Fundamental Limits on the Electron-Phonon Coupling and Superconducting T_c

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 λ ≲ 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.