Fundamental limits on the electron-phonon coupling and superconducting $T_c$

TL;DR

This paper establishes fundamental upper bounds on electron-phonon coupling and superconducting transition temperature, explaining observed limitations and identifying hydrogen compounds as the only feasible room-temperature superconductors.

Contribution

It provides a theoretical framework for the intrinsic limits of electron-phonon interactions and predicts conditions for metastable high-$T_c$ superconductivity.

Findings

Electron-phonon coupling constants are limited to $\\lesssim 4$ due to lattice instability.

Room-temperature superconductivity via phonons is feasible only in hydrogen compounds.

Metastable superconductivity with higher $T_c$ can occur near the instability threshold.

Abstract

Fundamental upper bounds on the electron-phonon interaction strength and superconducting transition temperature $T_c$ in metals are established based on the intrinsic instability of the equilibrium between electrons and the crystal lattice under strong interaction. This instability explains why observed electron-phonon coupling constants are limited to $\lambda \lesssim 4$. The theory also accounts for the mechanism of metastable superconductivity with enhanced $T_c$, which emerges near the instability threshold. Based on theoretical analysis and comparison with experimental data, room-temperature phonon-mediated superconductivity is found to be feasible exclusively in hydrogen compounds.