A ferroelectric quantum phase transition inside the superconducting dome of Sr$_{1-x}$Ca$_{x}$TiO$_{3-δ}$

Abstract: SrTiO${3}$, a quantum paraelectric, becomes a metal with a superconducting instability after removal of an extremely small number of oxygen atoms. It turns into a ferroelectric upon substitution of a tiny fraction of strontium atoms with calcium. The two orders may be accidental neighbors or intimately connected, as in the picture of quantum critical ferroelectricity. Here, we show that in Sr${1-x}$Ca${x}$TiO${3-\delta}$ ($0.002<x<0.009$, $\delta<0.001$) the ferroelectric order coexists with dilute metallicity and its superconducting instability in a finite window of doping. At a critical carrier density, which scales with the Ca content, a quantum phase transition destroys the ferroelectric order. We detect an upturn in the normal-state scattering and a significant modification of the superconducting dome in the vicinity of this quantum phase transition. The enhancement of the superconducting transition temperature with calcium substitution documents the role played by ferroelectric vicinity in the precocious emergence of superconductivity in this system, restricting possible theoretical scenarios for pairing.

Ferroelectric Quantum Phase Transition in Sr${1-x}$Ca${x}$TiO$_{3-\delta}$

The paper investigates the interplay between ferroelectric order, metallicity, and superconductivity in the perovskite system Sr${1-x}$Ca${x}$TiO${3-\delta}$. This material provides a remarkable platform to explore these phenomena due to the distinct ability of SrTiO${3}$ to exhibit superconductivity upon minimal doping and to demonstrate ferroelectric behavior through calcium substitution.

Summary and Key Observations

The authors report several pivotal findings that uncover intricate interactions among competing quantum orders in Sr${1-x}$Ca${x}$TiO$_{3-\delta}$:

1. Coexistence of Ferroelectricity and Metallic State: The team observed a coexisting ferroelectric-like order within a dilute metallic state in a specific range of Ca content (0.002 < x < 0.009) and minimal oxygen vacancies. The data indicate that the ferroelectric transition, while structurally apparent in the insulating form, persists even in the dilute metallic form, marked by anomalies in electric resistivity and supplemented by corroborating thermal expansion and Raman spectroscopy data.

2. Impact on the Superconducting Dome: The paper discusses a notable enhancement in the superconducting transition temperature (T$_c$) upon calcium substitution. Within a narrow doping concentration regime, superconductivity not only coexists with but also appears to be enhanced by the nearness of the ferroelectric order. The authors propose that fluctuations associated with the ferroelectric quantum phase transition might contribute to pairing mechanisms leading to superconductivity.

3. Quantum Phase Transition: The critical observation that a quantum phase transition could suppress the ferroelectric order at a carrier density that depends on the calcium content suggests complex screening interactions at play. The authors speculate that Friedel oscillations may interfere with ferroelectric dipole alignment, leading to the loss of ferroelectricity past a threshold electron density.

4. Implications for Theories of Superconductivity: Due to the enhancement of superconducting properties in proximity to a ferroelectric phase, these observations provide substantial input for theoretical models proposing ferroelectric fluctuations as a mechanism for superconductivity in SrTiO$_{3}$. The study corroborates theoretical frameworks suggesting that tuning the ferroelectric parameter space could directly modify superconducting behavior, engaging with broader questions of quantum critical phenomena.

Implications and Future Directions

This investigation contributes critically to the understanding of the complex relationship between ferroelectricity, metallicity, and superconductivity. By demonstrating how ferroelectric-like states can persist in a metallic environment, the resulting phase diagram opens avenues for exploring unconventional superconductors where ferroelectric interactions are significant.

In terms of future research directions, further theoretical and experimental efforts are necessary to precisely elucidate the roles of different bosonic modes (such as phonons or plasmons) in producing the observed effects. Additionally, detailed studies using advanced spectroscopy and scattering techniques could probe the microscopic origins of the coexistence phenomenon and deepen the understanding of the dipolar interactions in the metallic state.

This paper reinforces the growing significance of engineered quantum phase transitions and their influence on material properties, motivating continued interdisciplinary investigations into emergent phenomena in complex oxide systems.