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arxiv: 1907.09925 · v1 · pith:VFBP3ZUJnew · submitted 2019-07-23 · ❄️ cond-mat.supr-con

Topological pairings in Janus monolayer TaSSe

W. P. Chen This is my paper

Pith reviewed 2026-05-24 16:57 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords topological superconductorJanus monolayerTaSSeRashba effectpairing symmetryChern numberZ2 invariantTMD
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The pith

H-TaSSe Janus monolayer realizes a time-reversal invariant topological superconductor with Z2=1 via s+f+p pairing.

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

This paper solves the linearized gap equation for the superconducting state in Janus monolayer H-TaSSe to determine its pairing symmetry. The strong Rashba spin splitting from broken mirror symmetry leads to mixed pairing states that are topologically nontrivial. At chemical potentials above -0.08 eV the favored state is a full-gap s+f+p-wave mixture that is time-reversal invariant with Z2 topological index equal to 1. Below that value a time-reversal breaking d+p+f pairing from the E representation can appear and support a Chern number as large as -6. The findings indicate that this material is a candidate platform for helical or chiral topological superconductivity unlike its symmetric parent monolayers.

Core claim

At the chemical potential μ > -0.08 eV, a time-reversal invariant s+f+p-wave mixed pairing state is obtained that is full-gap and topologically nontrivial with Z2=1. At lower chemical potential, a time-reversal broken d+p+f pairing belonging to the two-dimensional irreducible representation E appears and can host a large Chern number C=-6 at appropriate pairing strengths.

What carries the argument

The linearized gap equation at the critical temperature Tc, which determines the pairing symmetry influenced by the Rashba effect from out-of-plane mirror symmetry breaking.

If this is right

  • The pairing symmetry changes with chemical potential, allowing tuning between helical and chiral topological phases.
  • The topological invariants imply the existence of protected boundary states in the superconducting phase.
  • The Janus structure introduces differences in pairing compared to H-TaS2 and H-TaSe2.
  • Appropriate pairing strengths enable large Chern numbers in the broken time-reversal case.

Where Pith is reading between the lines

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

  • Gate voltage could be used to switch between different topological superconducting regimes in this material.
  • Similar Janus TMDs may exhibit comparable topological pairings due to the common Rashba mechanism.
  • Experimental probes of the gap symmetry or thermal Hall conductivity could test the Chern number prediction.

Load-bearing premise

The single-particle band structure, Fermi surface details, and electron-electron interaction parameters of H-TaSSe are taken to be sufficiently accurate that the linearized gap equation produces the stated pairing symmetries and topological numbers.

What would settle it

Direct observation of a full superconducting gap with no nodes together with signatures of helical edge states at chemical potentials above -0.08 eV, or a Chern number of -6 via thermal Hall measurements at lower potentials, would test the predictions.

Figures

Figures reproduced from arXiv: 1907.09925 by W. P. Chen.

Figure 1
Figure 1. Figure 1: FIG. 1: . (a) Crystal structure of monolayer H-TaSSe, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: . Dispersions of the gap function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: . The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: . Energy spectra of the topological (a)TRI [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

The Janus monolayer transition metal dichalcogenides[TMDs] MXY[M=Mo,W, etc. and X,Y=S,Se, etc.] has been synthesized recently, and the Rashba spin splitting arises in it owing to the breaking of out-of-plane mirror symmetry[\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.235404}{Phys. Rev. B 97, 235404 (2018)}]. Here we study the pairing symmetry of superconducting Janus monolayer H-TaSSe by solving the linearized gap equation at the critical temperature $T_c$. We find that the strong Rashba effect in H-TaSSe could produce topological superconducting states which differs from that in its parent monolayer H-TaS$_2$ and H-TaSe$_2$. More specifically, at the chemical potential $\mu>-0.08$eV, we obtain a time-reversal invariant s+f+p-wave mixed pairing state. This pairing state is full-gap and topologically nontrivial, i.e. $\mathbb{Z}_2=1$. However, a time-reversal broken d+p+f pairing belonging to the 2-dimensional irreducible representation $E$ appears at lower chemical potential. It can host a large Chern number $C=-6$ at appropriate pairing strengths. The results suggest the monolayer H-TaSSe to be a candidate helical or chiral topological superconductor.

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 / 0 minor

Summary. The paper claims that solving the linearized gap equation for superconducting Janus monolayer H-TaSSe yields a time-reversal invariant s+f+p-wave mixed pairing state that is full-gap and topologically nontrivial (Z2=1) for μ > -0.08 eV, while at lower chemical potential a time-reversal broken d+p+f pairing in the two-dimensional E irreducible representation appears and can host Chern number C=-6 at appropriate pairing strengths, making the material a candidate for helical or chiral topological superconductivity distinct from its parent compounds due to the Rashba effect.

Significance. If the underlying band structure and interaction model are accurate and the numerical solution is reproducible, the work would identify a new Janus TMD platform for topological superconductivity with tunable pairing symmetries and invariants, extending the known candidates beyond the parent H-TaS2 and H-TaSe2 monolayers.

major comments (2)
  1. [Abstract] Abstract: the claim that the gap equation was solved to obtain the reported pairing symmetries and topological numbers supplies no information on the single-particle Hamiltonian, the form or strength of the interaction kernel V(k,k'), the numerical cutoff, Brillouin-zone discretization, or convergence checks, preventing any assessment of whether the central claims are supported by the calculation.
  2. [Abstract] Abstract: the chemical potential threshold μ = -0.08 eV and the pairing interaction amplitudes are scanned or selected to produce the stated Z2=1 and C=-6 values; the topological invariants are therefore outputs of these adjustable parameters rather than predictions derived from first-principles inputs whose accuracy is independently validated in the manuscript.

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: [Abstract] Abstract: the claim that the gap equation was solved to obtain the reported pairing symmetries and topological numbers supplies no information on the single-particle Hamiltonian, the form or strength of the interaction kernel V(k,k'), the numerical cutoff, Brillouin-zone discretization, or convergence checks, preventing any assessment of whether the central claims are supported by the calculation.

    Authors: We agree that the abstract is too concise and omits key technical information present in the main text. The single-particle Hamiltonian is the tight-binding model incorporating the Rashba term arising from broken out-of-plane mirror symmetry (detailed in the Methods and Eq. (1)). The interaction kernel is taken as a momentum-independent attractive interaction whose strength is fixed by the linearized gap equation at Tc (Eq. (2)). Numerical implementation uses a discrete Brillouin-zone sum whose convergence was verified in the supplementary calculations. We will revise the abstract to include a short statement summarizing these elements. revision: yes

  2. Referee: [Abstract] Abstract: the chemical potential threshold μ = -0.08 eV and the pairing interaction amplitudes are scanned or selected to produce the stated Z2=1 and C=-6 values; the topological invariants are therefore outputs of these adjustable parameters rather than predictions derived from first-principles inputs whose accuracy is independently validated in the manuscript.

    Authors: The value μ = -0.08 eV is the point at which the leading eigenvalue of the gap equation switches from the time-reversal-invariant channel to the E representation; it is obtained by explicit solution across a range of μ. The pairing amplitudes are indeed phenomenological parameters, not computed from first principles. The resulting Z2 and Chern numbers are direct consequences of the gap functions that emerge for those parameters. We do not claim ab-initio prediction of the interaction strength, but rather demonstrate that the Rashba-split bands of H-TaSSe allow topological phases distinct from the parent compounds. We will revise the abstract to clarify the model nature of the calculation. revision: partial

Circularity Check

0 steps flagged

No circularity: standard linearized gap equation yields model-dependent outputs

full rationale

The derivation solves the linearized gap equation on an input single-particle Hamiltonian (with Rashba term from external citation) plus interaction kernel to obtain pairing symmetries, the μ = -0.08 eV threshold, Z2=1, and C=-6. These are numerical outputs of the standard BCS procedure, not definitions, fitted renamings, or self-citation reductions. No quoted equation equates a claimed result to its own input by construction, and the method remains externally falsifiable against independent band-structure or interaction benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claims rest on the standard mean-field treatment of superconductivity plus a specific Rashba-split band structure for the Janus monolayer; no new entities are introduced.

free parameters (2)
  • chemical potential μ
    Scanned across values to locate the two reported pairing regimes; the threshold -0.08 eV is material-specific.
  • pairing interaction amplitudes
    Adjusted to realize the stated Chern number of -6 and the full-gap condition.
axioms (2)
  • domain assumption Linearized gap equation is sufficient near Tc
    Standard weak-coupling approximation invoked without further justification in the abstract.
  • domain assumption Rashba splitting arises from broken out-of-plane mirror symmetry
    Taken from the cited 2018 PRB paper on Janus TMDs.

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