A theory of criticality for quantum ferroelectric metals

TL;DR

This paper develops a comprehensive theoretical framework for understanding the quantum critical behavior of ferroelectric metals, revealing complex phase transitions and the influence of external strain on their phase diagrams.

Contribution

It introduces a minimal model coupling electrons to polar phonons with spin-orbit interaction, analyzing quantum criticality, phase transitions, and the effects of strain in ferroelectric metals.

Findings

Identification of Fermi and non-Fermi liquid phases.

Prediction of enhanced pairing in singlet and triplet channels.

Phase diagram with second order, first order, and finite-momentum transitions.

Abstract

A variety of compounds, for example doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the normal state properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. Starting from a minimal model of electrons coupled to a \emph{transverse} polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second order, first order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.