  Heterostructures of topological insulator Bi$_2$Se$_3$ on transition metal
dichalcogenides (TMDCs) offer a new materials platform for studying novel
quantum states by exploiting the interplay among topological orders, charge
orders and magnetic orders. The diverse interface attributes, such as material
combination, charge re-arrangement, defect and strain, can be utilized to
manipulate the quantum properties of this class of materials. Recent
experiments of Bi$_2$Se$_3$/NbSe$_2$ heterostructures show signatures of strong
Rashba band splitting due to the presence of a BiSe buffer layer, but the
atomic level mechanism is not fully understood. We conduct first-principles
studies of the Bi$_2$Se$_3$/BiSe/TMDC heterostructures with five different TMDC
substrates (1T phase VSe$_2$, MoSe$_2$, TiSe$_2$, and 2H phase NbSe$_2$,
MoSe$_2$). We find significant charge transfer at both BiSe/TMDC and
Bi$_2$Se$_3$/BiSe interfaces driven by the work function difference, which
stabilizes the BiSe layer as an electron donor and creates interface dipole.
The electric field of the interface dipole breaks the inversion symmetry in the
Bi$_2$Se$_3$ layer, leading to the giant Rashba band splitting in two quintuple
layers and the recovery of the Dirac point in three quintuple layers, with the
latter otherwise only occurring in thicker samples with at least six
Bi$_2$Se$_3$ quintuple layers. Besides, we find that strain can significantly
affect the charge transfer at the interfaces. Our study presents a promising
avenue for tuning topological properties in heterostructures of two-dimensional
materials, with potential applications in quantum devices.
