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arxiv: 2504.08674 · v2 · submitted 2025-04-11 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Time-reversal symmetric topological superconductivity in Machida-Shibata lattices

Ioannis Ioannidis , Ching-Kai Chiu , Thore Posske This is my paper

Pith reviewed 2026-05-22 20:21 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords topological superconductivityMajorana zero modesMachida-Shibata latticestime-reversal symmetryDIII symmetry classsinglet triplet pairingsadatom systemshelical edge modes
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The pith

Hybridizing Machida-Shibata states in lattices produces time-reversal symmetric topological superconductivity in class DIII via competing singlet and triplet pairings.

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

The paper examines how spin-degenerate Andreev bound states known as Machida-Shibata states, engineered in atomic cages of adatoms on superconductors, can be hybridized into lattices. Under the assumption of small on-site electron repulsion, the resulting low-energy theory shows that singlet and triplet superconducting pairings compete to create topologically non-trivial phases protected by time-reversal symmetry. This leads to the prediction that one-dimensional chains support Kramers pairs of Majorana zero modes at their ends, while two-dimensional versions feature helical Majorana edge modes. The repulsion further resolves areas in momentum space where pairings would otherwise vanish. Such systems open routes to control topological superconductivity without magnetic fields in adatom setups.

Core claim

Recent experiments have created special spin-degenerate Andreev bound states in atomic cages of adatoms on superconductors, called Machida-Shibata states. By hybridizing multiple such states into lattices and assuming small on-site electron repulsion, the low-energy theory demonstrates that competing emerging singlet and triplet superconducting pairings drive the formation of topologically non-trivial phases in symmetry class DIII. Consequently, Kramers pairs of Majorana zero modes are predicted at the ends of Machida-Shibata chains, and two-dimensional lattices host helical Majorana edge modes. Extended regions in the Brillouin zone with vanishing superconducting pairings are lifted by the

What carries the argument

Low-energy theory of hybridized Machida-Shibata states in which competing singlet and triplet pairings realize time-reversal symmetric topological superconductivity in symmetry class DIII.

Load-bearing premise

The analysis assumes small on-site electron repulsion to determine the electronic topological properties and to lift regions of vanishing superconducting pairings.

What would settle it

Tunneling spectroscopy on a fabricated one-dimensional chain of adatoms that either detects or fails to detect pairs of zero-bias conductance peaks at the chain ends.

Figures

Figures reproduced from arXiv: 2504.08674 by Ching-Kai Chiu, Ioannis Ioannidis, Thore Posske.

Figure 1
Figure 1. Figure 1: FIG. 1: Setup: Adatom manipulation on the surface of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Flattening of effective couplings in the low-energy theory for one-dimensional chains. (a) Long-range [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Non-trivial topological phases and Majorana Kramers pairs in a one-dimensional chain. The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Localization of edge modes in two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Suppression of singlet superconductivity in the presence of repulsive on-site interactions, U. (a) Free energy [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Topological phase diagram for two-dimensional lattices with periodic boundary conditions. Topological [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

Recent experiments engineered special spin-degenerate Andreev bound states in atomic cages of adatoms on superconductors, the Machida-Shibata states, a promising building block for quantum matter. Here, we investigate the formation of time-reversal symmetric bands by hybridizing multiple such states and analyzing their electronic topological properties assuming small on-site electron repulsion. The low-energy theory shows that competing emerging singlet and triplet superconducting pairings drive the formation of topologically non-trivial phases in symmetry class DIII. We, therefore, predict Kramers pairs of Majorana zero modes appear at the ends of Machida-Shibata chains, while two-dimensional lattices host helical Majorana edge modes. Additionally, we discover extended regions in the Brillouin zone with vanishing superconducting pairings, which are lifted by the repulsive electron interactions. Our findings offer new perspectives for manipulating topological superconductivity and pairings in non-magnetic adatom systems.

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 / 0 minor

Summary. The manuscript investigates hybridizing multiple Machida-Shibata states (spin-degenerate Andreev bound states in atomic cages of adatoms on superconductors) to form time-reversal symmetric bands. Assuming small on-site electron repulsion, the low-energy theory shows competing singlet and triplet superconducting pairings driving topologically non-trivial phases in symmetry class DIII. This leads to predictions of Kramers pairs of Majorana zero modes at the ends of 1D Machida-Shibata chains and helical Majorana edge modes in 2D lattices, with repulsive interactions lifting extended Brillouin-zone regions of vanishing pairings.

Significance. If the low-energy derivation and DIII classification hold under the stated assumptions, the work identifies a new non-magnetic adatom platform for engineering time-reversal symmetric topological superconductivity, with concrete predictions for Majorana modes that could be tested in scanning-tunneling experiments on engineered lattices.

major comments (1)
  1. [Abstract, final paragraph] Abstract (final paragraph) and the low-energy theory section: the central claim that competing singlet/triplet pairings produce class DIII topology with protected Majorana modes rests on the assumption of small on-site electron repulsion both to fix the band structure and to lift gapless regions. No explicit derivation or parameter scan is shown demonstrating that the topological gap and DIII classification remain robust for moderate U; if the repulsion is not small, the vanishing-pairing regions can persist or the effective pairing competition can shift, potentially closing the gap or changing the symmetry class.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and valuable feedback on our manuscript. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract, final paragraph] Abstract (final paragraph) and the low-energy theory section: the central claim that competing singlet/triplet pairings produce class DIII topology with protected Majorana modes rests on the assumption of small on-site electron repulsion both to fix the band structure and to lift gapless regions. No explicit derivation or parameter scan is shown demonstrating that the topological gap and DIII classification remain robust for moderate U; if the repulsion is not small, the vanishing-pairing regions can persist or the effective pairing competition can shift, potentially closing the gap or changing the symmetry class.

    Authors: We agree that our results are based on the assumption of small on-site electron repulsion U, as explicitly stated in the abstract and throughout the low-energy theory section. The derivation of the effective band structure and the competing singlet and triplet pairings is performed in this perturbative limit. We do not present a parameter scan for moderate U, as the manuscript focuses on the small-U regime where the Machida-Shibata states hybridize to form the DIII topological superconductor. For larger U, the band structure may be modified and the gapless regions might not be lifted in the same way, potentially affecting the topology, but this lies outside the scope of the current work. To address the referee's concern, we will revise the manuscript to include an additional sentence in the abstract and a brief discussion in the low-energy theory section clarifying the assumption and the limited scope regarding U. revision: yes

Circularity Check

0 steps flagged

No circularity: low-energy model with explicit assumption

full rationale

The paper derives topological superconductivity in class DIII from a low-energy theory of hybridized Machida-Shibata states, with competing singlet and triplet pairings leading to Kramers Majorana modes. The assumption of small on-site repulsion is stated explicitly in the abstract and used to determine band structure and lift vanishing pairing regions. No quoted step shows a prediction reducing to a fitted parameter by construction, a self-definitional loop, or load-bearing self-citation. The derivation is self-contained against the stated model inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only. The model rests on the low-energy effective theory and the assumption of small on-site repulsion; no free parameters, invented entities, or non-standard axioms are explicitly introduced in the provided text.

axioms (1)
  • standard math Symmetry class DIII classification for time-reversal symmetric topological superconductors
    Invoked in abstract to classify the phases.

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