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SIMULATION SUMMARY v3.0 — Topological Cooper Scaffold
Scientific question: Robustness to interface non-uniformity
Run: 2026-06-29 12:40:08
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CALIBRATION
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λ₀ (Allen-Dynes):           0.3306
Tc₀ check:                  1.7000K ✓
~Pauli threshold:           0.256 meV
Optimal mean Δ_ex (U=1.0):  0.184 meV

UNIFORMITY PARAMETER U_Δ
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U_Δ = 1.0: perfectly uniform (ideal limit)
U_Δ = 0.7-0.9: patterned nanoribbon array (estimated)
U_Δ = 0.3-0.5: continuous cobalt film (estimated rough)
U_Δ = 0.0: completely random Δ_ex (no spatial control)

Physical model: σ_Δ = (1 - U_Δ) × Δ_mean
Pair-broken fraction: f_pb = P(Δ_ex,local > Δ_pb) [Gaussian tail]
Effective Tc: Tc_eff = Tc_uniform × (1 - α × f_pb), α = 1.5

PEAK ΔTc AT EACH UNIFORMITY LEVEL
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U_Δ      Peak ΔTc (K)    Goldilocks width (meV)    In predicted range [0.5,2.0K]?
0.20     +0.920K         0.193 meV                 YES ✓
0.40     +1.183K         0.203 meV                 YES ✓
0.60     +1.505K         0.216 meV                 YES ✓
0.80     +1.834K         0.229 meV                 YES ✓
0.95     +1.900K         0.246 meV                 YES ✓
1.00     +1.900K         0.253 meV                 YES ✓

ROBUSTNESS FINDINGS
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U_Δ threshold for ΔTc ≥ 0.5K (paper lower bound): ~0.01
Goldilocks window width at U=0.40 (rough film):    0.203 meV
Goldilocks window width at U=0.95 (nanoribbons):   0.246 meV
Window width improvement (0.40→0.95):              1.2× wider

NANORIBBON GEOMETRY ADVANTAGES (independent of Litz/Roebel analogy)
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1. Additional fabrication parameters: N (count), w (width), fill factor
2. Tunable spatial frequency of Δ_ex modulation (at moiré unit cell scale)
3. Reduced strain from continuous cobalt film
4. Better interface quality per nanoribbon vs continuous film
5. Independent optimisation of U_Δ separate from mean Δ_ex
6. Nanoribbon count N sweep is new testable prediction (PR2)

KEY SCIENTIFIC RESULT (RECOMMENDED PAPER WORDING)
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"The robustness of the Topological Cooper Scaffold mechanism to realistic
interface non-uniformity was investigated by introducing an interface
uniformity parameter U_Δ ∈ [0,1], where U_Δ = 1 represents a perfectly
uniform exchange field and smaller values represent increasing spatial
variance. The fraction of k-space where the local exchange splitting
exceeds the pair-breaking threshold increases rapidly as U_Δ decreases.
The simulation shows that the scaffold mechanism produces ΔTc within the
predicted [0.5, 2.0] K range for U_Δ ≳ 0.01. A continuous cobalt
film is estimated to achieve U_Δ ≈ 0.3–0.5, which may produce only modest
ΔTc. Patterned cobalt nanoribbon arrays, which allow independent control
of spatial Δ_ex distribution through geometric parameters (ribbon count N,
width w, fill factor), are estimated to achieve U_Δ ≈ 0.7–0.9, potentially
widening the effective Goldilocks window by 1.2× and bringing
ΔTc into the paper's predicted range. These results motivate patterned
nanoribbon geometry as a future-work direction, independent of any
cross-domain analogy."

DISCLAIMER
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U_Δ is a new parameter requiring experimental calibration.
Estimated U_Δ ranges for film vs nanoribbon geometries are order-of-magnitude
estimates only. The simulation framework is semi-microscopic, not DFT.
α_pb (Tc sensitivity to pair-broken k-space fraction) = 1.5 is a model
assumption requiring validation.
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