Oxide heterostructures built by layering the Mott insulator LaTiO3 and the band insulator SrTiO3 host an interfacial electron gas whose charge profile, orbital polarization, and magnetism are shaped by large ferroelectric-like distortions of the TiO6 octahedra. Okamoto, Millis, and Spaldin [Phys. Rev. Lett. 97, 056802 (2006)] computed the relaxed structure with LDA+U and, via a Hartree-Fock treatment of a realistic three-band (t2g) tight-binding model, predicted novel xy-orbital ordering at the interface, but they explicitly flagged three unresolved aspects: the Hartree-Fock phase diagrams say nothing reliable about excitation spectra, finite-temperature properties, and dynamics; the phenomenological dielectric constant cannot capture the highly enhanced long-wavelength nonlinear dielectric response of quantum-paraelectric SrTiO3 (overestimating how fast the interfacial charge density decays at low densities, ntot≲0.05n_{\mathrm{tot}}\lesssim 0.05 electrons per unit cell); and the predicted screening and charge profiles are sensitive to the exchange-correlation treatment and to the handling of localized La f states. Establish, with a many-body treatment beyond static mean field, the excitation energies, ordering transition temperatures, and dynamical properties of the interface orbital and magnetic phases of the relaxed LaTiO3/SrTiO3 superlattice, coupled self-consistently to the nonlinear lattice polarizability of SrTiO3, with a controlled account of the exchange-correlation and localized-state dependence. Charge-self-consistent DFT+DMFT (Lechermann et al., 2013) has treated the paramagnetic spectral physics of the relaxed structure at room temperature, and DFPT-based nonlinear polarization models (Hamann et al., 2006) have repaired the charge-decay profile at the band-structure level, but no published work establishes the correlated ordering temperatures, phase diagram, or collective dynamics, nor unifies correlation physics with nonlinear long-wavelength phonon screening.

Background

Perovskite oxide heterostructures stack crystalline layers with the formula ABO3 (a cube of corner-sharing BO6 octahedra with A-site cations in between) with atomic-layer control. When a layer of LaTiO3, a Mott insulator (an insulator whose gap arises from electron-electron repulsion U rather than band filling), is embedded in SrTiO3, a band insulator, the substitution of trivalent La for divalent Sr donates one electron per La, and charge redistributes ('electronic reconstruction') over several Ti layers next to the interface, producing a confined, high-density two-dimensional electron gas. This was first measured by Ohtomo et al. (2002), who used scanning transmission electron microscopy to map the Ti 3d occupancy across LaTiO3 monolayers in SrTiO3 and found a roughly 2-3 unit-cell-wide conducting region.

Theory developed in stages. Okamoto and Millis (2004) introduced the electronic-reconstruction picture and studied a model Mott/band-insulator heterostructure with single-site dynamical mean field theory (DMFT, a method that treats local quantum and thermal correlation effects exactly by mapping each site onto a self-consistent quantum impurity model, but neglects spatial correlations). Okamoto, Millis, and Spaldin (2006) then computed the actual atomic structure of LaTiO3/SrTiO3 superlattices with LDA+U (the local-density approximation corrected by a Hubbard repulsion U on the Ti 3d states, with U=5U=5 eV and Hund's exchange J=0.64J=0.64 eV; an additional Uf=11U_f=11 eV was required on the La 4f states to push these otherwise spuriously low-lying empty bands away from the Fermi level). They found large ferroelectric-like polar distortions of the TiO6 octahedra near the La layers, of order 0.1-0.2 Angstrom, which screen the interfacial charge, reduce the central-layer density into agreement with experiment, and modify the Ti-O-Ti hopping amplitudes. Fitting a three-band tight-binding model (the three t2g orbitals dxy, dxz, dyz, with rotationally invariant 'Kanamori' on-site Coulomb and exchange interactions) to the relaxed and unrelaxed band structures, they solved the model in the unrestricted Hartree-Fock approximation (a static mean-field treatment of the interactions, equivalent in spirit to DFT+U) and computed ground-state spin-orbital phase diagrams versus interaction strength U and La-layer thickness n. The relaxation shifts phase boundaries and favors a novel uniform xy-orbital-polarized ordered phase (Oxy) at the interface that does not occur in bulk LaTiO3 or in the hypothetical unrelaxed structure.

Three limitations of that work frame the present problem. First, Hartree-Fock is a zero-temperature static mean field: it describes symmetry-broken ground states but misses the competing correlated paramagnetic state, dynamical quasiparticle and collective-mode spectra, and all finite-temperature ordering transitions, so the predicted orbital and magnetic phases lack excitation energies, transition temperatures, and dynamics. Second, the Hartree-Fock screening was modeled by a spatially uniform dielectric constant (ε=15\varepsilon=15 for the relaxed structure), whereas SrTiO3 is a quantum paraelectric, a crystal that remains incipient-ferroelectric down to low temperature with a giant, strongly nonlinear and frequency-dependent dielectric response driven by soft transverse optical phonons; the constant-epsilon model was shown by the authors themselves to overestimate the rate at which the conduction-band charge density decays far from the La layers in the low-density regime (ntot≲0.05n_{\mathrm{tot}}\lesssim 0.05 electrons per unit cell), precisely because the true nonlinear long-wavelength lattice polarizability differs from any linear dielectric constant. Contemporaneously, Hamann, Muller, and Hwang (2006) treated the same superlattices within plain GGA density functional theory (no Hubbard U) plus density-functional perturbation theory (DFPT, a linear-response technique that computes phonon frequencies and the electronic/ionic dielectric contributions from a single set of first-principles calculations); they found similar distortions but reported that the lattice polarization slightly overscreens the La layer and produces a spurious charge peak at the center of their supercell, and they showed that anharmonic finite-temperature effects must be included to reproduce the measured charge densities. Third, the Okamoto-Millis-Spaldin results depended visibly on methodological choices - omitting UfU_f on the La f states reduces the predicted distortions by about 50%, and the GGA (no-U) treatment disagreed on the screening and charge profile - so the dependence of the predicted screening and charge profiles on the exchange-correlation approximation and on the treatment of localized states remained undetermined.

Subsequent work has substantially developed the tool set relevant to these limitations. Dynamical mean field theory merged with density functional theory (DFT+DMFT) can treat the correlated paramagnetic metal, compute spectra at finite temperature, and (in charge-self-consistent form) let correlation feed back on the charge distribution; Lechermann, Boehnke, and Grieger (2013) applied exactly this to LaTiO3/SrTiO3 superlattices with the relaxed orthorhombic structure. Multiorbital DMFT with rotationally invariant Kanamori interactions, needed for the three-band t2g problem, was established by Chan, Werner, and Millis (2009) for the bulk model. What no work has yet done, for this system, is combine the three ingredients - realistic relaxed structure, beyond-Hartree-Fock correlations, and the nonlinear long-wavelength lattice polarizability of SrTiO3 - into a theory of the orbital and magnetic phases themselves, including their ordering temperatures and dynamics.

Problem Statement

For LaTiO3/SrTiO3 superlattices with the lattice relaxation computed by Okamoto, Millis, and Spaldin (ferroelectric-like TiO6 distortions near the La layers plus the derived three-band t2gt_{2g} tight-binding parameters and Kanamori interactions, U≈5U\approx 5 eV, J≈0.64J\approx 0.64 eV), establish the orbital and magnetic phase behavior of the interface electron system with a many-body treatment that goes beyond the static Hartree-Fock (DFT+U-level) mean field used in the original work. Specifically: (i) determine the ordering transition temperatures and the correlated paramagnetic state that competes with the predicted ordered phases, including the fate of the novel uniform xy-orbital-polarized interface phase and of the staggered orbital orderings as a function of interaction strength and La-layer thickness; (ii) compute the excitation spectra (quasiparticle dispersions and Hubbard bands -- the incoherent, interaction-scale spectral weight characteristic of Mott systems -- layer- and orbital-resolved) and the dynamical and collective properties of these phases, quantities for which Hartree-Fock is acknowledged to be unreliable; and (iii) couple this correlated-electron physics self-consistently to a treatment of lattice polarizability that captures the highly enhanced nonlinear long-wavelength dielectric response of quantum-paraelectric SrTiO3 - in particular producing quantitatively correct charge-density profiles far from the La layers in the low-density regime (ntot≲0.05n_{\mathrm{tot}}\lesssim 0.05 electrons per unit cell), where the constant-ε\varepsilon screening model is known to overestimate the decay rate - together with a controlled determination of how the predicted screening and charge profiles depend on the exchange-correlation approximation and on the treatment of localized states such as the La 4f levels. A complete answer would constitute a quantitatively reliable, correlation- and lattice-polarization-accurate theory of the orbital and magnetic phases of this prototypical Mott/band-insulator interface, and would make contact with experimental probes of the predicted orbital ordering.

References

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