Charge Transport in a Polar Metal

TL;DR

This study investigates how dilute ferroelectricity and dipole interactions influence charge transport in Sr$_{1-x}$Ca$_x$TiO$_{3- ext{delta}}$, revealing a threshold carrier density where the polar phase transition disappears and complex temperature-dependent resistivity behaviors emerge.

Contribution

It provides the first detailed analysis of the interplay between ferroelectric dipoles and metallic conduction in a polar metal with dilute ferroelectricity, highlighting the dipole-dipole interaction's role in phase transition suppression.

Findings

Phase transition signature diminishes when one electron per ~8 dipoles is introduced.

Resistivity exhibits non-monotonic temperature dependence below the threshold carrier density.

Resistivity follows a T-square law above the threshold, with upturns likely due to oxygen vacancies.

Abstract

The fate of electric dipoles inside a Fermi sea is an old issue, yet poorly-explored. Sr$_{1-x}$Ca$_x$TiO$_{3}$ hosts a robust but dilute ferroelectricity in a narrow ($0.002<x<0.02$) 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$_{1-x}$Ca$_x$TiO$_{3-\delta}$, 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 $7.9\pm0.6$ 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 $n\geq n^*(x)$, 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.