Indeed, when the $t_{2g}$-$e_g$ energy splitting is set to be infinite in Table \[tab:heff\], all the results from the $t_{2g}$-only TB models [-@Khalsa2013; -@YKim2013; -@PKim2014; -@Scheurer2015] are recovered, including the absence of $k$-linear Rashba in the lower $d_{xz/yz}$ band near $\Gamma$. In the case of 3D cubic KTO, the $t_{2g}$-$e_g$ energy separation at $\Gamma$ is calculated to be $\approx 4.6~\mathrm{eV}$, which is larger than that of our system (Fig. \[fig:bandpdos\]a, b). Compared with the 3D cubic bulk case, Figure \[fig:bandpdos\]b shows considerable portion of $d_{z^2}$ states close in energy, [*i.e.*]{}, less than bandwidth, to the $t_{2g}$ bands; this is due to the absence of an O atom in one of the octahedral points surrounding Ta. Hence, as shown in Fig. \[fig:bandpdos\]c, the local atomic configuration for the Ta atom is close to a square pyramid, where the $d_{z^2}$ and lower $d_{xz/yz}$ are close in energy. This can be taken as a generic result for the case where the 2DEG wave function is confined almost entirely to the outermost layer. The height difference of Ta and O atoms ($\approx 0.20$ Å) in the TaO$_2$ layer enhances the $t_{2g}$-$e_g$ coupling in both ways; the larger effect being the enhancement of the ISB 