Ferroelectric Order and Enhanced Interfacial Superconductivity in Lightly-Doped Quantum Paraelectric KTa$_{1-x}$Nb$_x$O$_3$

Abstract

Ferroelectric quantum criticality in perovskite oxides offers a fertile ground for emergent collective phenomena. Here we develop a first-principles-inspired quantum-statistics-based theoretical analysis of the ferroelectric order and interfacial superconductivity in lightly-doped quantum paraelectric, niobium (Nb)-doped KTaO$_3$. We demonstrate that local distortions induced by the doped Nb atoms beyond its quantum critical composition induce a long-range ferroelectric order. The predicted dielectric properties quantitatively agree with the experimental measurements over the entire temperature range from the symmetry-broken ferroelectric phase across the phase transition to the paraelectric region. As the same soft phonon mode that governs dielectric behavior provides the essential pairing channel for interfacial superconductivity of KTaO$_3$, we predict a pronounced enhancement of this superconductivity on (111) surface when the system is tuned to its quantum-critical composition via Nb doping, providing a concrete avenue for experimental verification. This finding establishes ferroelectric quantum criticality as a unique design principle for engineering enhanced superconductivity and discovering emergent quantum phases in polar oxide heterostructures, explicitly suggesting that similar materials-tuning strategies (e.g., epitaxial strain) could be exploited to enhance superconductivity in quantum paraelectric systems.

Figures (4)

• Figure 1: Schematic illustration of the ground state in the presence of random local lattice distortions, showing the spatial distribution of the order parameter (lattice distortion $\phi$). Left and right panels correspond to the doping cases in a classical paraelectric (far away from ferroelectric instability) and a quantum paraelectric (on the verge of ferroelectric instability), respectively, while the middle panel denotes an intermediate case. When impurities seed local polar regions, dilute dipolar distortions cannot drive classical paraelectric into globally ferroelectric state and remain isolated and uncorrelated. In quantum paraelectric, the nearly gapless soft phonon mode efficiently mediates long-range correlations, triggering a collective condensation of the host lattice into globally ferroelectric phase.
• Figure 2: Dielectric behavior of Nb-doped KTaO$_3$. (a) Inverse dielectric function $1/\varepsilon$ at the low-temperature limit for various Nb compositions. (b) Temperature dependence of $1/\varepsilon$ at different Nb doping levels. The solid curves in (a) and (b) represent the theoretical results, while the experimental data (squares) are taken from Ref. 10.1103/physrevlett.39.1158. In panel (b), because the experimentally reported Nb compositions may contain calibration uncertainties, doping compositions in our theoretical calculations are adjusted slightly by aligning $1/\varepsilon(T=0,x)$ to match the experimental data. (c) Zero-point polarization and (d) transition temperature as functions of Nb concentration. The circles correspond to our calculated results, and the dashed lines represent the empirical relations proposed experimentally 10.1103/physrevlett.39.1158. We set $\phi = 0.304\pi$, corresponding to polarization along the [100] direction and the measurement field applied along [111] direction.
• Figure 3: (a) Carrier density dependence of the superconducting onset temperature $T_{\rm os}^{\rm SC}$ of the 2DEG formed at undoped KTaO$_3$ (111) interface. Experimental data are taken from Ref. 10.1038/s41467-023-36309-2 for EuO/KTaO$_3$ (111) interface. b Theoretical prediction of $T_{\rm os}^{\rm SC}$ (solid curve) and renormalized soft-phonon gap (dashed curve) as a function of Nb doping for interfacial superconductivity at the EuO/KTa$_{1-x}$Nb$_x$O$_3$(111) interface, showing a pronounced maximum and minimum near the quantum critical composition ($x=0.8\%$), respectively.
• Figure SIV: Fitted parameters $b_0(x)$ (left panel) and $\kappa(x)$ (right panel) as functions of Nb composition $x$. Here, $b_0(0)=0.37\times(2\pi)^3/\varepsilon_0$ (undoped case). The fits yield $b_0(x)/b_0(0)\approx0.65\exp(-100x)+0.35$, showing a rapid suppression of the anharmonic coefficient with Nb doping followed by saturation, consistent with a self-consistent-like renormalization of the polarization nonlinearity. In contrast, $\kappa(x)$ increases approximately linearly with $x$, reflecting the enhanced polarization–defect orientational coupling as the dopant concentration rises.