theoretical model for proximity-induced superconductivity in a 2D d-wave altermagnet (AM) layer coupled to a 3D s-wave superconductor (SC). By integrating out the SC degrees of freedom, an effective Hamiltonian and Green's function are derived to obtain and classify the induced pairing amplitudes (even-parity singlet and triplet) in the AM layer. Introduction of Rashba spin-orbit coupling (RSOC) is shown to generate odd-parity triplet components, leading to both weak and strong topological superconducting phases characterized by winding number and Chern number, with associated edge-localized modes.

Significance. If the effective model holds, the work provides a route to engineer odd-parity topological superconductivity in altermagnetic systems that lack net magnetization but exhibit spin-split bands. This could be relevant for spintronics and topological quantum computing platforms. The use of standard Green's function techniques and topological invariant calculations is a strength, though the result depends on the accuracy of the proximity approximation.

major comments (1)
  1. [Derivation of effective Hamiltonian and Green's function] The central claim that RSOC enables weak and strong topological SC phases with winding/Chern numbers and edge modes rests on the effective Green's function and self-energy correctly classifying even/odd-parity pairings. The integration of the 3D s-wave SC into the 2D d-wave AM (described in the derivation of the effective Hamiltonian) assumes perturbative tunneling and neglects higher-order interface hybridization, lattice mismatch, or 3D momentum conservation effects. These could renormalize the induced triplet components or shift the topological transition points, undermining the classification and band topology analysis.
minor comments (2)
  1. [Pairing classification] The abstract states that even-parity singlet and triplet pairings are found, but the transition to odd-parity via RSOC would benefit from an explicit statement of which pairing channels are symmetry-allowed before and after RSOC addition.
  2. [Band topology analysis] Clarify whether the topological invariants (winding number, Chern number) are computed for the full effective Hamiltonian including RSOC or for a simplified model; specify the parameter regime (e.g., strength of RSOC relative to AM splitting) where the weak/strong phases appear.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive feedback. We address the major comment on the derivation of the effective Hamiltonian below, providing clarification on our modeling assumptions while agreeing to strengthen the discussion of limitations.

read point-by-point responses

  1. Referee: [Derivation of effective Hamiltonian and Green's function] The central claim that RSOC enables weak and strong topological SC phases with winding/Chern numbers and edge modes rests on the effective Green's function and self-energy correctly classifying even/odd-parity pairings. The integration of the 3D s-wave SC into the 2D d-wave AM (described in the derivation of the effective Hamiltonian) assumes perturbative tunneling and neglects higher-order interface hybridization, lattice mismatch, or 3D momentum conservation effects. These could renormalize the induced triplet components or shift the topological transition points, undermining the classification and band topology analysis.

    Authors: We thank the referee for this important observation. Our derivation follows the standard perturbative tunneling approach commonly used to integrate out the degrees of freedom of a 3D s-wave superconductor in proximity to a 2D layer, yielding an effective self-energy and Green's function. This framework is appropriate for the weak-coupling regime relevant to proximity-induced superconductivity and enables the analytic classification of induced pairing amplitudes by parity, frequency, and spin. We agree that higher-order hybridization, lattice mismatch, and full 3D momentum conservation are neglected and could quantitatively renormalize the induced amplitudes or shift transition points. However, the qualitative emergence of even-parity singlet and triplet components, as well as the odd-parity triplet terms generated by Rashba SOC, arises directly from the symmetry properties of the altermagnet and the interface and remains robust within the model's scope. To address the concern, we will revise the manuscript by adding an explicit discussion of these approximations in the methods and conclusions sections, including their potential impact on topological invariants and a statement that more microscopic treatments could refine the quantitative details. This constitutes a partial revision focused on improved transparency rather than altering the core calculations. revision: partial

Circularity Check

0 steps flagged

No circularity: standard integration and topological analysis from model assumptions

full rationale

The derivation begins from an explicit model Hamiltonian for the 2D d-wave altermagnet coupled to 3D s-wave superconductor, applies the standard technique of integrating out SC degrees of freedom to obtain a self-energy and effective Green's function, classifies the resulting even-parity pairings by parity/frequency/spin, adds an RSOC term to generate odd-parity components, and computes winding/Chern numbers plus edge modes directly from the resulting effective Hamiltonian. None of these steps reduce to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation; each is an independent calculation whose output is falsifiable against the input model. The paper is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard models for altermagnets and proximity effects; no free parameters, invented entities, or ad-hoc axioms are explicitly introduced beyond domain assumptions.

axioms (2)
  • domain assumption Altermagnets are modeled as two-dimensional d-wave systems with spin-split spectra but vanishing net magnetization.
    This is the defining property of altermagnets invoked to set up the heterostructure.
  • domain assumption Integrating out the three-dimensional s-wave superconductor degrees of freedom produces a valid effective self-energy and Green's function for the altermagnet layer.
    This is the standard technique used to derive proximity-induced modifications.

pith-pipeline@v0.9.0 · 5780 in / 1480 out tokens · 42572 ms · 2026-05-18T03:14:06.355345+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Interplay between Superconductivity and Altermagnetism in Disordered Materials and Heterostructures

    cond-mat.supr-con 2025-12 unverdicted novelty 7.0

    Spatial variations of the superconducting order parameter in altermagnets induce magnetization through a new coupling, producing proximity-induced magnetization and 0-pi transitions in Josephson junctions.

  2. Topological superconductivity and superconducting diode effect mediated via unconventional magnet and Ising spin-orbit coupling

    cond-mat.mes-hall 2025-12 unverdicted novelty 6.0

    A 1D model with unconventional magnetism plus Rashba and Ising SOC supports topological superconductivity with four Majorana end modes in both BCS and FFLO channels and yields a field-free SDE with diode efficiency ar...

  3. Competition and coexistence of superconducting symmetries in $p$-wave magnets

    cond-mat.supr-con 2026-05 unverdicted novelty 4.0

    Self-consistent BdG calculations on a p-wave magnet model show magnetic coupling drives transitions from dominant s-wave to mixed p_x-wave and then to equal-spin p_y-wave superconductivity with coexistence and competi...

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