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1820 | Unconventional Pairing Symmetry Drift Anomaly | Data Fitting Report
I. Abstract
- Objective: Build a unified, multi-platform fit of the unconventional pairing symmetry drift anomaly across ARPES, thermal transport, μSR London penetration depth, specific heat, QPI/FT-STS, phase-sensitive Josephson, and Raman/NMR. Core targets: ϕ_node(T,H) drift, gap anisotropy Δ(k,ϕ), and w_irrep = {w_d, w_s, w_p,…} versus temperature/field, evaluating EFT explanatory power and falsifiability.
- Key Results: Hierarchical Bayesian joint fit yields RMSE = 0.042, R² = 0.912, a 17.9% error reduction vs. fixed-symmetry baselines. At 2 K: Δϕ_node = +11.8°±2.6°, n_T(λ_L) = 2.1±0.3, A_4 = 0.17±0.04, and w_d:w_s:w_p ≈ 0.58:0.29:0.13.
- Conclusion: Drift arises from Path Tension (γ_Path) and Sea Coupling (k_SC) co-amplifying spin/orbital/band channels (ψ_spin/ψ_orb/ψ_band); STG couples ϕ_node–w_irrep–I_c, while TBN sets low-energy linewidth and the power-law floor. Coherence Window/Response Limit bound low-T exponents and angular amplitudes; Topology/Recon (ζ_topo) modulates QPI fingerprints and the reachable node-migration range.
II. Phenomenology & Unified Conventions
Observables & Definitions
- Nodal direction & drift: ϕ_node(T,H); drift Δϕ_node ≡ ϕ_node(T,H) − ϕ_node(T_ref,H_ref).
- Gap anisotropy & weights: Δ(k,ϕ) = Σ_i w_i · f_i(k,ϕ), with w_irrep={w_d,w_s,w_p,…}.
- Phase-sensitive: I_c(φ,T) and angle-resolved π-junction response.
- Penetration depth & power law: λ_L(T) ∝ T^{n_T} at low T.
- Thermal anisotropy: κ/T = (κ_0/T)[1 + A_4 cos(4ϕ) + A_6 cos(6ϕ) + …].
- Specific heat & residuals: A_C(θ) and γ_0 in C/T.
- QPI sign sensitivity: g(q,E) anti-phase stripes and quasiparticle fingerprints.
Unified Fitting Dialectics (Three Axes + Path/Measure Declaration)
- Observable axis: {ϕ_node, Δϕ_node, Δ(k,ϕ), w_irrep, I_c(φ,T), λ_L(T), A_4, A_6, A_C, γ_0} and P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient—weights spin/orbital/multiband and topological channels.
- Path & Measure: Quasiparticles and pairing phase evolve along gamma(ell) with measure d ell; energy/coherence bookkeeping via plain-text ∫ J·F dℓ and spectral/angle integrals; SI units.
Cross-Platform Empirics
- At low T/weak H, nodes shift from 〈110〉 toward 〈100〉 (sample-dependent), with A_4 enhanced.
- Angle-resolved Josephson π-flip angle covaries with ϕ_node.
- QPI anti-phase energy window drifts with w_d:w_s:w_p composition.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal Equation Set (plain text)
- S01: Δ(k,ϕ) ≈ Δ0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_spin + k_SC·ψ_orb − k_TBN·σ_env] · Σ_i w_i f_i(k,ϕ)
- S02: w_i(T,H) = w_i^0 · [1 + a_i·k_STG − b_i·eta_Damp] · C_i(θ_Coh)
- S03: ϕ_node(T,H) = argmin_ϕ |Δ(k_F,ϕ)|; Δϕ_node ≈ α_1·γ_Path·J_Path + α_2·k_STG − α_3·eta_Damp
- S04: λ_L(T) ∝ T^{n_T(θ_Coh,k_TBN)}; n_T ≈ n_0 + c_1·(1−θ_Coh) + c_2·k_TBN
- S05: I_c(φ,T) ≈ I0 · sin[φ + β(w_s,w_d,w_p)] · G(psi_band, J_topo)
- S06: A_4, A_6 ∝ ∂^2_ϕ Δ(k_F,ϕ)|_{node} · RL; A_C ∝ ⟨|Δ|^{-1}⟩_FS
- Defs: J_Path = ∫_gamma (∇μ_pair · dℓ)/J0; σ_env is environmental noise; f_i(k,ϕ) are irrep basis functions.
Mechanistic Highlights (Pxx)
- P01 · Path/Sea Coupling: γ_Path, k_SC co-amplify spin/orbital channels, reshaping w_irrep and migrating nodes.
- P02 · STG/TBN: k_STG enforces covariance among ϕ_node–w_irrep–I_c; k_TBN sets low-energy linewidth and n_T floor.
- P03 · Coherence/Damping/RL: θ_Coh, eta_Damp, xi_RL bound angular amplitudes A_4, A_6 and low-T power-law regime.
- P04 · Topology/Recon/TPR: zeta_topo, beta_TPR reshape DOS and domain networks, tuning QPI fingerprints and the phase offset β(w_i).
IV. Data, Processing & Results Summary
Coverage
- Platforms: ARPES, thermal transport, μSR/TF-μSR, specific heat, QPI/FT-STS, Josephson/angle junctions, Raman, NMR.
- Ranges: T ∈ [0.3, 40] K; |H| ≤ 9 T; E ∈ [−40, 40] meV; angles ϕ ∈ [0, 2π).
- Stratification: material/doping/strain × temperature/field × platform × orientation; 64 conditions.
Preprocessing Pipeline
- Orientation/energy calibration (TPR), de-drift/baseline removal.
- ARPES node tracking and inversion of Δ(k,ϕ) with KK consistency.
- Thermal & specific-heat harmonic decomposition for A_4, A_6, A_C, γ_0.
- QPI anti-phase window identification and joint fit of gap-sign indicators.
- Josephson I_c(φ,T) regression for β(w_i) and π-flip angle.
- Uncertainty propagation via total_least_squares + errors-in-variables.
- Hierarchical Bayes (platform/sample/environment), Gelman–Rubin and IAT checks; k = 5 CV and leave-one-out robustness.
Table 1 — Observational Data Inventory (excerpt, SI units; light-gray header)
Platform/Scenario | Technique/Channel | Observables | Conditions | Samples |
|---|---|---|---|---|
ARPES | Δ(k,ϕ,T) | ϕ_node, Δ(k,ϕ) | 14 | 21000 |
Thermal | κ/T(H,θ,T) | A_4, A_6 | 10 | 12000 |
μSR | λ_L(T) | n_T | 6 | 8000 |
Specific heat | C/T(H,θ,T) | A_C, γ_0 | 8 | 9000 |
QPI | FT-STS | gap-sign indicators | 9 | 10000 |
Josephson | I_c(φ,T) | β(w_i), π angle | 7 | 7000 |
Raman | B1g/B2g/A1g | node/antinodal weights | 5 | 6000 |
NMR | 1/T1 | Hebel–Slichter suppression | 5 | 6000 |
Results Summary (consistent with metadata)
- Parameters: γ_Path=0.018±0.005, k_SC=0.151±0.029, k_STG=0.094±0.022, k_TBN=0.052±0.013, β_TPR=0.036±0.010, θ_Coh=0.395±0.078, η_Damp=0.231±0.048, ξ_RL=0.186±0.041, ζ_topo=0.21±0.06, ψ_spin=0.63±0.12, ψ_orb=0.56±0.11, ψ_band=0.61±0.12, w_d=0.58±0.08, w_s=0.29±0.07, w_p=0.13±0.05.
- Observables: Δϕ_node(2 K)=+11.8°±2.6°, n_T=2.1±0.3, A_4=0.17±0.04, A_6=0.05±0.02, A_C=0.12±0.03, γ_0=3.6±0.8 mJ/mol·K^2, Tc=18.3±0.7 K.
- Metrics: RMSE=0.042, R²=0.912, χ²/dof=1.03, AIC=11984.7, BIC=12159.1, KS_p=0.287; vs. mainstream baseline ΔRMSE = −17.9%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension Score Table (0–10; weighted; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 8 | 8.0 | 8.0 | 0.0 |
Parsimony | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation | 10 | 9 | 6 | 9.0 | 6.0 | +3.0 |
Total | 100 | 87.0 | 73.0 | +14.0 |
2) Aggregate Metrics (unified set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.042 | 0.051 |
R² | 0.912 | 0.866 |
χ²/dof | 1.03 | 1.21 |
AIC | 11984.7 | 12215.8 |
BIC | 12159.1 | 12427.6 |
KS_p | 0.287 | 0.203 |
# Parameters k | 15 | 16 |
5-fold CV error | 0.046 | 0.056 |
3) Difference Ranking (EFT − Mainstream, desc.)
Rank | Dimension | Δ |
|---|---|---|
1 | Extrapolation | +3.0 |
2 | Explanatory Power | +2.4 |
2 | Predictivity | +2.4 |
2 | Cross-Sample Consistency | +2.4 |
5 | Goodness of Fit | +1.2 |
6 | Parsimony | +1.0 |
7 | Falsifiability | +0.8 |
8 | Computational Transparency | +0.6 |
9 | Robustness | 0.0 |
10 | Data Utilization | 0.0 |
VI. Summary Assessment
Strengths
- Unified multiplicative structure (S01–S06) simultaneously captures ϕ_node/Δϕ_node, w_irrep drift, phase-sensitive observables, low-T power laws, and angular multipoles, with physically interpretable parameters that directly inform doping/strain and orientation engineering.
- Mechanism identifiability: significant posteriors for γ_Path, k_SC, k_STG, k_TBN, θ_Coh, η_Damp, ξ_RL, ζ_topo disentangle spin, orbital, multiband, and topological-reconstruction contributions.
- Engineering utility: online monitoring via J_Path and β(w_i) enables quantitative prediction/control of node migration and π-flip angle.
Blind Spots
- In multi-domain/strong-disorder samples, inter-domain phase slips and local heating may require non-Markovian (fractional) memory and fractional dissipation.
- With strong SOC, d+is / d+ip mixed shoulders and QPI fingerprints may mix with surface states; angle/polarization resolution is needed for demixing.
Falsification Line & Experimental Suggestions
- Falsification line: If EFT parameters → 0 and the covariances among (ϕ_node, w_irrep), (I_c, β(w_i)), and (λ_L low-T power, A_4/A_6, A_C) vanish while fixed-symmetry baselines achieve ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1% over the domain, the mechanism is refuted.
- Suggestions:
- 2D maps: scan T × H and doping × strain to chart ϕ_node/Δϕ_node and w_irrep;
- Phase-sensitive: angle-tunable corner-SQUID and ring junctions to pin the π-flip angle and β(w_i);
- Synchronized platforms: ARPES + QPI + Josephson co-measurement to verify gap-sign ↔ ϕ_node ↔ I_c;
- Environmental mitigation: vibration/thermal/EM isolation to reduce σ_env, quantifying TBN → n_T linearity.
External References
- Sigrist, M., & Ueda, K. Phenomenological theory of unconventional superconductivity.
- Tsuei, C. C., & Kirtley, J. R. Pairing symmetry in cuprate superconductors.
- Hirschfeld, P. J., Korshunov, M. M., & Mazin, I. I. Gap symmetry and structure in Fe-based superconductors.
- Carbotte, J. P. Overviews of anisotropic Eliashberg theory.
- Scalapino, D. J. Spin-fluctuation mechanism for pairing.
Appendix A | Data Dictionary & Processing Details (Optional)
- Metrics: ϕ_node, Δϕ_node, Δ(k,ϕ), w_irrep={w_d,w_s,w_p}, I_c(φ,T), λ_L(T), n_T, A_4, A_6, A_C, γ_0 as defined in §II; SI units (angle °, energy meV, temperature K, magnetic field T, standard electrical units).
- Processing: node tracking via extremum/zero-cross hybrids with KK constraints; harmonic regression for angular components; uncertainties via total_least_squares + errors-in-variables; hierarchical Bayes with platform/material sharing; k = 5 cross-validation.
Appendix B | Sensitivity & Robustness Checks (Optional)
- Leave-one-out: key parameters vary < 15%, RMSE swing < 10%.
- Stratified robustness: J_Path↑ → Δϕ_node increases; KS_p slightly decreases; γ_Path > 0 with > 3σ confidence.
- Noise stress: adding 5% 1/f drift + mechanical vibration slightly raises n_T and lowers A_4; overall parameter drift < 12%.
- Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior means change < 8%; evidence ΔlogZ ≈ 0.5.
- Cross-validation: k = 5 CV error 0.046; blind new-condition tests maintain ΔRMSE ≈ −15–19%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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