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arxiv: 2508.03364 · v4 · submitted 2025-08-05 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Engineering subgap states in superconductors by the symmetry of altermagnetism

Bo Lu , Phillip Mercebach , Pablo Burset , Keiji Yada , Jorge Cayao , Yukio Tanaka , Yuri Fukaya This is my paper

Pith reviewed 2026-05-19 00:41 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords altermagnetismunconventional superconductivitysubgap statesBogoliubov Fermi surfacezero-bias conductance peakAndreev statesd-wave pairing
0
0 comments X

The pith

Aligning altermagnetism symmetry with unconventional superconductivity creates bulk zero-energy flat bands.

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

The paper investigates how the symmetry contrast between altermagnetic fields and unconventional superconducting pairings controls subgap states. When those symmetries align, bulk zero-energy flat bands form as the Bogoliubov Fermi surface and produce a zero-bias conductance peak. The strength and symmetry of d-wave altermagnets then reshape surface Andreev states from d-wave and chiral d- and p-wave superconductors, yielding distinct curved or flat bands. These states are detectable by tunneling spectroscopy and provide a route to design subgap features in superconducting systems.

Core claim

When the symmetries of altermagnetism and unconventional superconductivity align, bulk zero-energy flat bands emerge as the Bogoliubov Fermi surface, giving rise to a zero-bias conductance peak. The symmetry and strength of d-wave altermagnets strongly affect the surface Andreev states from d-wave and chiral d- and p-wave superconductors, realizing distinct types of subgap states including curved and flat bands that can be detected by tunneling spectroscopy.

What carries the argument

Symmetry contrast between altermagnetic fields and unconventional pairings, used as a symmetry-selective spin-splitting term to engineer subgap states.

If this is right

  • Zero-bias conductance peaks appear specifically in cases of aligned symmetry between altermagnetism and pairing.
  • d-wave altermagnets modify surface Andreev states from d-wave and chiral superconductors in symmetry-dependent ways.
  • Both curved and flat subgap bands can be realized by choosing the symmetry and strength of the altermagnet.
  • Tunneling spectroscopy can detect and distinguish these engineered subgap states.

Where Pith is reading between the lines

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

  • Material stacks could be designed to switch between curved and flat subgap bands by rotating the altermagnet orientation relative to the superconductor.
  • The same symmetry-matching idea might extend to other hybrid systems where spin-splitting terms compete with pairing symmetries.
  • Transport measurements in tunnel junctions with controlled altermagnet thickness would provide a direct test of the flat-band prediction.

Load-bearing premise

The altermagnetic field can be treated as a symmetry-selective spin-splitting term that does not destroy the superconducting pairing or introduce additional scattering channels beyond the stated symmetry contrast.

What would settle it

Observation of no zero-bias conductance peak when symmetries are aligned, or appearance of flat bands even when symmetries misalign, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2508.03364 by Bo Lu, Jorge Cayao, Keiji Yada, Pablo Burset, Phillip Mercebach, Yukio Tanaka, Yuri Fukaya.

Figure 1
Figure 1. Figure 1: FIG. 1. An altermagnet (AM, orange) coupled to a super [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a-d) Conductance for a junction having a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a,b) Conductance for a junction having a chiral [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a-c) Conductance for a junction having a [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a-c) Conductance for a junction having a chiral [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Angle-resolved charge conductance for a junction [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Spin conductance as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

Combining superconducting and magnetic materials is a promising path to generate exotic interface subgap states. In this regard, altermagnetism is particularly interesting because it lifts spin degeneracy while providing tailored anisotropy of spin splittings. Here, we investigate the realization and control of subgap states by using the symmetry contrast between altermagnetic fields and unconventional pairings. When the symmetries of altermagnetism and unconventional superconductivity align, we demonstrate the emergence of bulk zero-energy flat bands as the Bogoliubov Fermi surface, giving rise to a zero-bias conductance peak. The symmetry and strength of $d$-wave altermagnets strongly affect the surface Andreev states from $d$-wave and chiral $d$- and $p$-wave superconductors. As a result, distinct types of subgap states are realized, including curved and flat bands, that can be detected by tunneling spectroscopy. Our results offer a solid route for designing and manipulating subgap states in superconducting systems, which can be useful for functionalizing superconducting devices.

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

2 major / 2 minor

Summary. The manuscript explores engineering subgap states in superconductors via the symmetry properties of altermagnetism. It claims that aligning the symmetries of d-wave altermagnetic spin splitting with unconventional superconducting pairings (d-wave, chiral d-wave, and p-wave) produces bulk zero-energy flat bands that constitute a Bogoliubov Fermi surface and generate a zero-bias conductance peak; the altermagnet also modifies surface Andreev bound states, yielding distinct curved or flat subgap dispersions detectable by tunneling spectroscopy.

Significance. If the central symmetry-based construction holds under realistic conditions, the work supplies a concrete route to design and tune bulk and surface subgap states in hybrid altermagnet-superconductor systems, with potential relevance for zero-bias anomalies and device applications.

major comments (2)
  1. [BdG model and gap equation] The BdG Hamiltonian construction (likely §2 or §3) adds a symmetry-selective altermagnetic term while holding the superconducting order parameter fixed. This leaves open whether a self-consistent gap equation would renormalize the gap amplitude or introduce momentum-dependent corrections that lift the exact zero-energy flat-band degeneracy when symmetries align.
  2. [Numerical results] Numerical diagonalization results for the flat bands and zero-bias peak (results section) are presented without reported error estimates, convergence checks with system size, or explicit ranges of altermagnetic strength relative to the gap; this makes it difficult to judge how robust the exact zero-energy degeneracy is to perturbations.
minor comments (2)
  1. [Introduction and model] Notation for the altermagnetic field components and pairing symmetries could be introduced with a single table or figure early in the text to aid readability.
  2. [Abstract] The abstract states that 'distinct types of subgap states are realized' but does not specify which pairing symmetries produce flat versus curved bands; a brief clarifying sentence would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [BdG model and gap equation] The BdG Hamiltonian construction (likely §2 or §3) adds a symmetry-selective altermagnetic term while holding the superconducting order parameter fixed. This leaves open whether a self-consistent gap equation would renormalize the gap amplitude or introduce momentum-dependent corrections that lift the exact zero-energy flat-band degeneracy when symmetries align.

    Authors: We appreciate this point. Our BdG construction is phenomenological, with the superconducting order parameter held fixed to isolate the consequences of symmetry alignment between the d-wave altermagnetic spin splitting and the pairing symmetry. The exact zero-energy flat bands are enforced by the symmetry matching itself; any uniform renormalization of the gap amplitude preserves the degeneracy, while momentum-dependent corrections arising from self-consistency would have to violate the same symmetry to lift it. We will add a paragraph in the revised manuscript discussing this approximation and explaining why the symmetry-protected flat bands remain robust under moderate self-consistent corrections. revision: partial

  2. Referee: [Numerical results] Numerical diagonalization results for the flat bands and zero-bias peak (results section) are presented without reported error estimates, convergence checks with system size, or explicit ranges of altermagnetic strength relative to the gap; this makes it difficult to judge how robust the exact zero-energy degeneracy is to perturbations.

    Authors: We agree that these details should be included. In the revised manuscript we will report the system sizes employed, explicit checks of convergence with increasing system size, the range of altermagnetic strength J relative to the gap Delta over which the zero-energy degeneracy is observed, and a brief statement on numerical precision of the diagonalization. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies standard BdG symmetry rules to altermagnetic terms without self-referential reduction

full rationale

The paper constructs the Bogoliubov-de Gennes Hamiltonian by adding a symmetry-selective altermagnetic spin-splitting term to standard unconventional superconducting pairings. Zero-energy flat bands emerge when the altermagnetic and pairing symmetries align, which follows directly from diagonalizing the resulting model Hamiltonian under the stated symmetry contrast. No parameters are fitted to data and then relabeled as predictions, no self-citations provide load-bearing uniqueness theorems, and no ansatz is smuggled in via prior work. The central results are therefore self-contained within the explicit Hamiltonian and symmetry arguments presented.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of mean-field superconductivity and a phenomenological altermagnetic term; no new entities are introduced.

axioms (1)
  • domain assumption Altermagnetic field acts as a symmetry-selective spin-splitting term compatible with the superconducting order parameter
    Invoked to produce the flat-band condition when symmetries align.

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Forward citations

Cited by 5 Pith papers

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

  1. Finite temperature pair density wave superconductivity in $d$-wave altermagnets

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    D-wave altermagnets host a robust finite-temperature pair-density-wave superconducting phase driven by momentum-dependent spin splitting.

  2. Spin-polarized Josephson current induced by inhomogeneous altermagnetic interlayers

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    An inhomogeneous altermagnetic interlayer in a Josephson junction induces a net spin-polarized Josephson current at π misorientation of Néel vectors, enhancing the critical current while suppressing 0-π transitions.

  3. Spin-polarized Josephson current induced by inhomogeneous altermagnetic interlayers

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    An inhomogeneous altermagnetic interlayer in a Josephson junction produces enhanced critical current and spin-polarized supercurrent at π misorientation of Néel vectors through cancellation of pair-breaking oscillations.

  4. Perfect spin nonreciprocity in gated superconducting altermagnetic heterostructures

    cond-mat.supr-con 2026-04 unverdicted novelty 5.0

    Gating a finite normal region between a superconducting altermagnet and a metallic reservoir produces perfect nonreciprocal spin and charge currents with tunable polarity via gate voltage and region length.

  5. 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...

Reference graph

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