the (001) perovskite transition metal oxide 2DEG with maximal ISB, where the 2DEG wave function profile is required to be concentrated on the surface-terminating TM-O$_2$ layer. In such an environment, the effective crystal field on the 2DEG $d$ orbitals should be quite different from that of the cubic perovskite, with much lower energy level at least for the $d_{z^2}$ orbital. Even if we use alternative materials for our heterostructure — viability of substituting BHO by BaSnO$_3$ or TaO$_2$ by WO$_2$ still remains to be investigated — we expect a significant role of the transition metal $e_g$ orbitals if the Rashba-Dresselhaus splitting is comparably large. It is also found that compressive strain on the BHO substrate, which might be needed for the feasible deposition of the thin film taking into account relatively large lattice mismatch between KTO and BHO, does not substantially affect the band splitting (see Appendix D and Fig. A2). Considering that 2DEG in an artificial film-substrate system is realized experimentally in SrVO$_3$ thin films on Nb-doped STO [-@Yoshimatsu2011], we expect that our system can be realized in experiments using the state-of-the-art layer-by-layer growth control of perovskite oxide thin films [-@Thiel2006].

**Methods**

[**Theoretical approach.**]{} We performed density functional theory 