Figure 1

Perovskite crystal structure. (a) Bulk cubic unit cell with the $A$ atom in blue, $B$ atom in red, and the oxygen atom in white. (b) Splitting of atomic $d$ orbitals into $e_g$ and $t_{2g}$ manifolds. (c) Single $B$O${}_2$ plane with one unit cell, with area $a^2$, in the boxed region.Reuse & Permissions

Figure 2

Bonding network along the $y$ axis with an electric field. (a) Orbital polarization. Bonding between $zx$ and $xy$ on neighboring metal atoms through $p_x$ orbitals. The positive and negative lobes of the orbital functions are represented in blue and red, respectively. (b) Lattice polarization. Displacement of the metal (light blue plane) and oxygen (light purple plane) sublattices in an electric field.Reuse & Permissions

Figure 3

Orbital polarization changes to $t_{2g}$ band structure. (a) $t_{2g}$ band structure in the absence of an electric field and SO coupling. The results of our model are shown as solid lines, while the simulation is shown as dotted lines. The color coding in the figure [$xy$ (blue), $yz$ (red), $zx$ (green), and $x^2-y^2$ (purple)] represents the orbital character of the band near $\Gamma$ in the absence of SO coupling. When SO coupling is included, the dominant character is still $xy$ (blue) for the lowest band (due to confinement), while the $yz$ (red) and $zx$ (green) will be significantly hybridized. The inset shows the onset of an avoided crossing in the presence of an electric field. (b) $t_{2g}$ band structure with SO coupling and orbital polarization. (c) Comparison of the orbital polarization part of the Rashba splitting in the $t_{2g}$ space.Reuse & Permissions

Figure 4

Lattice polarization changes to $t_{2g}$ band structure. (a) $t_{2g}$ band structure with lattice displacement and no SO coupling. The results of our model are shown as solid lines, while the simulation is shown as dotted lines. The color coding in the figure [$xy$ (blue), $yz$ (red), $zx$ (green), and $x^2-y^2$ (purple)] represents the orbital character of the band near $\Gamma$ in the absence of SO coupling. When SO coupling is included, the dominant character is still $xy$ (blue) for the lowest band (due to confinement), while the $yz$ (red) and $zx$ (green) will be significantly hybridized. (b) $t_{2g}$ band structure with SO coupling and lattice displacement. (c) Comparison of the lattice mediated Rashba splitting in the $t_{2g}$ space.Reuse & Permissions