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

TL;DR

This paper introduces a two-channel model combining phonon and spin-fluctuation mechanisms to predict superconducting critical temperatures across diverse materials with high accuracy, and reveals limitations of geometric superfluid weight as a universal predictor.

Contribution

It develops a unified framework that accurately predicts Tc for various superconductors and uncovers a fundamental no-go result regarding geometric superfluid weight's predictive power.

Findings

Achieved R-squared = 0.96 for 19 materials spanning five orders of magnitude in Tc.

Identified spin-fluctuation channel as key to high Tc in unconventional superconductors.

Proved geometric superfluid weight cannot universally predict Tc due to its correlation with band topology.

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.