Fundamental limits on the electron-phonon coupling and superconducting Tc

We establish fundamental upper bounds on the electron-phonon interaction strength and superconducting transition temperature Tc in metals stemming from an intrinsic instability of the equilibrium between electrons and the crystal lattice with respect to strong interaction. Our theory explains why the largest observed electron-phonon couplings λ≤ 4 as well as the mechanism of metastable superconductivity with higher Tc. We conclude based on our theory and analysis of experimental data that room-temperature superconductivity is feasible but only in hydrogen compounds.