Two-dimensional electron systems in $A{\mathrm{TiO}}_3$ perovskites ($A=\mathrm{Ca}$, Ba, Sr): Control of orbital hybridization and energy order

We report the existence of a two-dimensional electron system (2DES) at the $\left(001\right)$ surface of ${\mathrm{CaTiO}}_3$. Using angle-resolved photoemission spectroscopy, we find a hybridization between the $d_{xz}$ and $d_{yz}$ orbitals, not observed in the 2DESs at the surfaces of other $A{\mathrm{TiO}}_3$ perovskites, e.g., ${\mathrm{SrTiO}}_3$ or ${\mathrm{BaTiO}}_3$. Based on a comparison of the 2DES properties in these three materials, we show how the electronic structure of the 2DES (bandwidth, orbital energy order, and electron density) is coupled to different typical lattice distortions in perovskites. The orbital hybridization in orthorhombic ${\mathrm{CaTiO}}_3$ results from the rotation of the oxygen octahedra, which can also occur at the interface of oxide heterostructures to compensate strain. More generally, the control of the orbital energy order in 2DES by choosing different $A$-site cations in perovskites offers a gateway toward 2DESs in oxide heterostructures beyond ${\mathrm{SrTiO}}_3$.

Figure 1

(a), (b) Fermi surface intensity maps of the 2DES measured at the surface of ${\mathrm{CaTiO}}_3$(001) close to ${\mathrm{\Gamma }}_{005}(h\nu =57$ eV) using LH polarization, and close to ${\mathrm{\Gamma }}_{115}(h\nu =67$ eV) using LV polarization, respectively. (c), (d) $E-k$ intensity maps measured at ${\mathrm{\Gamma }}_{005}$ using LH and LV polarization. The red curves are based on a one-layer tight-binding model assuming orbital hybridization between the $d_{xz}$ and $d_{yz}$ orbitals. The yellow markers in (c) are the peak positions of the fits of the energy distribution curves (EDCs). (e), (f) Fermi surface and $E-k$ map corresponding to the electronic structure of the 2DES at the (001) surface of ${\mathrm{SrTiO}}_3$. The shown intensity maps are a superposition of measurements using LH polarization at $h\nu =90$ eV and LV polarization at $h\nu =47$ eV. The red curves are, in this case, based on a tight-binding model without hybridization between the different $t_{2g}$ orbitals. (g)–(i) Momentum-resolved fraction of orbital character of the $d_{xz}$ or $d_{yz}$ band visible in the $E-k$ maps in (c), (d), and (f) based on the tight-binding model showing the orbital hybridization in the 2DES at the (001) surface of ${\mathrm{CaTiO}}_3$.

Figure 2

(a) Top: Total, Ti-, Ca-, and O-projected densities of states of bulk ${\mathrm{CaTiO}}_3$ obtained from $\mathrm{DFT}-\mathrm{HSE}06$ calculations. Bottom: Decompositions into Ti $e_g$ ($d_{z^2}+d_{x^2-y^2}$) and Ti $t_{2g}$ ($d_{xy}+d_{yz}+d_{xz}$) components shows that the conduction band minimum of ${\mathrm{CaTiO}}_3$ is mainly formed of $t_{2g}$ orbitals (see details in the DFT section of the Supplemental Material [25]). (b) Cut into the pseudo-${\mathrm{TiO}}_2$ plane (blue plane) of the charge density plot (white contours) for the lower-energy state of the conduction band in ${\mathrm{CaTiO}}_3$. Ca, Ti, and O atoms are represented by cyan, gray, and red spheres, respectively. Orange arrows show the $(x,y,z)$ axes of the pseudocubic unit cell.

Figure 3

Oxygen octahedra in $A{\mathrm{TiO}}_3$ ($A=\text{Sr}$, Ba, Ca) perovskites and schematic of band dispersion observed in the 2DESs in ${\mathrm{SrTiO}}_3$ (a), ${\mathrm{BaTiO}}_3$ (b), and ${\mathrm{CaTiO}}_3$ (c). The black arrows in (b) and (c) indicate the distortion occurring in ${\mathrm{BaTiO}}_3$ and ${\mathrm{CaTiO}}_3$. The broad red band and the question mark in (b) indicate that the band structure of the $d_{xy}$ band was not resolved well by ARPES in ${\mathrm{BaTiO}}_3$. The colors of the bands correspond to different orbital characters. The size of the blue filled and green empty circles in (c) represents the fraction of the $d_{xz}$ (green) and the $d_{yz}$ (blue) in the band dispersion.