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. Photoemission[1] and tunneling[2] have revealed multiple phonon replica bands, and the challenge to theory is to reconcile these observations of a very strongly coupled normal state with the apparently conventional weakly-coupled BCS superconducting state[3]. We propose a simple model that extends an Engelsberg-Schrieffer theory of electrons coupled to a single longitudinal optic (LO) phonon mode to self-consistently include the effects of electronic 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. We calculate spectral signatures of our model and the superconducting phase diagram, including vertex corrections crucial in this strongly-coupled regime, and compare to experiment.

[1] Wang et al. Nat Mater 15, 835 (2016)
[2] Swartz et al. PNAS 115, 1475 (2018)
[3] Thiemann et al. PRL 120, 237002 (2018)