Superconducting materials: Judge and jury of BCS-electron–phonon theory

By a recent count, there are 32 different classes of superconducting materials [Physica C: Special Issue, “Superconducting materials: conventional, unconventional and undetermined. Dedicated to Theodore H. Geballe on the year of his 95th birthday,” edited by J. E. Hirsch, M. B. Maple, F. Marsiglio (▪, 2015), Vol. 514, pp. 1–444.], only 12 of which are generally believed to be “conventional,” i.e., described by the conventional BCS-electron–phonon theory of superconductivity. In this Perspective, I critically examine the successes and failures of the conventional theory to describe conventional superconductors and discuss what is understood and not understood about hydrogen-rich materials claimed to be high temperature conventional superconductors under high pressure. I argue that the materials' evidence accumulated to date calls for dethroning the conventional theory of its privileged status and seriously explore the alternative possibility that a single theory, different from the conventional theory, may describe superconductivity of all materials in a unified way.