  Phosphorene, a monolayer of black phosphorus, is a two-dimensional material
that lacks a multivalley structure in the Brillouin zone and has negligible
spin-orbit coupling. This makes it a promising candidate for investigating the
orbital Hall effect independently of the valley or spin Hall effects. To model
phosphorene, we utilized a DFT-derived tight-binding Hamiltonian, which is
constructed with the pseudo atomic orbital projection method. For that purpose,
we use the PAOFLOW code with a newly implemented internal basis that provides a
fairly good description of the phosphorene conduction bands. By employing
linear response theory, we show that phosphorene exhibits a sizable orbital
Hall effect with strong anisotropy in the orbital Hall conductivity for the
out-of-plane orbital angular momentum component. The magnitude and sign of the
conductivity depend upon the in-plane direction of the applied electric field.
These distinctive features enable the observation of the orbital Hall effect in
this material unambiguously. The effects of strain and of a perpendicularly
applied electric field on the phosphorene orbital-Hall response are also
explored. We show that a supplementary electric field applied perpendicular to
the phosphorene layer in its conductive regime gives rise to an induced
in-plane orbital magnetization.
