Electrostatically confined quantum dots in bilayer phosphorene

Abstract

Since the isolation of few-layer graphene in 2004 by Geim and Novoselov, materials in their lamellar versions have received great attention from the scientific and technological community due to their peculiar electronic, optical, and transport properties that are not present in their bulk forms. Among these two-dimensional materials, black phosphorus, an allotrope of phosphorus, exhibits high electron mobility and, unlike graphene, is a semiconductor whose energy gap strongly depends on the number of layers. The wide frequency range covered by the tunable gap (~ 2.0 eV for the monolayer down to ~0.3 eV in the bulk, combined with the anisotropic properties of its electronic structure, makes this material promising for various applications, especially in optoelectronics. In this work, we investigate the electronic properties of charge carriers confined in quantum dots defined exclusively through a position-dependent electrostatic potential, without the need for physical patterning of the material. This potential breaks the inversion symmetry of bilayer phosphorene, locally modulating the gap and allowing for charge carrier confinement. We employ the tight-binding method to numerically investigate the electronic states and their wave functions under circularly symmetric potentials, both in the absence and presence of a perpendicular magnetic field. As the main results, we identify the closing of the gap at a critical value of the applied potential, the consequent emergence of Dirac cones, and that the quantum dot energy gap follows a power-law dependence on the dot radius, Eg(R) ∝ 1/R1.38, highlighting the combined role of electrostatic confinement and material anisotropy.