Limits of Eliashberg Theory and Bounds for Superconducting Transition Temperature

Abstract

The discovery of record - breaking values of superconducting transition temperature $T_c$ in quite a number of hydrides under high pressure was an impressive demonstration of capabilities of electron - phonon mechanism of Cooper pairing. This lead to an increased interest to foundations and limitations of Eliashberg - McMillan theory as the main theory describing superconductivity in a system of electrons and phonons. Below we shall consider both elementary basics of this theory and a number of new results derived only recently. We shall discuss limitations on the value of the coupling constant related to lattice instability and a phase transition to another phase (CDW, bipolarons). Within the stable metallic phase the effective pairing constant may acquire arbitrary values. We consider extensions beyond the traditional adiabatic approximation. It is shown that Eliasberg - McMillan theory is also applicable in the strong antiadiabatic limit. The limit of very strong coupling, being most relevant for the physics of hydrides, is analyzed in details. We also discuss the bounds for $T_c$ appearing in this limit.

arXiv comment18 pages, 9 figures, talk given at the Scientific Session of Physics Division of the RAS, May 12, 2021

References in corpus (28)

• 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
• A Perspective on Conventional High-Temperature Superconductors at High Pressure: Methods and Materials
• Anomalous high-temperature superconductivity in YH${}_6$
• Anomalous Normal-State Properties of High-T${}_c$ Superconductors -- Intrinsic Properties of Strongly Correlated Electron Systems?
• Superconductivity at 253 K in lanthanum-yttrium ternary hydrides
• Superconductivity to 262 kelvin via catalyzed hydrogenation of yttrium at high pressures
• Superconducting hydrides under pressure
• High Pressure and Road to Room Temperature Superconductivity
• Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study
• Gap formation and soft phonon mode in the Holstein model
• Phonon mechanism in the most dilute superconductor: n-type SrTiO3
• High-throughput discovery of high-temperature conventional superconductors
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Hole-Doped Room-Temperature Superconductivity in H${}_3$S${}_{1-x}$Z${}_x$ (Z=C, Si)
• Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling
• Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands
• A bound on superconducting $T_c$'s
• Pseudogap crossover in the electron-phonon system
• Notes on calculating temperature of the superconducting transition: interacting fermi gas and phonon mechanisms in non-adiabatic regime
• High Temperature Superconductivity in FeSe Monolayers
• On peculiarities of superconductivity in the single-layer FeSe/SrTiO3 interfa
• Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials
• Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems
• Antiadiabatic phonons, Coulomb pseudopotential and superconductivity in Eliashberg - McMillan theory
• Electron - phonon coupling in Eliashberg - McMillan theory beyond adiabatic approximation
• Antiadiabatic Phonons and Superconductivity in Eliashberg-McMillan Theory

Cited by in corpus (5)

• Upper limit for superconducting transition temperature in Eliashberg-McMillan theory
• Strong-coupling theory of condensate-mediated superconductivity in 2D materials
• Instability of metals with respect to strong electron-phonon interaction
• Collective modes in the charge-density wave state of K${}_{0.3}$MoO${}_3$: The role of long-range Coulomb interactions revisited
• Upper limit for superconducting transition temperature in electron-phonon superconductors: very strong coupling