Charge transport in a polar metal

The fate of electric dipoles inside a Fermi sea is an old issue, yet poorly explored. Sr1_-x?Ca_x?TiO₃? hosts a robust but dilute ferroelectricity in a narrow (0.0018 <x <0.02 ?) window of substitution. This insulator becomes metallic by removal of a tiny fraction of its oxygen atoms. Here, we present a detailed study of low-temperature charge transport in Sr1_-x?Ca_x?TiO3_-δ?, documenting the evolution of resistivity with increasing carrier concentration (n ?). Below a threshold carrier concentration, n^*(x ) ?, the polar structural-phase transition has a clear signature in resistivity and Ca substitution significantly reduces the 2 K mobility at a given carrier density. For three different Ca concentrations, we find that the phase transition fades away when one mobile electron is introduced for about 7.9 ±0.6 ? dipoles. This threshold corresponds to the expected peak in anti-ferroelectric coupling mediated by a diplolar counterpart of Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Our results imply that the transition is driven by dipole-dipole interaction, even in presence of a dilute Fermi sea. Charge transport for n <n^*(x ) ? shows a non-monotonic temperature dependence, most probably caused by scattering off the transverse optical phonon mode. A quantitative explanation of charge transport in this polar metal remains a challenge to theory. For n ≥n^*(x ) ?, resistivity follows a T-square behavior together with slight upturns (in both Ca-free and Ca-substituted samples). The latter are reminiscent of Kondo effect and most probably due to oxygen vacancies.