Ultrathin films of black phosphorus as suitable platforms for unambiguous observation of the orbital Hall effect
Tarik P. Cysne, Marcio Costa, Marco Buongiorno Nardelli, R. B. Muniz, Tatiana G. Rappoport
Abstract
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 density-functional-theory-derived tight-binding Hamiltonian, which is constructed with the pseudoatomic 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 on 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.