Theory of superconductivity due to quadratic coupling to near-critical transverse phonons.

Superconductivity near the quantum ferroelectric critical point is the subject of active research due to both conceptual interest in systems with competing order parameters, and practical need to understand peculiar superconductivity in very diluted metal Strontium Titanate (STO) , which keeps being superconducting down to tiny  concentrations ~ 10^17 electrons per cubic centimeters. Fermi energy is much below Debye energy in so much diluted metal,  rendering classical Migdal-Eliashberg approach to phonon-induced superconductivity inapplicable.   Surprisingly enough,  the first microscopic theory of superconductivity, developed by Bardeen, Cooper and Schrieffer, is strongly relevant to this case.    I will show that interaction of electron density with a pair of  two (virtual) soft  transverse optical phonons [1]  leads to static attractive potential between electrons whose  decay length scales inversely with soft optical gap.  in pristine STO this length is close to 3 nm, thus dilute metal with concentration below 10^18 can be considered as a Fermi-gas with local attraction, those superconductivity was treated in details in Ref.[2]. The proposed model leads to the dependence of critical temperature in electron concentration  in agreement with experimental data [3] for low doping. In addition, I will show that suppression of Tc by hydrostatic pressure [4] and strong increase of Tc due to isotopic substitution 16 O →18 O observed in [5]  are both  explained within the same theory.   The talk is based upon the results published in [6].

[1] K. L. Ngai, Phys. Rev. Lett. 32, 215 (1974);

[2] L.P.Gor’kov and T.K.Melik-Barkhudarov, Sov.Phys. -JETP 40, 1452-1458 (1961)

[3] Xiao Lin, et al, Phys. Rev. Lett. 112, 207002 (2014).

[4] C. Enderlein et al, , Nature Comm. (2020), https://doi.org/10.1038/

[5] A. Stucky et al, Scientific Reports, 6:37582 (2016) | DOI: 10.1038/srep37582

[6]  D.E.Kiseliov and M.V.Feigel'man, arxiv:2106.09530