Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics

Abstract

Experimental evidence suggests that superconductivity in SrTiO${}_3$ is mediated by a soft transverse ferroelectric mode which, according to conventional theories, has negligible coupling with electrons. A phenomenological Rashba type coupling has been proposed on symmetry arguments but a microscopic derivation is lacking. Here we fill this gap and obtain a linear coupling directly from a minimal microscopic model of the electronic structure. We find that the effective electron-electron pairing interaction has a strong momentum dependence. This yields an unusual situation in which the leading $s$-wave channel is followed by a sub-leading $p$-wave state which shows a stronger pairing instability than the $d$-wave state. The bare Rashba coupling constant is estimated for the lowest band of doped SrTiO${}_3$ with the aid of first-principles computations. Extrapolating the estimation to the multi-band regime we show that it can explain bulk superconductivity. For densities where the Meissner effect has not been observed an extra softening due to inhomogeneities is needed to explain the zero resistance state.

10 pages, 3 figures

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• Synergetic ferroelectricity and superconductivity in zero-density Dirac semimetals near quantum criticality
• A theory of criticality for quantum ferroelectric metals
• Anisotropic Rashba coupling to polar modes in KTaO3
• Majorana-Weyl cones in ferroelectric superconductors
• Phonon-Induced Collective Modes in Spin-Orbit Coupled Polar Metals
• Modeling polar order in compressively strained SrTiO${}_3$
• Superconductivity in tin telluride films grown by molecular beam epitaxy
• Electronic spin susceptibility in metallic strontium titanate
• Effects of Homogeneous Doping on Electron-Phonon Coupling in SrTiO3
• Spin-dependent anisotropic electron-phonon coupling in KTaO${}_3$
• Superconductivity from the Slater mode: Application to KTaO3 heterostructures
• Effects of doping on polar order in SrTiO${}_3$ from first-principles modeling