{"id":"7611f0b3-5053-4ba1-9040-52ad88d53142","arxiv_id":"2505.10336","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Nonunitary mixed parity superconductivity maps by Schrieffer-Wolff transformation onto an effective normal-state Hamiltonian with spin-orbit coupling and an exchange field, producing Edelstein, spin-current, and altermagnetic effects.","lead":"This paper rewrites the Hamiltonian of a superconductor with both singlet and triplet pairing so that it looks like a magnet with spin-orbit coupling, without any real magnetism or spin-orbit interaction. It then derives several spin-dependent effects, including an Edelstein-like spin polarization and an altermagnetic spin texture, from the superconducting pairing alone.","discovery_kind":"unification","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Schrieffer-Wolff mapping is perturbative, and the exact-Green-function argument does not establish the claimed equivalence for all gap magnitudes; the central claim overreaches.","rationale":"The Schrieffer-Wolff algebra leading to Eq.(4) is correct, and the exact Green function calculations for the superconductor are self-contained and valuable. The load-bearing problem is the inference from the presence of g and h in the exact Green function to the exact equivalence with a normal-state magnet with spin-orbit coupling. Because the abstract states that the Hamiltonian 'can be recast' into that for magnetism with spin-orbit coupling, and the paper explicitly claims validity for all g,h, this overreach affects the scope of the central claim. The exact Green function contains pairing magnitudes in the denominator A, and its particle component is not the Green function of any static normal-state Hamiltonian with spin-orbit and exchange fields; a concrete spectral comparison shows deviations at order (Δ/ξ)² in the squared energies. This does not invalidate the exact Kubo formulas, but it requires the correspondence to be stated as a low-energy or weak-pairing mapping. The reader's weakest assumption identified the same perturbative-to-nonperturbative leap, so the conditional verdict is appropriate and no adjustment is needed.","tokens_in":9051,"tokens_out":14107,"duration_ms":132367,"concrete_test":"Diagonalize the exact BdG Hamiltonian and the effective H' of Eq.(4) for a single k with Δs=0 and d=Δt(1,i,0)/√2 over a range Δt/ξ ∈ {0.1, 0.3, 1.0}. Compare the four quasiparticle energies of H with the eigenvalues of H' = H0 + τ3 ε σ0 + τ0 b·σ, using ε=|Δt|²/(2ξ) and b=|Δt|²/(2ξ) ẑ. If the spectra agree to order Δt² but differ by terms of order Δt⁴/ξ³ (i.e., the relative difference grows as (Δt/ξ)²), the exact 'valid for all g,h' claim is refuted. This settles whether the central equivalence is exact or only weak-coupling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that H' in Eq.(4) can be regarded as a normal-state magnet with spin-orbit coupling. Eq.(4) is obtained from the second-order Schrieffer-Wolff transformation with S in Eq.(3), and the paper itself notes this is justified only for gap functions smaller than xi. However, after Eq.(8) the paper asserts that the identification is valid for all g and h because the exact Green function (6) contains f± = g ± h. This inference is not valid. The exact particle Green function is (iω+ξ)(A+f+·σ)/(A²−|f+|²), with A = −ω²−ξ²−|Δs|²−|d|². This is not the Green function of any static normal-state Hamiltonian with spin-orbit and exchange fields, which would be [iω−ξ−ε−(a+b)·σ]⁻¹ with a static denominator (iω−ξ−ε)²−|a+b|². The pairing magnitudes M=|Δs|²+|d|² enter A and therefore modify the quasiparticle dispersion and response functions at higher order in Δ/ξ. For example, with Δs=0 and d=Δt(1,i,0)/√2, the exact BdG eigenvalues squared are ξ² and ξ²+2|Δt|², while H' gives eigenvalues whose squares differ by terms of order |Δt|⁴/ξ². Thus the exact recasting of the Hamiltonian holds only to leading order; the 'valid for all g,h' claim is an overreach. The quantitative Kubo results are computed from the exact BdG Green function and remain valid for the superconductor, but they do not substantiate the exact normal-state equivalence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes a correspondence between nonunitary mixed parity superconductivity and a normal-state magnet with spin-orbit coupling. After defining a BdG Hamiltonian with simultaneous singlet Δs and triplet d-vector pairing, the author performs a Schrieffer-Wolff transformation to obtain the effective Hamiltonian H' in Eq. (4) with momentum-dependent a(k)=Re(Δs* d)/ξ and b(k)=i d×d*/(2ξ). The paper interprets a(k) as a pairing-induced spin-orbit field and b(k) as a pairing-induced exchange field, and then claims, on the basis of the exact Green function (6), that this identification is valid for arbitrary gap magnitudes. Four applications are presented: Dzyaloshinskii-Moriya-type interactions, supercurrent-induced Edelstein spin polarization, supercurrent-induced spin current, and momentum-dependent spin polarization resembling altermagnetism. All effects are claimed to arise purely from superconductivity without intrinsic magnetism or spin-orbit coupling.","tokens_in":9416,"tokens_out":28152,"duration_ms":225105,"significance":"If the central correspondence were exact, it would unify two active fields and provide a new route to spin-orbit-like physics from pairing alone. The paper's strengths are its compact algebraic derivation of a(k) and b(k), the correct symmetry assignment of these fields, and several concrete, checkable response formulas. The proposed temperature dependence near Tc is a useful experimental discriminator between pairing-induced and intrinsic-SOC mechanisms. However, the exactness claim is overstated, and two of the four demonstration calculations contain algebra that does not follow from the preceding equations, so the quantitative predictions require revision before the significance can be assessed.","major_comments":[{"comment":"The claim that the identification 'is valid for all (not necessarily small) g(k) and h(k)' is not supported by the exact Green function.  The Green function (6) has denominator A^2 - |f|^2 with A = -ω_n^2 - ξ^2 - |Δs|^2 - |d|^2, which is not the denominator of a static normal-state Hamiltonian with spin-orbit and exchange fields, namely (iω - ξ - ε)^2 - |a+b|^2.  For the explicit nonunitary state Δs=0, d=Δt(1,i,0)/√2, the BdG eigenvalues squared are ξ^2 and ξ^2+2|Δt|^2, while the H' eigenvalues squared from Eq. (4) are ξ^2 and (ξ+|Δt|^2/ξ)^2; the two disagree at order |Δt|^4/ξ^2.  The Schrieffer-Wolff mapping is therefore only a leading-order equivalence, and the all-g,h statement overreaches.","section":"Paragraph after Eq. (8)"},{"comment":"The current-induced spin polarization coefficient χ'_xy is claimed to scale as 1/γ^3, where γ is an unmeasured damping rate.  This makes the result diverge as γ→0 and renders the prediction controlled by the ad hoc lifetime rather than by the pairing scale.  There is also an algebraic inconsistency: from Eq. (18), ∫_{-εF}^{∞} dξ/(γ^2+ξ^2)^2 = π/(2γ^3) + O(1/εF), which yields χ'_xy ≈ e k_F Δs Δt/(4π γ^3), not the printed 8π γ^3.  Additionally, Eq. (19) as written has a prefactor 1/γ^2 multiplying a dimensionless bracket, which scales as 1/γ^2 in the εF≫γ limit, not 1/γ^3.  These expressions need to be rederived and stated with their validity conditions.","section":"Eqs. (16)-(20), quasiparticle Edelstein response"},{"comment":"Equation (28) does not follow from the exact Green function (6) for the stated d-vector d = Δt(kx, i ky, 0)^t.  Substituting h = 2kxky|Δt|^2 \\hat z into Eq. (26) gives the denominator (ω_n^2+ξ^2+|Δt|^2(kx^2+ky^2))^2 - 4|Δt|^4 kx^2 ky^2, not (ω_n^2+ξ^2)(ω_n^2+ξ^2-2|Δt|^2).  Consequently Eq. (29) and the claim of d-wave spin polarization are not derived from the stated model; please provide the corrected expression or specify the additional approximation used to arrive at Eq. (28).","section":"Eqs. (28)-(29), altermagnetism"}],"minor_comments":[{"comment":"The sentence stating that a(k) and b(k) are 'respectively, even and odd in k' is reversed: from Eq. (5), a(k) is odd in k and b(k) is even in k.","section":"After Eq. (5)"},{"comment":"Please check the numerical factor in Eq. (15): evaluating the integral in Eq. (14) gives χxy = -7 e k_F Δs Δt ζ(3)/(4 ħ T^2), a factor of 2 smaller than printed.  If a different convention is used, the derivation should state it explicitly.","section":"Eq. (15)"},{"comment":"There are typos: 'supercondutor' before Eq. (9) and 'd-vactor' before Eq. (17) should be 'superconductor' and 'd-vector'.","section":"Text before Eq. (9) and before Eq. (17)"},{"comment":"The notation (kx ky 0)^t is introduced as a unit vector along k, but later equations such as (11), (12), and (28) appear to treat kx and ky as full momentum components.  Please clarify whether these are unit-vector components or dimensionful momenta, since the denominators in Eqs. (11)-(12) and (28)-(29) depend on this distinction.","section":"Eqs. (10)-(12) and (28)"},{"comment":"The Dzyaloshinskii-Moriya result is quoted from Ref. [30]; the text should clearly indicate that this subsection is a consistency check rather than a new derivation.","section":"Dzyaloshinskii-Moriya subsection"}],"recommendation":"major_revision","confidential_remarks":"The paper is a compact single-author note with several unnumbered sections.  The central Schrieffer-Wolff construction is clean, but the all-g,h exactness claim and the algebraic issues in the Edelstein and altermagnetism calculations are load-bearing for the paper's quantitative claims.  I recommend requesting corrected derivations and a clearly bounded statement of the correspondence before further consideration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Main thing to know: the Schrieffer-Wolff step is correct, and the response calculations are a useful addition to the noncentrosymmetric-superconductor toolkit. But the advertised mapping is not exact for arbitrary pairing amplitudes, and the text overreaches when it claims the identification with a normal-state magnet plus spin-orbit coupling holds for all g and h.\n\nI checked Eq. (4). With the generator S in Eq. (3), the commutator reproduces a(k) = Re(Δs* d)/ξ and b(k) = i d×d*/(2ξ), with the stated parities. That is real, clean algebra. The Edelstein coefficient (Eqs. 9–15), the spin-current response (Eqs. 21–25), and the d-wave spin texture (Eqs. 26–29) are computed from the exact BdG Green function, so they stand on their own as predictions for the superconducting state, even if the normal-state interpretation is only asymptotic. I like the d-wave altermagnetic texture; that is a concrete, falsifiable signature. The DM discussion is mostly an application of the author's prior work with Ref. 30, not a new derivation, but the paper does not hide that.\n\nSoft spots. The central claim of exact recasting is not supported. The exact particle Green function in Eq. (6) has denominator A²−|f|² with A = −ω_n²−ξ²−|Δs|²−|d|², which is not the denominator of any static normal-state Hamiltonian with spin-orbit and exchange fields. The stress-test example with d = Δt(1,i,0)/√2 shows the exact BdG spectrum and the spectrum from H′ are not identical beyond leading order; the correspondence is a weak-coupling statement. So the sentence after Eq. (8), claiming the identification is valid for all g and h, should go. Since the response calculations use the exact Green function, this overreach does not invalidate them, but it changes the framing from useful asymptotics to a false exactness.\n\nTwo minor things. The claim that the Edelstein effect for mixed parity pairings \"has not been theoretically investigated so far\" is stated without a comprehensive citation search; I would soften it. The quasiparticle Edelstein result depends on an unmeasured γ and behaves as 1/γ³, so the numerical comparison to the topological-insulator surface is illustrative, not quantitative.\n\nWho benefits: people working on noncentrosymmetric superconductors, superconducting spintronics, and altermagnetism. This deserves a serious referee. The algebra is sound, the response formulas are new enough, and the altermagnetism connection is worth having in the literature. I would accept with major revision, asking the author to reframe the central claim as a weak-coupling equivalence and to drop or prove the all-g,h claim.","headline":"A correct Schrieffer-Wolff mapping to a normal-state magnet with spin-orbit coupling in the weak-coupling limit, plus useful response calculations; the claim that the equivalence is exact for all gap amplitudes overreaches.","tokens_in":9931,"tokens_out":10205,"would_cite":true,"duration_ms":96935,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that every nonunitary mixed-parity superconductor behaves like a magnet with spin-orbit coupling, because pairing alone generates an effective spin-orbit field $\\mathbf{a}(k)$ and an effective exchange field…","keywords":["nonunitary superconductivity","mixed parity pairing","Schrieffer-Wolff transformation","effective spin-orbit coupling","Edelstein effect","supercurrent-induced spin current","altermagnetism","Dzyaloshinskii-Moriya interaction"],"falsifier":"Compute the second-order Schrieffer-Wolff commutator $[S,[S,H_\\Delta]]$ or the full vertex-corrected Kubo response for a concrete mixed-parity model with finite $\\Delta_s$ and $\\mathbf{d}$: if any spin-dependent term beyond $\\tau_3\\mathbf{a}(k)\\cdot\\boldsymbol{\\sigma}+\\tau_0\\mathbf{b}(k)\\cdot\\boldsymbol{\\sigma}$ appears, the claim that the state is exactly equivalent to a magnet with spin-orbit coupling fails, and the predicted transport coefficients would change.","tokens_in":8844,"feed_emoji":"🧲","tokens_out":8370,"duration_ms":73837,"temperature":0.7,"pith_summary":"The paper claims that a superconductor carrying both even-parity (singlet) and odd-parity (triplet) pairing, with the triplet part in a nonunitary configuration ($d\\times d^*\\neq 0$), is secretly the same kind of object as an ordinary metal with both magnetism and spin-orbit coupling. Using a Schrieffer-Wolff transformation, the pairing terms are folded into an effective normal-state Hamiltonian whose two new fields are $\\mathbf{a}(k)=\\mathrm{Re}(\\Delta_s^*\\mathbf{d})/\\xi$, odd in momentum and therefore spin-orbit-like, and $\\mathbf{b}(k)=i\\,\\mathbf{d}\\times\\mathbf{d}^*/(2\\xi)$, even in momentum and therefore exchange-field-like. Because these fields come entirely from the superconducting condensate, all the phenomena they produce — Dzyaloshinskii-Moriya-type interactions, Edelstein-type spin polarization, supercurrent-induced spin currents, and altermagnetic spin textures — would occur in materials that contain no actual magnetism and no spin-orbit coupling. The paper also shows the same two fields appear in the exact Green function, suggesting the mapping is not an artifact of the perturbative derivation.","feed_headline":"Superconductivity alone mimics spin-orbit magnetism","feed_subtitle":"Pairing alone yields effective spin-orbit and exchange fields, driving Edelstein and altermagnetic effects.","key_machinery":"The load-bearing object is the Schrieffer-Wolff generator $S=(1/2\\xi)(\\tau_+\\Delta-\\tau_-\\Delta^\\dagger)$, which block-diagonalizes the BCS Hamiltonian to leading order and produces the effective normal-state form in Eq. (4). The pairing-induced fields $\\mathbf{a}(k)$ and $\\mathbf{b}(k)$ carry the argument: their parity and reality properties, rather than any material-specific detail, force the interpretation as spin-orbit coupling and exchange field. The paper backs this with the exact Green function, whose particle block contains $f_\\pm=\\mathbf{g}\\pm\\mathbf{h}$ with $\\mathbf{g}=2\\mathrm{Re}(\\Delta_s^*\\mathbf{d})$ and $\\mathbf{h}=i\\mathbf{d}\\times\\mathbf{d}^*$, showing that the same two vectors survive beyond perturbation theory; these vectors then enter the Kubo formulas for spin polarization, spin current, and momentum-resolved spin texture.","core_discovery":"Writing the BCS Hamiltonian as $H=H_0+H_\\Delta$ with $H_\\Delta=\\sum_k (\\tau_+\\Delta+\\tau_-\\Delta^\\dagger)$ and $\\Delta=\\Delta_s(k)\\sigma_0+\\mathbf{d}(k)\\cdot\\boldsymbol{\\sigma}$, the paper derives an effective Hamiltonian $$H'=H_0+\\tau_3(\\varepsilon_k\\sigma_0+\\mathbf{a}(k)\\cdot\\boldsymbol{\\$\\sigma$})+\\tau_0\\mathbf{b}(k)\\cdot\\boldsymbol{\\$\\sigma$},$$ with $\\varepsilon_k=(|\\Delta_s|^2+|\\mathbf{d}|^2)/(2\\xi)$, $\\mathbf{a}(k)=\\mathrm{Re}(\\Delta_s^*\\mathbf{d})/\\xi$, and $\\mathbf{b}(k)=i\\,\\mathbf{d}\\times\\mathbf{d}^*/(2\\xi)$. Since $\\Delta_s$ is even and $\\mathbf{d}$ is odd in $k$, $\\mathbf{a}$ is odd (it breaks inversion symmetry, playing the role of spin-orbit coupling) and $\\mathbf{b}$ is even (it breaks time reversal, playing the role of a magnetic field). The central claim is that this effective Hamiltonian can be regarded as that for a magnet with spin-orbit coupling in the normal state, and the paper demonstrates the identification through four effects: Dzyaloshinskii-Moriya-type spin-spin interactions set by $\\mathbf{g}=2\\mathrm{Re}(\\Delta_s^*\\mathbf{d})$, a supercurrent-induced Edelstein effect whose coefficient is proportional to $\\Delta_s\\Delta_t$, a supercurrent-induced spin current controlled by $\\mathbf{h}=i\\mathbf{d}\\times\\mathbf{d}^*$, and a $d$-wave altermagnetic spin texture arising from $\\mathbf{g}$ and $\\mathbf{h}$.","pith_inferences":["If the two-field identification survives higher-order corrections, it becomes a design principle: any nonunitary mixed-parity superconductor, regardless of crystal inversion symmetry, should show spin-orbit-like transport with an energy scale $\\sqrt{|\\Delta_s\\Delta_t|}$, typically of the order of 1 meV and comparable to Rashba splittings.","The same algebra with orbital-space matrices in place of spin Pauli matrices suggests orbital analogues of these effects in multiband superconductors, an extension the paper only sketches; one could look for orbital Edelstein responses in centrosymmetric multiband systems.","Because $\\mathbf{g}$ enters the quasiparticle Edelstein response while $\\mathbf{h}$ enters the supercurrent spin-current response, a combined measurement of both responses on the same material could cleanly separate the two pairing-generated fields without needing magnetic probes.","The temperature dependence near $T_c$ offers a direct experimental discriminant: pairing-generated effects die out at $T_c$, whereas intrinsic spin-orbit effects persist, so a sign of the mechanism is the simultaneous disappearance of spin polarization and superconductivity."],"forward_implications":["A nonunitary mixed-parity superconductor should exhibit a Dzyaloshinskii-Moriya-type interaction set by $\\mathbf{g}(k)=2\\mathrm{Re}(\\Delta_s^*\\mathbf{d})$, and this contribution vanishes at the superconducting transition temperature, distinguishing it from intrinsic spin-orbit mechanisms.","A supercurrent should induce a bulk spin polarization even in a centrosymmetric superconductor, with the low-temperature coefficient $\\chi_{xy}\\simeq -7e k_F \\Delta_s\\Delta_t \\zeta(3)/(2\\hbar T^2)$ for a Rashba-like $\\mathbf{d}$-vector.","Quasiparticle charge current should also generate spin polarization, with coefficient $\\chi'_{xy}\\simeq e k_F \\Delta_s\\Delta_t/(8\\pi\\gamma^3)$ in the $\\varepsilon_F\\gg\\gamma$ limit.","When the triplet pairing is nonunitary ($\\mathbf{h}\\neq 0$), a supercurrent drives a spin current whose direction is set by $\\mathbf{h}$, with magnitude scaling as $|\\Delta_t|^2/T^2$ near $T_c$.","Momentum-resolved spin polarization in these superconductors develops the $d$-wave texture characteristic of altermagnetism, for example $\\propto k_x k_y$ for $\\mathbf{d}=\\Delta_t(k_x,ik_y,0)$."],"supporting_citations":[{"why":"Provides the Schrieffer-Wolff transformation method used to fold pairing into an effective normal-state Hamiltonian.","marker":"23–25"},{"why":"Reports a similar effective Hamiltonian in a different context, corroborating that the two-field form in Eq. (4) is not unique to this derivation.","marker":"26"},{"why":"Supports the exchange-field interpretation of the pairing-generated vector $\\mathbf{h}$, the basis for calling $\\mathbf{b}$ a magnetic field.","marker":"27"},{"why":"Previous prediction that mixed-parity superconductivity generates Dzyaloshinskii-Moriya interactions determined by $\\mathbf{g}$, which the correspondence reproduces.","marker":"30"},{"why":"Original Edelstein effect in polar superconductors with spin-orbit coupling, the baseline against which the pairing-only spin-polarization response is defined.","marker":"31"},{"why":"Supplies the Rashba-like $\\mathbf{d}$-vector form $\\mathbf{d}=\\Delta_t(k_y,-k_x,0)$ used in the explicit Edelstein and spin-texture calculations.","marker":"33"},{"why":"Edelstein's spin polarization by electric current in two-dimensional systems, the normal-state analogue used to interpret the quasiparticle current-induced polarization.","marker":"35"},{"why":"Defines the altermagnetic momentum-dependent spin-splitting phenomena that the paper's $d$-wave spin texture is compared with.","marker":"41–46"}],"fun_headline_variants":["Superconductivity impersonates spin-orbit magnetism","Pairing alone creates spin-orbit and magnetic effects","No spin-orbit? No magnet? Superconductivity does it anyway","Nonunitary pairing mimics spin-orbit coupled magnetism","Superconductors: spin-orbit and magnetic effects without either"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation of the clean two-field effective Hamiltonian is perturbative in the ratio of gap size to kinetic energy $\\xi$, but the paper's applications use the exact Green function and claim the identification holds for all gap sizes; the paper does not prove that higher-order Schrieffer-Wolff terms or Kubo vertex corrections introduce no additional momentum-dependent spin couplings.","fun_headline_variants_meta":{"raw":{"variants":["Superconductivity impersonates spin-orbit magnetism","Pairing alone creates spin-orbit and magnetic effects","No spin-orbit? No magnet? Superconductivity does it anyway","Nonunitary pairing mimics spin-orbit coupled magnetism","Superconductors: spin-orbit and magnetic effects without either"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000543,"raw_usage":{"total_tokens":2623,"prompt_tokens":992,"completion_tokens":1631,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":1550}},"tokens_in":608,"tokens_out":1631,"duration_ms":12594,"temperature":1.0,"reasoning_tokens":1550,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:11:24.020481+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the second-order Schrieffer-Wolff commutator $[S,[S,H_\\Delta]]$ or the full vertex-corrected Kubo response for a concrete mixed-parity model with finite $\\Delta_s$ and $\\mathbf{d}$: if any spin-dependent term beyond $\\tau_3\\mathbf{a}(k)\\cdot\\boldsymbol{\\sigma}+\\tau_0\\mathbf{b}(k)\\cdot\\boldsymbol{\\sigma}$ appears, the claim that the state is exactly equivalent to a magnet with spin-orbit coupling fails, and the predicted transport coefficients would change.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports a similar effective Hamiltonian in a different context, corroborating that the two-field form in Eq. (4) is not unique to this derivation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the exchange-field interpretation of the pairing-generated vector $\\mathbf{h}$, the basis for calling $\\mathbf{b}$ a magnetic field."},{"cited_title":"Dzyaloshinskii-Moriya-type spin-spin interaction from mixed-parity superconductivity","cited_arxiv_id":"2407.07144","evidence_quote":"Previous prediction that mixed-parity superconductivity generates Dzyaloshinskii-Moriya interactions determined by $\\mathbf{g}$, which the correspondence reproduces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Rashba-like $\\mathbf{d}$-vector form $\\mathbf{d}=\\Delta_t(k_y,-k_x,0)$ used in the explicit Edelstein and spin-texture calculations."}],"review_version":1}