Van de Walle
Computational Materials Group | (805) 893-7144

Materials Department, University of California, Santa Barbara, CA 93106-5050


Two-dimensional electron gas at complex oxide interfaces

Understanding the mobility of complex oxide materials

Metal-insulator transition in ultra-thin SrTiO3 layers

The Mott-Hubbard gap of the rare-earth titanates

Two-dimensional electron gas at complex oxide interfaces

If an interface is formed between a polar and a nonpolar material, the layer in the polar material adjacent to the nonpolar material donates 1/2 electron to the right, i.e., to a "bulk-like" layer in the polar material. It is also trying to donate 1/2 electron to the layer to its left—but that layer belongs to a nonpolar material and does not need that electron to satisfy its bonding. This electron is therefore in principle available as a free electron, and the atomic layer on the polar side of the interface effectively acts as a layer of donors with a density of 1/2 of the areal density of atoms at the interface. In most materials, this is on the order of a few times 1014/cm2; i.e. a huge density compared to what is typically achieved in two-dimensional electron gases (2DEGs) at conventional interfaces.

Schematic representation showing an interface between a nonpolar (SrTiO3) and a polar (LaAlO3) material. Charges on layers are indicated, and arrows indicate electron transfer between layers in the polar material. SrTiO3 is charge neutral, and therefore the interfacial LaO plane acts as a delta-doped layer of donors with a density of 0.5 electrons per unit cell.

The polar discontinuity at the SrTiO3/LaAlO3 interface (STO/LAO) can therefore in principle sustain an electron density of 3.3×1014 cm−2 (0.5 electrons per unit cell). However, experimentally observed densities are more than an order of magnitude lower. Using a combination of first-principles and Schrödinger-Poisson simulations we have shown that the problem lies in the asymmetric nature of the structure, i.e., the inability to form a second LAO/STO interface that is a mirror image of the first, or to fully passivate the LAO surface. Our insights apply to oxide interfaces in general, explaining for instance why the SrTiO3/GdTiO3 interface has been found to exhibit the full density of 3.3×1014 cm−2. For these interfaces, a key issue is the band alignment, which determines on which side of the interface the 2DEG will reside, as well as the degree of confinement. We have use hybrid density functional calculations to determine the band alignments of a number of complex oxides, considering materials with different types of conduction-band character, polar or nonpolar character and band insulators as well as Mott insulators. We suggest promising materials combinations that could lead to a 2DEG with optimized properties, such as high density and high mobility – pointing to BaSnO3 as an interesting candidate as a host material for a 2DEG given its high room temperature mobility; much higher than that of SrTiO3.

Natural band alignments for a selection of complex oxides that may be part of an interface forming a 2DEG. Filled valence-band states in blue, empty conduction-band states in yellow. The valence band maximum of SrTiO3 was used as the zero of energy. Note that GdTiO3 and YTiO3 are Mott insulators; a gap opens in the partially filled 3d band due to strong electron-electron repulsion.

L. Bjaalie, B. Himmetoglu, L. Weston, A. Janotti and C. G. Van de Walle, New J. Phys. 16, 025005 (2014).

A. Janotti, L. Bjaalie, L. Gordon, and C. G. Van de Walle, Phys. Rev. B 86, 241108(R) (2012).

Understanding the mobility of complex oxide materials

The mobility of the electrons in the 2DEG is critical to potential applications, and we have therefore explored the mechanisms that govern the mobility. Strain can affect the energetic ordering and effective mass of the lowest conduction-band states in SrTiO3, made up of Ti 3d states. We predict that biaxial stress in the (001) or (110) planes results in the lowest-energy conduction-band state having significantly smaller electron mass in the in-plane directions compared to the unstrained SrTiO3, thus suggesting that pseudomorphic growth is a promising route to increasing the electron mobility in epitaxial films.

Band structure of SrTiO3 near the conduction-band minimum at Γ under (a) −1% compressive and (b) +1% tensile strain in the (001) plane, plotted along the X-Γ-M and X-Γ-X̅ directions; (c) −1% compressive and (d) +1% tensile strain in the (110) plane, plotted along the M-Γ-X̅ and M̅ -Γ-X̅ directions. The effects of spin-orbit coupling are included. The zero of energy is set at the conduction-band minimum.

We have also investigated the electronic and vibrational spectra of SrTiO3, as well as the coupling between them. We compute electron-phonon scattering rates for the three lowest-energy conduction bands and use Boltzmann transport theory to calculate the room-temperature mobility of SrTiO3. The results agree with experiment and highlight the strong impact of longitudinal optical phonon scattering. Our analysis provides important insights into the key factors that determine room-temperature mobility, such as the number of conduction bands and the nature and frequencies of longitudinal phonons. Such insights provide routes to engineering materials with enhanced mobilities.

Electron-phonon scattering rates for conduction bands in SrTiO3.

A. Janotti, D. Steiauf, and C. G. Van de Walle, Phys. Rev. B 84, 201304(R) (2011).

B. Himmetoglu, A. Janotti, H. Peelaers, A. Alkauskas, and C. G. Van de Walle, Phys. Rev. B 90, 241204(R) (2014).

Metal-insulator transition in ultra-thin SrTiO3 layers

In addition to the metallic behavior seen at the interface between complex oxides such as SrTiO3 and GdTiO3, experimental results for ultrathin SrTiO3 layers inserted in GdTiO3 reveal a transition from metallic to insulating behavior, and suggest a strong interplay between electron-electron interaction and lattice distortions. We have shown that a metal-to-insulator transition can occur in SrTiO3 at extreme doping levels. We find that doping with 1/4 electron per Ti atom produces a metallic phase as expected, but that adding 1/2 electron per Ti results in a charge-ordered Mott-insulating phase. These excess electrons occupy the otherwise empty Ti 3d bands. This Mott-insulator phase was also found to occur in calculations of SrTiO3/LaAlO3 and SrTiO3/GdTiO3 heterostructures with ultrathin SrTiO3 layers [1].

P. Moetakef, C. A. Jackson, J. Hwang, L. Balents, S. J. Allen, and S. Stemmer, Phys. Rev. B 86, 201102(R) (2012).

L. Bjaalie, A. Janotti, B. Himmetoglu, and C. G. Van de Walle, Phys. Rev. B 90, 195117 (2014)

Charge-ordered Mott-insulating phase for ½ excess electron per Ti atom in bulk SrTiO3 (STO) (top) and in a SrTiO3/GdTiO3 (STO/GTO) heterostructure (bottom). The isosurfaces represent electrons in the Ti 3d bands.

The Mott-Hubbard gap of the rare-earth titanates

YTiO3 is a representative member of the rare-earth titanate Mott insulators. As explained above, these materials have become the focus of great interest because of their use in complex-oxide heterostructures. This recent surge of interest has prompted us to scrutinize the fundamental properties, such as the magnitude of the Mott-Hubbard gap. Commonly accepted values for the gap in YTiO3 and other rare-earth titanates are in the range of 0.2 – 0.7 eV, based on optical conductivity spectra. However, we find a 2 eV gap in our hybrid functional calculations.

Band structure of YTiO3, showing a 2 eV band gap. Note that YTiO3 is a Mott insulator, meaning that a gap opens within the partially filled Ti 3d band due to strong electron-electron repulsion, splitting into a so-called lower and upper Hubbard band (LHB and UHB). The zero of energy is set at the top of the LHB.

We have proposed that the optical conductivity onset at 0.7 eV for YTiO3 is instead caused by the absorption of an electron in the lower Hubbard band to a small hole polaron state; holes tend to become self-trapped on the Ti lattice sites. The presence of small hole polarons is consistent with experimental reports of the rare-earth titanates being p-type.

Configuration-coordinate diagram for a self-trapped and delocalized hole in YTiO3. EST is the net energy gain from self-trapping, ES is the lattice energy cost, and ET is the vertical transition energy. The red arrow indicates the possibility of excitations below ET due to vibrational broadening, causing the 0.7 eV signal seen in optical conductivity measurements.

Since the magnitude of the Mott-Hubbard gap reflects the strength of the intra-atomic Coulomb repulsions in the material, knowing its value is essential for a correct understanding of the correlated nature of d-orbital derived bands. Our work can also serve as a guide to further developments in the theory of Mott insulators.

B. Himmetoglu, A. Janotti, L. Bjaalie, and C. G. Van de Walle, Phys. Rev. B 90, 161102(R) (2014).

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