Plasmon-Phonon Superconductivity in Strontium Titanate*

Strontium titanate (STO) is a bulk insulator that becomes a semiconducting superconductor at remarkably low carrier densities - below 10¹⁷ cm^-3 - with a characteristic superconducting dome as a function of doping which peaks at T_c~300mK, all in very close proximity to a ferroelectric quantum critical point. The normal state is perhaps even more enigmatic. I will give a biased introduction to this fascinating material, then I will investigate a scenario of superconductivity mediated by coupling to a strongly anti-adiabatic longitudinal optic phonon, by extending a simple Engelsberg-Schrieffer theory of electron-phonon coupling to include the effects of electronic Coulomb interactions. For the carrier densities of interest, there is a "cavity enhancement" of superconductivity by the material's open plasmons, which hybridize strongly with LO mode. Working within the cumulant expansion, I calculate the spectral signatures of this unusual regime to compare to photoemission¹ and tunneling² experiments, as well as the superconducting phase diagram.

¹Wang et al. Nat Mater 15, 835 (2016)
²Swartz et al. PNAS 115, 1475 (2018)