Ultrathin films of black phosphorus as suitable platforms for unambiguous observation of the orbital Hall effect

TL;DR

This study demonstrates that ultrathin black phosphorus (phosphorene) can serve as a clear platform for observing the orbital Hall effect, with anisotropic conductivity and tunable properties influenced by strain and electric fields.

Contribution

The paper introduces a detailed theoretical model of phosphorene's orbital Hall effect, highlighting its suitability for unambiguous experimental observation due to its unique electronic structure.

Findings

Phosphorene exhibits a sizable, anisotropic orbital Hall effect.

The orbital Hall conductivity depends on the in-plane electric field direction.

Perpendicular electric fields induce in-plane orbital magnetization.

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 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.