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Experimentally it is still challenging to epitaxially grow Bi(111) bilayer(BL) on conventional semiconductor substrate. Here, we propose a substrate of$\beta-$In$_2$Se$_3$(0001) with van der Waals like cleavage and large band gapof 1.2~eV. We have investigated the electronic structure of BL on onequintuple-layer (QL) $\beta-$In$_2$Se$_3$(0001) using density functional theorycalculation. It is found that the intermediate hybridization between BL and oneQL $\beta-$In$_2$Se$_3$(0001) results in the formation of bands with giantRashba spin splitting in the large band gap of the substrate. Furthermore theRashba parameter $\alpha_R$ can be increased significantly by tensile strain ofsubstrate. Our findings provide a good candidate substrate for BL growth toexperimentally realize spin splitting Rashba states with insignificant effectof spin degenerate states from the substrate.

Giant Rashba-Spin Splitting of Bi(111) Bilayer on Large Band Gap $\beta-$In$_2$Se$_3$