Anisotropic resistivity and superconducting instability in ferroelectric metals

Funding Information: Acknowledgments. We thank the Pirinem School of Theoretical Physics where all work was initiated for the warm hospitality. We thank A. T. Burkov and A. Y. Zyuzin for helpful discussions. V.A.Z. thanks A. Kumar and D. L. Maslov for hospitality during his stay at the UF. V.A.Z. is supported by the Russian Foundation for Basic Research (Grant No. 20-52-12 013), Deutsche Forschungsgemeinschaft (Grant No. EV 30/14-1) cooperation, and by the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS. A.A.Z. was supported by the Academy of Finland (Project No. 308339) and, in part, by the Academy of Finland Centre of Excellence program (Project No. 336810). Publisher Copyright: © 2022 American Physical Society.We propose a theoretical model of a ferroelectric metal where spontaneous electric polarization coexists with the conducting electrons. In our model we adopt a scenario when conducting electrons interact with two soft transverse optical phonons, generalize it to the case when there is a spontaneous ferroelectric polarization in the system, and show that a linear coupling to the phonons emerges as a result. We find that this coupling results in anisotropic electric transport which has a transverse to the current voltage drop. Importantly, the obtained transverse component of the resistivity has distinct linear dependence with temperature. Moreover, we show that the coupling enhances superconducting transition temperature of the ferroelectric metal. We argue that our results help to explain recent experiments on ferroelectric strontium titanate as well as provide new experimental signatures to look for.Peer reviewe