FirstPrinciples ManyBody Investigation of Correlated Oxide Heterostructures: FewLayerDoped SmTiO

Correlated oxide heterostructures pose a challenging problem in condensed matter research due to their structural complexity interweaved with demanding electron states beyond the effective singleparticle picture. By exploring the correlated electronic structure of SmTiO doped with few layers of SrO, we provide an insight into the complexity of such systems. Furthermore, it is shown how the advanced combination of band theory on the level of KohnSham density functional theory with explicit manybody theory on the level of dynamical meanfield theory provides an adequate tool to cope with the problem. Coexistence of bandinsulating, metallic and Mottcritical electronic regions is revealed in individual heterostructures with multiorbital manifolds. Intriguing orbital polarizations, that qualitatively vary between the metallic and the Mott layers are also encountered.
1 Introduction
Research on oxide heterostructures emerged in the beginning of the 2000s as a novel topical
field and belongs nowadays to a key focus in condensed matter and materials science (see e.g.
Refs. 1, 2, 3 for reviews). Thanks to
important advancements in experimental preparation techniques, the design of
oxide materials, e.g. by joint layering of different bulk compounds, opens new possibilities
to devise matter beyond nature’s original conception. Importantly, oxide heterostructures
are not only relevant because of their potentially future technological importance, but they
also challenge known paradigms in condensed matter physics. For instance, the obvious traditional
separation of electronic materials into metals, band insulators or Mott insulators may be
reconsidered in such materials. Since known bulk features of individual oxide
building blocks disperse within a given heterostructure, characterisics of various electronic
signatures may be detected [4, 5]. Notably, the distinguished role of interface
physics within a demanding quantummechanical environment is one of main concerns in this area.
Density functional theory (DFT) in the KohnSham representation is the standard tool for
materials science starting from the atomic scale. However, this theoretical approach has its
flaws for systems where the mutual interaction among the condensed matter electrons is
comparable or even larger than the dispersion energy from hopping on the underlying lattice.
For various reasons, many interesting oxide heterostructures are located in the latter regime,
marking them as correlated oxide heterostructures (COHs). Modeling these fascinating designed
materials, including the possibility for further engineering and prediction of intriguing
phenomenology, therefore asks for a theoretical approach beyond effective singleparticle
theory. The combination of DFT with the explicit manybody framework of dynamical meanfield
theory (DMFT), the socalled DFT+DMFT method, represents such an
approach (see e.g. Ref. 6 for a review).
In the present work, the charge selfconsistent DFT+DMFT framework is put into practice to
examine the correlated electronic structure of Mottinsulating SmTiO doped with a few
layers of SrO in an heterostructure architecture. This illustrates the challenges of COHs
as well as the capabilities of advanced electronic structure theory to address those.
Coexistence of different electronic phases is encountered, ranging from Mottinsulating,
metallic up to bandinsulating.
2 SrO doping layers in SmTiO
The rareearth titanate SmTiO is a distorted perovskite with orthorhombic
crystalsymmetry group. Electronically, it is a Mott insulator in the bulk [7], i.e.
electrons are localized in real space and cannot metallize the compound via hopping because of
the strong Coulomb repulsion. For this system, the mostrelevant Coulomb impact is on the
Ti shell, which is nominally filled with one electron since titanium is in a
formal Ti state. Moreover, calculations show that the electron dominantly
resides in a single effective orbital of kind [5], i.e. orbital polarization
is an important issue.
In the present work, a welldefined doped Mottinsulator shall be investigated in a
heterostructure architecture by inserting layers of SrO into SmTiO,
thereby replacing SmO layers, respectively (see Fig. 1). Because of the
different valence of Sr compared to Sm, this leads to an effective hole doping.
Experimental transport studies of such systems have recently been performed [8, 9].
To model these complex COHs in a firstprinciples setting, superlattices based on 140atom
unit cells are here considered. They consist of 14 TiO layers, and each layer is build
from two symmetryequivalenttreated Ti ions. With the inserted SrO layers, there are then
8 Ti sites different by symmetry, located in different layers (cf. Fig. 1).
The original lattice parameters [7] are brought in the directional
form of the experimental works [8, 9], but without lowering the
symmetry. The original axis is parallel to the doping layer and the original
axes are respectively inclined.
With fixed lattice parameters, all atomic positions in the supercell are structurally
relaxed within DFT(GGA) until the maximum individual atomic force settles below 5 mRyd/a.u..
The lattice distortions introduced by the inserted SrO layers are well captured by this
approach.
Note that the doped case of has been recently studied in detail by a similar
approach [5]. In this respect, the present work advances on this previous study and
renders it possible to follow the evolution of the correlated electronic structure of
heterostructuredoped SmTiO with further SrO layers.
3 Theoretical Approach
The charge selfconsistent DFT+DMFT method combines band theory and manybody theory on
an equal footing. The bandtheoretical aspect is delivered on the DFT level, and through
a downfolding to a correlated subspace of relevant sites and orbitals, electronic
correlations are evaluated in the manybody scope. Those correlations define an electronic
selfenergy that reenters the DFT level in updating the KohnSham potential. Thereby
a selfconsistency cycle is defined that at convergence provides the manybody electronic
structure beyond conventional exchangecorrelation functionals [10, 11, 12].
For the DFT part, a mixedbasis pseudopotential coding [13], based on
normconserving pseudopotentials as well as a combined basis of localized functions and plane
waves, is utilized. We here employ the generalizedgradient approximation (GGA) in the
PerdewBurkeErnzerhof form [14].
Here, we aim for a description of SrO layers in SmTiO.
The three Ti orbitals, splitoff from the remaing orbitals of the full
shell, host the keyrelevant single electron of SmTiO.
The correlated subspace therefore consists of the effective Ti() Wannierlike
functions, i.e. is locally threefold. These functions are obtained
from a projectedlocalorbital formalism [15, 16], using as projection
functions the linear combinations of atomic orbitals. The latter diagonalize the Ti
orbitaldensity matrix from DFT. A band manifold of 60 dominated
KohnSham states at lower energy are used to realize the projection. Local Coulomb
interactions within the correlated subspace in the socalled SlaterKanamori form of
a multiorbtial Hubbard Hamiltonian are parametrized by a Hubbard eV and a
Hund’s coupling eV [17]. The 8 coupled singlesite DMFT impurity
problems in the supercells are, respectively, solved by the continuoustime quantum
Monte Carlo (QMC) scheme [18, 19] as implemented in the TRIQS
package [20, 21].
A doublecounting correction of fullylocalized type [22] is utilized, which
accounts for correlation effects already included on the GGA level. About 4050 DFT+DMFT
iterations (of alternating KohnSham and DMFT impurity steps) are necessary for full
convergence. Note that DFT+DMFT, contrary to conventional DFT, explicitly treats finite
temperature. In all calculations presented in this scope, the temperature was set to
K.
The largescale calculations run in a parallelized computing architecture for the points
of the DFT part as well as for the QMC sweeps. Computations also ask for a sizable memory due
to the demanding supercell structures. Even on supercomputing machines, full convergence for
an individual superlattice at a given finite temperature still asks for several days of
computing time.
4 DFT+DMFT results for fewlayerdoped SmTiO
Key interest is in both, the global behavior as well as the layerresolved physics of these
artifical SrO/SmTiO systems. Importantly, the given structurally welldefined doping
of the Mott insulator, enables an account of the realistic manybody electron states which
is free of the usual disorder effects in common bulkdoped materials.
We first focus on the global electronic system by inspecting the total spectral function,
plotted in Fig. 2. In the effective singleparticle picture of conventional
DFT this function coincides with the density of states (DOS). The relevant DOS building
blocks for the present transitionmetal oxides are a dominantly O spectral part deep
in the occupied region, a Tilike part at low energy and a Tilike
part energetically higher in the unoccupied region.
As a first observation, both theoretical schemes, DFT(GGA) and DFT+DMFT, mark the present
COHs as metallic, in line with experiment [8, 9]. In addition, the case of
doped SmTiO is identified as conducting [8, 9, 5].
For a comparison of the different SrOdoping cases it is important to realize that replacing SmO layers with SrO ones actually results in new finite building blocks of effective SrTiO. In bulk form, the latter perovskite is a band insulator with nominal Ti filling. Thus by increasing the number of SrO layers, the originally Mottinsulating system is replaced in parts by a bandinsulating system. It is a particularly interesting scenario to have the different insulator concepts, i.e. the band insulator from band theory and the Mott insulator from interacting manybody theory, conjoint within a single electronic structure problem. Concretely, this means that the present doping with more and more SrO layers should not simply result in a successive strengthening of the metallic character. There are 28 Ti atoms in the supercell, which from yields also 28 electrons in the occupied part of the spectral function. Each SrO layer, incorporating two Sr sites, adds two holes, resulting in a nominal doping of 1/14 holes per Ti site. Accordingly, from to the Tidominated occupied part of the spectrum shrinks from 28 to 16 electrons, as visualized in Fig. 2. The degree of metallicity is more elusive since to a first approximation encoded in the height and width of the quasiparticle (QP) peak around the Fermi level. For , the QP peak is higher than for , but the width is slighly larger for the latter case. Compared to these cases, the QP peak is clearly diminished for . At higher energies in the occupied spectrum, DFT+DMFT accounts for the lower Hubbard band at eV, denoting the degree of realspace localization, which is missing in the DFT description. The transfer of spectral weight from the QP peak to the Hubbard peaks with increasing correlation strength is a hallmark of strongly correlated systems.
The competition between bandinsulating and Mottinsulating tendencies becomes more obvious on the layer and orbitalresolved local level. In the orthorhombic distorted systems, the Ti orbitals , and hybridze on each site, forming effective crystalfield orbitals , and [17, 4, 5]. Though the linear combinations are layerdependent, the qualitative character remains stable throughout the TiO layers. In bulk SmTiO, the electron majorly resides in the orbital. Table 1 provides the multiorbital fillings for the symmetryinequivalent Ti18 sites in layer SrO/SmTiO. Figure 3 shows furthermore the local spectral functions for each choice of for the given Ti sites, i.e. from the doping layers towards the bulklike region of SmTiO. Interestingly, when embedded by the SrO layers, the system quickly establishes bandinsulatinglike behavior. Meaning, the Ti states become completely depleted and the region gets inaccessible for electron transport. On the other hand, far away from the SrO layers the system is Mott critical, i.e. either is in a dopedMott or Mottinsulating regime. Inbetween these different insulating(like) parts, a seemingly moderatelycorrelated metallic region of 23 TiOlayers width is established, respectively. This metallic region shifts correspondingly with increasing in the superlattices. Surpisingly for each , in a single TiO layer of these metallic parts there is orbital polarization towards state , which is of dominant , i.e. inplane, contribution. Thereby associated is high QP peak of identical orbital flavor. Since the system is strongly polarized in the Mottcritical region similar to the bulk compound, this additional polarization is a unique heterostructure effect. Note that it is absent for the doped case [5], and hence could be important for the stronger Fermiliquid character in the cases [8].
4.1 Summary
Largescale firstprinciples manybody calculations based on the advanced DFT+DMFT framework are capable of addressing the challenging emerging physics of correlated oxide heterostructure on a realistic level. For the case of fewlayer doped SmTiO, the coexistence of different electronic phases, i.e. bandinsulating, metallic and Mottcritical are predicted on a multiorbital level. In addition, alternating orbital polarizations are revealed, that open further engineering possibilities. In general, the richness of various competing realspace regions of different electronic kind in a single equilibrium system should enable various technological applications.
Acknowledgments
The author gratefully acknowledges the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JURECA at the Jülich Supercomputing Centre (JSC) under project number hhh08.
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