  The van der Waals heterostructures of allotropes of phosphorene (${\alpha}$-
and $\beta-P$) with MoSe2 (H-, T-, ZT- and SO-MoSe2) are investigated in the
framework of state-of-the-art density functional theory. The semiconducting
heterostructures, $\beta$-P /H-MoSe2 and ${\alpha}$-P / H-MoSe2, forms
anti-type structures with type I and type II band alignments, respectively,
whose bands are tunable with external electric field. ${\alpha}$-P / ZT-MoSe2
and ${\alpha}$-P / SO-MoSe2 form ohmic semiconductor-metal contacts while
Schottky barrier in $\beta$-P / T-MoSe2 can be reduced to zero by external
electric field to form ohmic contact which is useful to realize
high-performance devices. Simulated STM images of given heterostructures reveal
that ${\alpha}$-P can be used as a capping layer to differentiate between
various allotropes of underlying MoSe2. The dielectric response of considered
heterostructures is highly anisotropic in terms of lateral and vertical
polarization. The tunable electronic and dielectric response of van der Waals
phosphorene/MoSe2 heterostructure may find potentials applications in the
fabrication of optoelectronic devices.
