be emphasized that the concentration of the surface state in the outermost layer is an important condition to maximize the ISB effect. For instance, if we consider a TaO$_{2}$ bilayer as opposed to the monolayer (Fig. \[fig:atomicstr\]c), the ISB effect is weakened as the surface state wave function no longer peaks at the outermost layer. We will show that the coupling of the $t_{2g}$ surface bands to the Ta $e_g$ bands, which comes from the local asymmetric environment of the surface Ta atoms, plays a key role in the enhanced splitting. The band splitting from intra-$t_{2g}$ coupling is smaller, due to specific orbital symmetry of Ta $d$ and O $p$ states that we will discuss. We will further show that the $t_{2g}$-$e_g$ coupling gives rise to the enhanced Rashba-Dresselhaus splitting not only at the band bottom at $\Gamma$ but also at the band saddle points at $\mathrm{X}$. Finally, we will consider the substitution of Ba atoms for K in the KO layer for electron doping of the system.

**Results**

[**Rashba splitting near the $\Gamma$ point.**]{} The electronic structures of TaO$_2$/KO monolayer on BHO (lattice constant $\approx 4.155$ Å) from our first-principles calculations are presented in Fig. \[fig:bandpdos\]. The bands near 