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If history teaches us anything, it is that the next breakthrough in superconductivity will not be the result of surveying the history of past breakthroughs, as they have almost always been a matter of serendipity resulting from undirected exploration into new materials. Still, there is reason to reflect on recent advances, work toward higher T_c of even an incremental nature, and recognize that it is important to explore avenues currently believed to be unpromising even as we attempt to be rational. In this paper we look at two remarkable new unusually high temperature superconductors (UHTS), MgB2 with Tc=40 K and (in less detail) high pressure Li with Tc=20 K, with the aim of reducing their unexpected achievements to a simple and clear understanding. We also consider briefly other UHTS systems that provide still unresolved puzzles; these materials include mostly layered structures, and several with strongly bonded C-C or B-C substructures. What may be possible in phonon-coupled superconductivity is reconsidered in the light of the discussion.
Discovery of high-temperature superconductivity in hydrogen-rich compounds has fuelled the enthusiasm for finding materials with more promising superconducting properties among hydrides. However, the ultrahigh pressure needed to synthesize and mainta
Motivated by the observation of two distinct superconducting phases in the moireless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superco
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We have evaluated the total carrier mass enhancement factor f_{t} for MgB_{2} from two independent experiments (specific heat and upper critical field). These experiments consistently show that f_{t} = 3.1pm0.1. The unusually large f_{t} is incompati
I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the ene