the inversion symmetry breaking (ISB) on the surface state (which can be quantified by various parameters, [*e.g.*]{} the chiral orbital angular momentum coefficient [-@SPark2011; -@BKim2012; -@CPark2012; -@PKim2014]), and hence significantly reduces the Rashba spin-orbit interaction.

![\[fig:atomicstr\]Atomic structure of a tantalate layer on BaHfO$_3$ (001). (a) Schematic illustration of TaO$_2$/KO on HfO$_2$-terminated BaHfO$_3$, and TaO$_2$ on BaO-terminated BaHfO$_3$. (b) Atomic structure of TaO$_2$/KO on BaHfO$_3$ from first-principles calculations; note the height difference between Ta and O at the top layer. (c) Wave function weight projected on $d_{xz/yz}$ of TMs for the lowest $d_{xz/yz}$ Rashba band at $\Gamma$. Monolayer (TaO$_2$/KO on HfO$_2$-terminated BaHfO$_3$) case is to be compared with bilayer (TaO$_2$/KO/TaO$_2$ on BaO-terminated BaHfO$_3$) case. The TM-O$_2$ layers are numbered starting from the outermost layer. ](fig1.pdf){width="40.00000%"}

![\[fig:bandpdos\]Electronic structure of TaO$_2$/KO on BaHfO$_3$ from first-principles calculations. (a) Calculated band structure along high symmetry points. Insets show the magnified view of the upper and lower $d_{xz/yz}$ bands near $\Gamma$, and the $d_{yz}$ bands near $\mathrm{X}$. (b) Projected weights of Ta $d$ states. The Fermi level is set to the valence band maximum. (c) Schematic illustration of energy levels at $\Gamma$ without SOC. The crystal field splitting of the monolayer-substrate heterostructure is different from that 