Plasmon-Polaron 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 Tc~300mK, all in very close proximity to a ferroelectric quantum critical point. We 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, we find that the plasmon hybridizes strongly with LO mode with one of the resulting coupled modes inherting the low energy scales of the softening ferroelectric mode. Working within the cumulant expansion, we calculate the spectral signatures of this unusual regime of coupling compare to experiment photoemssion[1] and tunneling[2] experiments, as well as the superconducting phase diagram including self-energy effects beyond one loop.

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