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Interplay between exchange split Dirac and Rashba-type surface states in MnBi$_2$Te$_4$/BiTeI interface

Based on the ab initio calculations, we study the electronic structure of the BiTeI/MnBi2Te4 heterostructure interface composed of the anti-ferromagnetic topological insulator MnBi$_2$Te$_4$ and the polar semiconductor trilayer BiTeI. We found significant difference in electronic properties at different types of contact between substrate and the overlayer. While the case of Te-Te interface forms natural expansion of the substrate, when Dirac cone state locates mostly in the polar overlayer region and undergoes slight exchange splitting, Te-I contact is the source of four-band state contributed by the substrate Dirac cone and Rashba-type state of the polar trilayer. Owing to magnetic proximity, the pair of Kramers degeneracies for this state are lifted, what produces Hall response in transport regime. We believe, our findings provide new opportunities to construct novel type spintronic devices.