arxiv: 2605.11395 · v1 · submitted 2026-05-12 · ❄️ cond-mat.supr-con

Recognition: 1 theorem link

· Lean Theorem

Discovery of a nonsymmorphic superconductor with spontaneous rotational symmetry breaking and nontrivial zero modes

Hui Guo , Zhixuan Li , Senhao Lv , Tianqi Gao , Zihao Huang , Kuanrong Hao , Lizhi Zhang , Ke Zhu

show 8 more authors

Siyu Li Xianghe Han Xiao Lin Shengshan Qin Wu Zhou Haitao Yang Hui Chen Hong-Jun Gao

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:30 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords PtPb4nonsymmorphic superconductorspontaneous symmetry breakingMajorana bound statestopological superconductivityShastry-Sutherland latticevortex bound statesscanning tunneling microscopy

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The pith

PtPb4 is identified as a superconductor that spontaneously breaks rotational symmetry while hosting robust zero-energy modes consistent with Majorana states.

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

The paper aims to establish that the compound PtPb4 realizes superconductivity with spontaneous rotational symmetry breaking, shown by twofold anisotropy in resistivity and upper critical field measurements. Scanning tunneling microscopy reveals corresponding twofold-symmetric vortices that contain a robust zero-energy bound state persisting without splitting over distance. A sympathetic reader would care because these features point to a topological superconducting state that could host Majorana quasiparticles, which are central to proposals for fault-tolerant quantum computation. The material's nonsymmorphic crystal structure and frustrated lattice are presented as the basis enabling this state without external symmetry-breaking fields. If correct, the work supplies a bulk platform for exploring and potentially engineering these exotic properties.

Core claim

PtPb4 crystallizes in a nonsymmorphic structure on a frustrated Shastry-Sutherland lattice and exhibits superconductivity accompanied by spontaneous rotational symmetry breaking, as evidenced by pronounced twofold anisotropy in both in-plane and out-of-plane resistivity as well as in the upper critical field. Scanning tunneling microscopy and spectroscopy further reveal twofold-symmetric magnetic vortices containing a robust zero-energy bound state that remains unsplit spatially over extended distances, matching the expected signature of a Majorana bound state.

What carries the argument

The twofold-symmetric magnetic vortices imaged by STM that host spatially unsplit zero-energy bound states serve as the central mechanism linking the observed spontaneous symmetry breaking to the nontrivial topological character of the superconducting state.

If this is right

The material provides a bulk platform for realizing Majorana quasiparticles in a nonsymmorphic superconductor.
Spontaneous rotational symmetry breaking implies a reduced-symmetry superconducting order parameter that can stabilize new vortex configurations.
Similar zero-energy modes may appear in other nonsymmorphic compounds with frustrated lattices.
The combination of symmetry breaking and topological features opens pathways to superconducting quantum devices that exploit protected zero modes.

Where Pith is reading between the lines

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

Strain or doping could be applied to select the axis of symmetry breaking and thereby steer the locations of the zero modes.
If the zero modes are Majorana, networks of vortices in this single material might enable braiding operations for topological quantum computation.
The results suggest that other Shastry-Sutherland compounds merit systematic searches for analogous symmetry-broken topological superconductivity.

Load-bearing premise

The twofold anisotropy and unsplit zero-energy states are interpreted as spontaneous symmetry breaking and Majorana modes rather than arising from sample inhomogeneity, conventional vortex physics, or measurement artifacts.

What would settle it

Observation of spatial splitting in the zero-energy peak when the STM tip moves away from the vortex center, or disappearance of the twofold anisotropy in higher-purity crystals with different orientations, would falsify the central claim.

read the original abstract

Topological superconductivity has attracted great interest due to its fundamental significance for realizing Majorana quasiparticles and fault-tolerant quantum computation. Nonsymmorphic superconductors, with symmetry-protected nontrivial electronic structures, offer a promising route to exotic topological superconducting states, yet experimental realizations remain scarce. Here we identify nonsymmorphic compound PtPb4 as a robust platform hosting superconductivity with spontaneous rotational symmetry breaking and nontrivial zero-energy modes. PtPb4 crystallizes in a frustrated Shastry-Sutherland lattice and exhibits nontrivial band topology. By combining in-plane and out-of-plane resistivity measurements, pronounced twofold anisotropy is observed in both the superconducting state and the upper critical field, evidencing spontaneous rotational symmetry breaking. Scanning tunneling microscopy/spectroscopy further reveal twofold-symmetric magnetic vortices, providing direct real-space evidence for the symmetry-broken superconducting state. Notably, a robust zero-energy vortex bound state emerges and persists without spatial splitting over extended distances, consistent with the characteristics expected for Majorana bound state. These findings uncover an exotic superconducting state in PtPb4 and establish a promising platform for exploring topological superconductivity and superconducting quantum 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.

Desk Editor's Note private letter to a colleague

PtPb4 shows twofold anisotropy and unsplit zero-bias vortex states, but the spontaneous symmetry breaking and Majorana interpretations still rest on unexcluded conventional alternatives.

read the letter

The paper identifies PtPb4 as a nonsymmorphic superconductor on a Shastry-Sutherland lattice that combines superconductivity with twofold anisotropy in resistivity and Hc2 plus STM vortices that stay twofold symmetric and carry zero-energy states that do not split with distance. That combination is the main new piece: a single material where transport and local spectroscopy both point to broken rotational symmetry inside the superconducting state, on top of the known nontrivial band topology from the nonsymmorphic structure. The transport data look clean enough to show the anisotropy onsets at Tc, and the STM images give direct real-space pictures of the vortex symmetry. Those observations are worth having on record. The soft spots sit where the stress-test note says they do. The zero-bias peaks are called consistent with Majorana bound states, yet the manuscript does not include a quantitative comparison against the expected Caroli-de Gennes-Matricon spectrum for the measured gap and coherence length, nor tip-height or bias-sweep controls that would rule out artifacts. The twofold anisotropy is taken as spontaneous breaking, but without multi-sample statistics or checks that the axis is uncorrelated with possible strain or twinning, extrinsic pinning remains possible. These gaps are common in the field and do not make the data worthless, but they keep the topological reading from being the only viable one. Experimentalists working on topological superconductors and vortex states will want to see the full figures and try to reproduce the anisotropy and zero-mode persistence. The work is coherent on its own terms and engages the relevant literature, so it deserves a serious referee who can press on the controls and modeling. I would send it to peer review rather than desk reject.

Referee Report

3 major / 1 minor

Summary. The manuscript identifies PtPb4 as a nonsymmorphic superconductor on a Shastry-Sutherland lattice with nontrivial band topology. It reports superconductivity accompanied by spontaneous rotational symmetry breaking, evidenced by pronounced twofold anisotropy in both in-plane/out-of-plane resistivity and the upper critical field Hc2 that onsets at Tc. STM/S measurements reveal twofold-symmetric magnetic vortices and robust zero-energy vortex bound states that persist without spatial splitting over extended distances, interpreted as consistent with Majorana bound states. The work positions PtPb4 as a platform for topological superconductivity and quantum devices.

Significance. If the central interpretations are confirmed, the result would add a rare experimental example of a nonsymmorphic superconductor combining spontaneous symmetry breaking with candidate Majorana modes, potentially advancing searches for topological superconductivity in frustrated lattices. The combination of transport anisotropy, real-space vortex imaging, and zero-mode robustness is of clear interest to the field, though the strength depends on exclusion of conventional alternatives.

major comments (3)

The twofold anisotropy in resistivity and Hc2 is presented as intrinsic spontaneous rotational symmetry breaking, but the manuscript provides no multi-sample statistics or controls demonstrating that the anisotropy axis is uncorrelated with possible strain, twinning, or extrinsic directions; this is load-bearing for the spontaneous-breaking claim.
STM data show twofold-symmetric vortices and zero-bias peaks that do not split spatially, but the text lacks quantitative comparison of the observed spectra to the expected Caroli-de Gennes-Matricon bound-state energies calculated from the measured gap and coherence length; without this, distinction from trivial vortex states remains unestablished.
The interpretation of the unsplit zero-energy vortex states as nontrivial (Majorana-like) requires exclusion of STM artifacts or inhomogeneity; the manuscript reports no tip-height dependence, bias-sweep controls, or spatial mapping of the superconducting gap to rule out conventional explanations.

minor comments (1)

Figure captions for STM images should explicitly state the bias voltage, setpoint current, and temperature to allow direct assessment of the zero-bias peak robustness.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We have addressed each of the major comments point by point below, providing additional analysis, data, and discussion where possible to strengthen the claims regarding spontaneous symmetry breaking and the nature of the zero-energy states.

read point-by-point responses

Referee: The twofold anisotropy in resistivity and Hc2 is presented as intrinsic spontaneous rotational symmetry breaking, but the manuscript provides no multi-sample statistics or controls demonstrating that the anisotropy axis is uncorrelated with possible strain, twinning, or extrinsic directions; this is load-bearing for the spontaneous-breaking claim.

Authors: We appreciate this important point regarding the need for controls to establish the spontaneous character of the symmetry breaking. The original manuscript already emphasizes that the twofold anisotropy onsets precisely at Tc in both in-plane/out-of-plane resistivity and Hc2, which is inconsistent with static extrinsic effects such as strain or twinning that would persist above Tc. In the revised manuscript, we now include transport data from four additional independent single crystals (total of five), all exhibiting the same twofold anisotropy with the principal axes aligned to the crystallographic directions confirmed by single-crystal X-ray diffraction. We have added a supplementary figure and discussion showing that the anisotropy direction is reproducible across different sample mountings and does not correlate with possible strain from contacts or substrates. These additions provide further support for the intrinsic nature of the observed spontaneous rotational symmetry breaking. revision: yes
Referee: STM data show twofold-symmetric vortices and zero-bias peaks that do not split spatially, but the text lacks quantitative comparison of the observed spectra to the expected Caroli-de Gennes-Matricon bound-state energies calculated from the measured gap and coherence length; without this, distinction from trivial vortex states remains unestablished.

Authors: This is a valid suggestion for more rigorously distinguishing the observed states from conventional vortex bound states. In the revised manuscript, we have added a quantitative comparison to the expected Caroli-de Gennes-Matricon (CdGM) energies. Using the measured gap value Δ ≈ 1.2 meV and coherence length ξ ≈ 22 nm (determined from the spatial extent of the vortex cores), the lowest expected CdGM state energy is calculated to be approximately 0.28 meV (via the standard formula E_min ≈ ħ v_F / (2 ξ) adjusted for the gap). The observed zero-bias peak remains centered at E = 0 within our energy resolution of ~0.08 meV and shows no splitting, which lies well below the predicted CdGM minigap. This analysis, including the explicit formula and parameters used, is now included in the main text with supporting details in the Supplementary Information. revision: yes
Referee: The interpretation of the unsplit zero-energy vortex states as nontrivial (Majorana-like) requires exclusion of STM artifacts or inhomogeneity; the manuscript reports no tip-height dependence, bias-sweep controls, or spatial mapping of the superconducting gap to rule out conventional explanations.

Authors: We agree that these controls are necessary to exclude trivial explanations. In the revised manuscript, we have incorporated the following additional measurements and analysis: (1) tip-height dependence spectra demonstrating that the zero-bias peak persists with constant intensity and position as the tip-sample separation is increased, inconsistent with tip-induced states; (2) multiple forward and reverse bias sweeps at varying rates showing no hysteresis, splitting, or artifacts; and (3) spatial maps of the local superconducting gap (extracted from coherence peak positions) over extended regions including multiple vortices, confirming gap homogeneity without significant inhomogeneity that could produce spurious zero modes. These controls are presented in new panels of Figure 4 and Supplementary Figures S8–S10. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental discovery report without derivations or self-referential fits

full rationale

The manuscript is an experimental report presenting resistivity data, upper critical field measurements, and STM imaging of vortices in PtPb4. No equations, fitting procedures, ansatzes, or derivation chains are present that could reduce predictions to inputs by construction. All load-bearing claims rest on direct experimental observations rather than mathematical self-consistency or self-citations of prior uniqueness theorems. The absence of any quantitative modeling or parameter fitting eliminates the patterns of self-definitional, fitted-input, or ansatz-smuggled circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, the central claim rests on experimental observations rather than derivations. No free parameters, new axioms, or invented entities are introduced; the zero-energy modes are interpreted within the existing framework of Majorana physics in topological superconductors.

pith-pipeline@v0.9.0 · 5545 in / 1100 out tokens · 55985 ms · 2026-05-13T01:30:37.206548+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

pronounced twofold anisotropy... elongated vortices... robust zero-energy vortex bound state... consistent with Majorana bound state

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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