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

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.

main text updated, new supplemental material added, 27 pages, 6 figures, 5 tables

References in corpus (21)

• Conventional superconductivity at 203 K at high pressures
• Superconductivity at 250 K in lanthanum hydride under high pressures
• Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures
• Anomalous high-temperature superconductivity in YH${}_6$
• Superconductivity at 253 K in lanthanum-yttrium ternary hydrides
• High-Temperature Superconductivity in Cerium Superhydrides
• Superconductivity to 262 kelvin via catalyzed hydrogenation of yttrium at high pressures
• Enhancement of the superconducting critical temperature realized in the La-Ce-H system at moderate pressures
• Efficient route to achieve superconductivity improvement via substitutional La-Ce alloy superhydride at high pressure
• High-temperature superconductivity on the verge of a structural instability in lanthanum superhydride
• Pressure-induced high-temperature superconductivity retained at ambient
• A bound on superconducting $T_c$'s
• Heuristic bounds on superconductivity and how to exceed them
• Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity
• Isotope effect in superconducting lanthanum hydride under high compression
• Universal diamond edge Raman scale to 0.5 terapascal: The implication to metallization of hydrogen
• Prediction of Room-Temperature Superconductivity in Quasi-atomic H2-Type Hydrides at High Pressure
• Superconductivity near a quantum critical point in the extreme retardation regime
• Excitonic Insulator to Superconductor Phase Transition in Ultra-Compressed Helium
• Upper limit for superconducting transition temperature in Eliashberg-McMillan theory
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $\gamma$-model

Cited by in corpus (5)

• The Maximum $T_c$ of Conventional Superconductors at Ambient Pressure
• Stability and Superconductivity of Ternary Polyhydrides
• Transmission of radio-frequency waves and nuclear magnetic resonance in lanthanum superhydrides
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. III: Einstein phonons
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. II: Dispersive phonons