We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a two orders of magnitude difference in the thermal Hall conductivity between $SrTi^{16}O_3$ and $^{18}O$-enriched $SrTi^{18}O_3$ samples. In most temperature ranges, the magnitude of thermal Hall conductivity ($κ_{xy}$) in $SrTi^{18}O_3$ is proportional to the magnitude of the longitudinal thermal conductivity ($κ_{xx}$), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the thermal Hall angle ratio ($|κ_{xy}/κ_{xx}|$) shows anomalously decreasing behavior below the ferroelectric Curie temperature $T_c$ ~$25 K$. This observation suggests a new underlying mechanism, as the conventional scenario cannot explain such differences within the slight change in phonon spectrum. Notably, the difference in magnitude of thermal Hall conductivity and rapidly decreasing thermal Hall angle ratio in $SrTi^{18}O_3$ is correlated with the strength of quantum critical fluctuations in this displacive ferroelectric. This relation points to a link between the quantum critical physics of strontium titanate and its thermal Hall effect, a possible clue to explain this example of an exotic phenomenon in non-magnetic insulating systems.
Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean-free-path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries o…
We report torque magnetometry measurements of an oxide heterostructure consisting of an amorphous Al$_2$O$_3$ thin film grown on a crystalline SrTiO$_3$ substrate ($a$-AO/STO) by atomic layer deposition. We find a torque response that resembles previous studies of crystalline LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterointerfaces, consistent with strongly anisotropic magnetic ordering in the plane of the interface. Unlike crystalline LAO, amorphous Al$_2$O$_3$ is nonpolar, indicating that planar magnetism at an oxide interface is possible without the strong internal electric fields generated within th…
The relaxation rate in Nb-doped strontium titanate involving different scattering channels is investigated theoretically. It is demonstrated that the total relaxation rate in SrTiO_{3} is provided mainly by two mechanisms. The Baber electron-electron scattering with participation of both Coulomb and phonon-mediated electron-electron interactions provides the T^{2}-dependence of the relaxation rate. The scattering on the potential landscape caused by impurities is responsible for the residual relaxation rate at low temperatures. A good agreement with experiment is achieved accounting for all ph…
The photoluminescence (PL) spectra of Ar-ion irradiated single crystals of SrTiO3 (STO) excited by the 325 nm line of a He-Cd laser are compared with those of pristine crystals, epitaxial films, and amorphous layers of STO at several temperatures down to 20 K. The 550 eV Ar-beam irradiation activates three distinctly visible PL peaks: blue (~430 nm), green (~550 nm), and infrared (~820 nm) at room temperature, making the photoluminescence multicolored. The abrupt changes in PL properties below ~100 K are discussed in relation with the antiferrodistortive structural phase transition in SrTiO3 f…
We investigated the nanosecond-scale time decay of the blue-green light emitted by nominally pure SrTiO$_3$ following the absorption of an intense picosecond laser pulse generating a high density of electron-hole pairs. Two independent components are identified in the fluorescence signal that show a different dynamics with varying excitation intensity, and which can be respectively modeled as a bimolecular and unimolecolar process. An interpretation of the observed recombination kinetics in terms of interacting electron and hole polarons is proposed.
We show that the Bloch states in the conduction band of SrTiO$_3$ arise from the interplay between highly anisotropic hopping in sub-bands derived from the Ti $t_{2g}$ orbitals and spin-orbit coupling that mixes these orbitals. Because of the nearly flat-band characteristics for one of the principal axes, at sufficiently high doping these Bloch states become unstable with respect to electron interactions, resulting in Mott-like singlet correlations. These findings may be relevant to the anomalous electronic properties of SrTiO$_3$, including its unusual superconductivity.
Cooling oxygen-deficient strontium titanate to liquid-helium temperature leads to a decrease in its electrical resistivity by several orders of magnitude. The temperature dependence of resistivity follows a rough T$^{3}$ behavior before becoming T$^{2}$ in the low-temperature limit, as expected in a Fermi liquid. Here, we show that the roughly cubic resistivity above 100K corresponds to a regime where the quasi-particle mean-free-path is shorter than the electron wave-length and the interatomic distance. These criteria define the Mott-Ioffe-Regel limit. Exceeding this limit is the hallmark of …
Electric double layer transistor configurations have been employed to electrostatically dope single crystals of insulating SrTiO_{3}. Here we report on the results of such doping over broad ranges of temperature and carrier concentration employing an ionic liquid as the gate dielectric. The surprising results are, with increasing carrier concentration, an apparent carrier-density dependent conductor-insulator transition, a regime of anomalous Hall effect, suggesting magnetic ordering, and finally the appearance of superconductivity. The possible appearance of magnetic order near the boundary b…
Extended Mean-Field Theory for the 2D Hubbard Model in Degenerate Dilute Electron Gases: Fluctuations, Superconducting Dome, and Interaction Mechanisms in Strontium Titanate
We present a study of thermal conductivity, $κ$, in undoped and doped strontium titanate in a wide temperature range (2-400 K) and detecting different regimes of heat flow. In undoped SrTiO$_{3}$, $κ$ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such a behavior, previously observed in a handful of solids, has been attributed to a Poiseuille flow of phonons, expected to arise when momentum-conserving scattering events outweigh momentum-degrading ones. The effect disappears in presence of dopants. In SrTi$_{1-x}$Nb$_{x}$O$_{3}$, a significant redu…
We analyze a minimal model of SrTiO3, such as has been historically used to analyze the superconducting state. Treating the electron-phonon and electron-electron interactions on an equal footing, we calculate the normal state properties, focusing on the spectral function. We find a density-driven crossover caused mostly by the adiabaticity of the bosonic modes, but the spectral features of our theory are dominated by coupled plasmon-phonon oscillations rather than the bare phonon features seen in experiment.
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the "extreme quantum limit" (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult, however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate, which remain good bulk conductors down to very low temperatures and high…
Room-temperature metallicity of lightly doped SrTiO$_3$ is puzzling, because the combination of mobility and the effective mass would imply a mean-free-path (mfp) below the Mott Ioffe Regel (MIR) limit and a scattering time shorter than the Planckian time ($τ_P=\hbar/k_BT$). We present a study of electric resistivity, Seebeck coefficient and inelastic neutron scattering extended to very high temperatures, which deepens the puzzle. Metallic resistivity persists up to 900 K and is accompanied by a large Seebeck coefficient whose magnitude (as well as its temperature and doping dependence) indica…
It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in presence of magnetic field. Recent studies of thermal Hall conductivity, $κ_{xy}$, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of $κ_{xy}$ in quantum paraelectric SrTiO$_3$, which is a non-magnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as 'giant'. Remarkably, $κ_{xy}(T)$ and $κ(T)$ peak at the same temperature and the …
We address the long-standing question of the nature of oxygen vacancies in strontium titanate, using a combination of density functional theory and dynamical mean-field theory (DFT+DMFT) to investigate in particular the effect of vacancy-site correlations on the electronic properties. Our approach uses a minimal low-energy electronic subspace including the Ti-$t_{2g}$ orbitals plus an additional vacancy-centered Wannier function, and provides an intuitive and physically transparent framework to study the effect of the local electron-electron interactions on the excess charge introduced by the …
SrTiO$_3$, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here we show that the amplitude of THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: i) heat is mostly tra…
Doped strontium titanate SrTiO$_3$ (STO) is one of the most dilute superconductors known today. The fact that superconductivity occurs at very low carrier concentrations is one of the two reasons that the pairing mechanism is not yet understood, the other is the role played by the proximity to a ferroelectric instability. In undoped STO, ferroelectric order can in fact be stabilized by substituting $^{16}$O with its heavier isotope $^{18}$O. Here we explore the superconducting properties of doped and isotope-substituted SrTi$(^{18}$O$_{y}^{16}$O$_{1-y})_{3-δ}$ for $0\le y \le 0.81$ and carrier…
Room temperature ferromagnetism was characterized for thin films of SrTi$_{0.6}$Fe$_{0.4}$O$_{3-δ}$ grown by pulsed laser deposition on SrTiO$_{3}$ and Si substrates under different oxygen pressures and after annealing under oxygen and vacuum conditions. X-ray magnetic circular dichroism demonstrated that the magnetization originated from Fe$^{2+}$ cations, whereas Fe$^{3+}$ and Ti$^{4+}$ did not contribute. Films with the highest magnetic moment (0.8 μB per Fe) had the highest measured Fe$^{2+}$:Fe${^3+}$ ratio of 0.1 corresponding to the largest concentration of oxygen vacancies (δ = 0.19). …
Spin-chiral electron-phonon coupling in metallic strontium titanate
Department of Physics, Faculty of Science, University of Zagreb（萨格勒布大学理学院物理系）；School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学学院）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）；Laboratoire National des Champs Magnétiques Intenses（强磁场国家实验室）；Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；Donostia International Physics Centre（圣塞巴斯蒂安国际物理中心）；Department of Physics, Bar-Ilan University（巴伊兰大学物理系）
We present the first study of thermal conductivity in superconducting SrTi$_{1-x}$Nb$_{x}$O$_{3}$, sufficiently doped to be near its maximum critical temperature. The bulk critical temperature, determined by the jump in specific heat, occurs at a significantly lower temperature than the resistive T$_{c}$. Thermal conductivity, dominated by the electron contribution, deviates from its normal-state magnitude at bulk T$_{c}$, following a Bardeen-Rickayzen-Tewordt (BRT) behavior, expected for thermal transport by Bogoliubov excitations. Absence of a T-linear term at very low temperatures rules out…
