Two-Channel Allen-Dynes Framework for Superconducting Critical Temperatures: Blind Predictions Across Five Orders of Magnitude and a Quantum-Metric No-Go Result

Jian Zhou

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arXiv · 2604.04719

Two-Channel Allen-Dynes Framework for Superconducting Critical Temperatures: Blind Predictions Across Five Orders of Magnitude and a Quantum-Metric No-Go Result

Jian Zhou

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Abstract

We present a two-channel extension of the Allen-Dynes framework that unifies phonon-mediated and spin-fluctuation-mediated pairing channels for predicting superconducting critical temperatures. Channel 1 employs the standard Allen-Dynes formula with material-specific electron-phonon coupling; Channel 2 incorporates a spin-fluctuation coupling parameter extracted from inelastic neutron scattering data. Blind predictions for 19 materials spanning conventional superconductors, MgB2, iron pnictides, iron chalcogenides, heavy fermions, cuprates, and hydrides achieve R-squared = 0.96 across five orders of magnitude in Tc (0.4-250 K) without free parameters. We further demonstrate a quantum-metric no-go result: the Peotta-Torma geometric superfluid weight, while essential for flat-band systems, cannot serve as a universal predictor of Tc because it correlates with band-structure topology rather than pairing strength. The framework identifies the spin-fluctuation channel as the dominant contributor to Tc enhancement in unconventional superconductors, providing quantitative design rules for materials with Tc above 100 K.

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Jian Zhou. 2026-04-06. Two-Channel Allen-Dynes Framework for Superconducting Critical Temperatures: Blind Predictions Across Five Orders of Magnitude and a Quantum-Metric No-Go Result. https://arxiv.org/abs/2604.04719

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