Quantifying Nonadiabaticity in Major Families of Superconductors

Abstract

The classical Bardeen–Cooper–Schrieffer and Eliashberg theories of the electron–phonon-mediated superconductivity are based on the Migdal theorem, which is an assumption that the energy of charge carriers, (Formula presented.), significantly exceeds the phononic energy, (Formula presented.), of the crystalline lattice. This assumption, which is also known as adiabatic approximation, implies that the superconductor exhibits fast charge carriers and slow phonons. This picture is valid for pure metals and metallic alloys because these superconductors exhibit (Formula presented.). However, for n-type-doped semiconducting SrTiO3, this adiabatic approximation is not valid, because this material exhibits (Formula presented.). There is a growing number of newly discovered superconductors which are also beyond the adiabatic approximation. Here, leaving aside pure theoretical aspects of nonadiabatic superconductors, we classified major classes of superconductors (including, elements, A-15 and Heusler alloys, Laves phases, intermetallics, noncentrosymmetric compounds, cuprates, pnictides, highly-compressed hydrides, and two-dimensional superconductors) by the strength of nonadiabaticity (which we defined by the ratio of the Debye temperature to the Fermi temperature, (Formula presented.)). We found that the majority of analyzed superconductors fall into the (Formula presented.) band. Based on the analysis, we proposed the classification scheme for the strength of nonadiabatic effects in superconductors and discussed how this classification is linked with other known empirical taxonomies in superconductivity. © 2022 by the author.