  We use first-principles calculations to show that van der Waals (vdW)
heterostructures consisting of few-layer Bi$_2$Se$_3$ and PtSe$_2$ exhibit
electronic and spintronics properties that can be tuned by varying the
constituent layers. Type-II band alignment with layer-tunable band gaps and
type-III band alignment with spin-splittings have been found. Most noticeably,
we reveal the coexistence of Rashba-type spin-splittings (with large
$\alpha_{\rm R}$ parameters) in both the conduction and valence band stemming
from few-layer Bi$_2$Se$_3$ and PtSe$_2$, respectively, which has been
confirmed by spin-texture plots. We discuss the role of inversion symmetry
breaking, changes in orbital hybridization and spin-orbit coupling in altering
electronic dispersion near the Fermi level. Since low-temperature growth
mechanisms are available for both materials, we believe that few-layer
Bi$_2$Se$_3$/PtSe$_2$ vdW heterostructures are feasible to realize
experimentally, offering great potential for electronic and spintronics
applications.
