Enhancing superconductivity with resonant antishielding and topological plasmon-polarons

By employing ab initio Migdal-Eliashberg calculations, we predict a fourfold enhancement of the superconducting critical temperature of $\mathrm{Mg}{\mathrm{B}}_{2}$ when proximity-coupled to the topological crystal ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. We support this result with calculations using the general Leavens scaling method. We show that this effect is a result of dynamic resonant antishielding of Cooper pairs by plasmon-polarons of Dirac electrons in the topological crystal. Our calculations show that such superconductivity enhancement varies strongly with Coulomb coupling between plasmon- polarons and Cooper pairs, with a pronounced maximum of ${T}_{\mathrm{c}}$ at a critical value of the coupling parameter. This feature is universal, and so can occur in other superconductor-topological crystal combinations, including with nonphonon mediated superconductors. We discuss methods to experimentally optimize the key coupling parameter.