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arxiv: 2510.14452 · v2 · submitted 2025-10-16 · ❄️ cond-mat.supr-con

Quasiclassical theory of vortex states in locally non-centrosymmetric superconductors: application to CeRh₂As₂

Akihiro Minamide , Youichi Yanase This is my paper

Pith reviewed 2026-05-18 06:33 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords CeRh2As2vortex stateslocal density of statesquasiclassical theoryodd-parity superconductivityeven-parity superconductivityinversion symmetry breakingvortex core
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The pith

The peak structure of local density of states at vortex cores distinguishes even-parity from odd-parity pairing in bilayer superconductors with locally broken inversion symmetry.

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

The paper develops a quasiclassical theory for vortex states in bilayer models that capture the local inversion symmetry breaking present in CeRh2As2. It finds that a c-axis magnetic field stabilizes an even-parity spin-singlet state at low fields and an odd-parity state with alternating sign between layers at higher fields. Calculation of the local density of states throughout the vortex lattice shows that this change in pairing symmetry produces distinct peak features right at the vortex core. Because local density of states is measurable by scanning tunneling spectroscopy, the result supplies a concrete experimental route to confirm the parity transition observed in the material.

Core claim

In the bilayer superconductor with locally broken inversion symmetry, the quasiclassical Green's functions yield a local density of states whose zero-bias and finite-energy peaks at the vortex center differ systematically between the even-parity and odd-parity order parameters; this difference directly encodes the sign-alternation pattern of the odd-parity state across neighboring layers.

What carries the argument

Quasiclassical Green's function formalism for a bilayer Hamiltonian that includes antisymmetric spin-orbit coupling, solved self-consistently in the vortex lattice for both even- and odd-parity gap functions to extract the local density of states.

If this is right

  • The local density of states peak pattern changes when the order parameter switches from even to odd parity.
  • This change supplies an observable signature for the field-induced parity transition.
  • Scanning tunneling spectroscopy can therefore test the theoretical assignment of the high-field phase.
  • The same quasiclassical framework applies to other bilayer systems that break inversion symmetry locally.

Where Pith is reading between the lines

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

  • Similar vortex-core spectroscopy could be applied to other locally non-centrosymmetric heavy-fermion compounds to look for parity switches.
  • The method may help interpret field-induced phase diagrams in materials where bulk probes give ambiguous parity information.
  • If the LDOS distinction holds, it could motivate targeted STM experiments on CeRh2As2 single crystals under c-axis fields.

Load-bearing premise

The quasiclassical approximation remains valid for the bilayer model with locally broken inversion symmetry across the relevant magnetic-field range, and the vortex lattice is assumed to be stable in both even- and odd-parity phases.

What would settle it

A scanning-tunneling-microscopy map of the local density of states at vortex cores in CeRh2As2 that shows identical peak structures in the low-field and high-field superconducting phases would falsify the claimed distinction between even- and odd-parity pairing.

Figures

Figures reproduced from arXiv: 2510.14452 by Akihiro Minamide, Youichi Yanase.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic figure of the bilayer Rashba model. This [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The magnetic field-dependence of (a) order pa [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The magnetic field-dependence of the vortex core [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The LDOS near the vortex core for the (a) BCS and (b) PDW states. The back and front sides of the figure correspond [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) The characteristic positions [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

CeRh$_{2}$As$_{2}$, a heavy fermion superconductor discovered in 2021, exhibits two distinct superconducting phases under a $c$-axis magnetic field. This unconventional phase diagram has been attributed to the local inversion symmetry breaking at the Ce sites. At low magnetic fields, a conventional even-parity spin-singlet superconducting state is realized, whereas at higher fields, an odd-parity spin-singlet superconducting state, in which the order parameter alternates sign between neighboring Ce layers, becomes stabilized. In this study, we employ a quasiclassical approach to investigate the vortex states of bilayer superconductors with locally broken inversion symmetry. We calculate the local density of states (LDOS) in the vortex lattice state and find that the pairing symmetry of different superconducting states is clearly manifested in the peak structure of LDOS at the vortex core. Since LDOS is experimentally observable, our work provides a pathway for experimental verification of the superconducting parity transition in CeRh$_{2}$As$_{2}$.

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 develops a quasiclassical theory for vortex states in bilayer superconductors with locally broken inversion symmetry, applied to CeRh₂As₂. It solves the Eilenberger equations including local inversion-breaking terms for even-parity and odd-parity spin-singlet states, computes the LDOS in the vortex lattice, and concludes that the peak structure of the LDOS at the vortex core distinguishes the two pairing symmetries, offering an experimentally accessible signature for the field-induced parity transition.

Significance. If the central LDOS results hold, the work supplies a direct, falsifiable prediction for scanning-tunneling spectroscopy on CeRh₂As₂ that could confirm the even-to-odd parity crossover. The calculation extends the standard quasiclassical framework to a bilayer model with local asymmetry and focuses on an observable quantity rather than fitting parameters, which is a clear strength for connecting microscopic theory to experiment in heavy-fermion systems.

major comments (2)
  1. [§2] §2 (model and quasiclassical setup): the validity of the quasiclassical expansion is assumed for the odd-parity state across the high-field regime without quantitative bounds on ħ/p_F ξ or checks for rapid spatial oscillations generated by the bilayer asymmetry terms. Because the reported LDOS peak differences are extracted from the Green's function along semiclassical trajectories, any breakdown of the slow-variation assumption near the core would directly undermine the claim that the peak structure distinguishes the symmetries.
  2. [§4] §4 (LDOS results): the vortex lattice is stated to be stable in both even- and odd-parity phases, yet no supporting calculation or reference to the free-energy comparison is given. If the odd-parity state favors a different lattice structure or becomes unstable at the fields where the LDOS is computed, the extracted core spectra cannot be used to distinguish the pairing symmetries as claimed.
minor comments (2)
  1. [Figure 3] Figure 3 caption: the color scale for LDOS is not labeled with units or normalized to the normal-state value, making quantitative comparison between panels difficult.
  2. [Eq. (3)] Notation: the definition of the local inversion-breaking term Δ_inv appears in the text but is not repeated in the Eilenberger equation (presumably Eq. (3)), which would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

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

read point-by-point responses

  1. Referee: [§2] §2 (model and quasiclassical setup): the validity of the quasiclassical expansion is assumed for the odd-parity state across the high-field regime without quantitative bounds on ħ/p_F ξ or checks for rapid spatial oscillations generated by the bilayer asymmetry terms. Because the reported LDOS peak differences are extracted from the Green's function along semiclassical trajectories, any breakdown of the slow-variation assumption near the core would directly undermine the claim that the peak structure distinguishes the symmetries.

    Authors: We agree that an explicit discussion of the quasiclassical approximation's range of validity would strengthen the presentation. In the revised manuscript we have added a paragraph in §2 supplying an order-of-magnitude estimate of ħ/p_F ξ based on the material parameters appropriate to CeRh₂As₂ and explaining that the rapid oscillations arising from the local inversion-breaking terms occur on the interlayer spacing and average to zero when the Green's functions are integrated along semiclassical trajectories to obtain the LDOS. This addition directly addresses the concern while leaving the central results unchanged. revision: yes

  2. Referee: [§4] §4 (LDOS results): the vortex lattice is stated to be stable in both even- and odd-parity phases, yet no supporting calculation or reference to the free-energy comparison is given. If the odd-parity state favors a different lattice structure or becomes unstable at the fields where the LDOS is computed, the extracted core spectra cannot be used to distinguish the pairing symmetries as claimed.

    Authors: Our calculations are performed for the conventional triangular vortex lattice in both phases, consistent with the c-axis field orientation and the in-plane tetragonal symmetry that remains unchanged across the parity transition. The layer-alternating sign of the odd-parity order parameter does not alter the London screening or the preferred lattice geometry within the present model. We have not performed an explicit free-energy minimization comparing alternative lattice structures. In the revised manuscript we have added a clarifying sentence in §4 together with a reference to prior quasiclassical studies of vortex lattices in bilayer systems, making the assumption explicit without altering the reported LDOS results. revision: partial

Circularity Check

0 steps flagged

Forward quasiclassical LDOS computation from bilayer model shows no circularity

full rationale

The derivation proceeds by solving the standard quasiclassical Eilenberger equations (augmented with local inversion-breaking terms for the bilayer) to obtain the Green's function and thence the LDOS at vortex cores for even- and odd-parity states. This is a direct forward calculation whose output (peak structure differences) is not fitted to data, not defined in terms of itself, and not reduced to a self-citation chain. The abstract and description present the LDOS features as emergent predictions from the microscopic model assumptions rather than tautological restatements of inputs. No load-bearing self-citations, ansatze smuggled via prior work, or fitted parameters renamed as predictions are indicated.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not enumerate free parameters or axioms, but the approach implicitly relies on standard quasiclassical approximations and a bilayer model whose microscopic parameters (hopping, pairing amplitudes, magnetic-field coupling) are not specified here.

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    Relation between the paper passage and the cited Recognition theorem.

    We employ a quasiclassical approach to investigate the vortex states... calculate the local density of states (LDOS) in the vortex lattice state and find that the pairing symmetry... is clearly manifested in the peak structure of LDOS at the vortex core.

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Reference graph

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120 extracted references · 120 canonical work pages · 1 internal anchor

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