[-@Reyren2012] as well as the measurement of similar magnetoresistance in the $\delta$-doped STO heterostructure where the inversion symmetry breaking is hardly present [-@MKim2012]. Meanwhile, theoretical calculations show the splitting near the $\Gamma$ point to be two orders of magnitude smaller than the bandwidth at the best  [-@Zhong2013; -@YKim2013; -@PKim2014]. One natural way to overcome this limitation is adopting 5$d$ TM oxides, such as tantalate, with a stronger atomic SOC. This has motivated the recent experiments on the 2DEG at the surface of KTaO$_3$ (KTO) [-@Santander2012; -@King2012].

However, the experiments on KTO have suggested that another important condition for enhancing the surface 2DEG Rashba spin-orbit interaction is to have the density profile of the surface state concentrated to the surface-terminating layer, which maximizes the effect of the broken inversion symmetry. The ARPES measurements on the KTO surface have seen no measurable spin splitting [-@Santander2012; -@King2012], in spite of not only the stronger SOC of Ta but also the polar nature of KTO (001) surface. According to a density functional theory calculation [-@Shanavas2014], the surface state penetrates deeply into the bulk as the surface confinement potential is made shallow by the atomic relaxation near the surface layer. This suppresses the effect of 