Charge transport in a polar metal

The fate of electric dipoles inside a Fermi sea is an old issue, yet poorly explored. Sr$${}_{1-x}$$1−xCa$${}_{x}$$xTiO$${}_{3}$$3 hosts a robust but dilute ferroelectricity in a narrow ($$0.0018\ <\ x\ <\ 0.02$$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 Sr$${}_{1-x}$$1−xCa$${}_{x}$$xTiO$${}_{3-\delta }$$3−δ, documenting the evolution of resistivity with increasing carrier concentration ($$n$$n). Below a threshold carrier concentration, $${n}^{* }(x)$$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 $$7.9\pm 0.6$$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 $$n\ <\ {n}^{* }(x)$$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 $$n\ge {n}^{* }(x)$$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.