Strongly enhanced Rashba splittings in an oxide heterostructure: A tantalate monolayer on ${\mathbf{BaHfO}}_3$

In the two-dimensional electron gas emerging at the transition metal oxide surface and interface, various exotic electronic ordering and topological phases can become experimentally more accessible with the stronger Rashba spin-orbit interaction. Here, we present a promising route to realize significant Rashba-type band splitting using a thin film heterostructure. Based on first-principles methods and analytic model analyses, a tantalate monolayer on ${\mathrm{BaHfO}}_3$ is shown to host two-dimensional bands originating from Ta $t_{2g}$ states with strong Rashba spin splittings, nearly 10% of the bandwidth, at both the band minima and saddle points. An important factor in this enhanced splitting is the significant $t_{2g}-e_g$ interband coupling, which can generically arise when the inversion symmetry is maximally broken due to the strong confinement of the 2DEG on a transition metal oxide surface. Our results could be useful in realizing topological superconductivity at oxide surfaces.

Figure 1

Atomic structure of a tantalate layer on ${\mathrm{BaHfO}}_3$ (001). (a) Atomic structure of ${\mathrm{TaO}}_2/\mathrm{KO}$ on ${\mathrm{BaHfO}}_3$ from first-principles calculations; note the height difference between Ta and O at the top layer. (b) Wave function weight projected on $d_{xz/yz}$ of TMs for the lowest $d_{xz/yz}$ Rashba band at $\mathrm{\Gamma }$. The $\mathrm{TM}-{\mathrm{O}}_2$ layers are numbered starting from the outermost layer.

Figure 2

Electronic structure of ${\mathrm{TaO}}_2/\mathrm{KO}$ on ${\mathrm{BaHfO}}_3$ from first-principles calculations. (a) Calculated band structure. (b) Projected weights of Ta $d$ states. The Fermi level is set to the valence band maximum. (c) Schematic illustration of energy levels at $\mathrm{\Gamma }$ without SOC. The crystal field splitting of the monolayer-substrate heterostructure is different from that of the cubic (octahedral) case.

Figure 3

Hopping strengths (in eV) between Wannier functions for Ta $d$ states at one site and the neighboring site in the $x$ direction. Both direct (horizontal arrows) and indirect (oblique arrows, via O $p$) paths are depicted. Empty arrows indicate terms that would be absent without ISB.

Figure 4

Angular momentum texture from first-principles calculations in close vicinity of $\mathrm{\Gamma }$ and $\mathrm{X}$. Orbital and spin angular momenta are presented for the lower Rashba band of (a) the $d_{xy}$, (b) the lower $d_{xz/yz}$, and (c) the upper $d_{xz/yz}$ bands near $\mathrm{\Gamma }$, and the lower Rashba-Dresselhaus band of the (d) $d_{yz}$ bands near $\mathrm{X}=(\pi ,0)$.

Figure 5

Electronic structure of a ${\mathrm{TaO}}_2$ layer on BaO-terminated ${\mathrm{BaHfO}}_3$ (001) from first-principles calculations. (a) Band structure. The dotted horizontal line denotes the energy level of the VHS in absence of the Rashba-Dresselhaus splitting, $E_{vH}$, with the Fermi level set to 0. (b) AM texture at $E_{vH}$ with constant energy lines. The red and blue arrows correspond to the orbital and spin AM, respectively.

Figure 6

Angular momentum texture from the tight-binding model. The angular momentum textures are calculated (a) at $E_{vH}$ and (b) near $\mathrm{X}$ using both $t_{2g}$ and $e_g$, and (c) at $E_{vH}$ and (d) near $\mathrm{X}$ using only $t_{2g}$. The red and blue arrows represent the orbital and spin AM, respectively.

Figure 7

Band structure of ${\mathrm{TaO}}_2/\mathrm{KO}$ on ${\mathrm{HfO}}_2$-terminated ${\mathrm{BaHfO}}_3$ with the lattice constant reduced by 2%.