Electronic properties of bilayer phosphorene quantum dots in the presence of perpendicular electric and magnetic fields

TL;DR

This study uses tight-binding methods to explore how perpendicular electric and magnetic fields influence the electronic and layer-polarization properties of bilayer phosphorene quantum dots, revealing field-dependent layer polarization and Landau level behaviors.

Contribution

It provides new insights into the layer-dependent electronic properties of bilayer phosphorene quantum dots under external fields, highlighting the effects of bias potential and magnetic field on layer polarization and Landau levels.

Findings

Edge states are layer-polarized without bias; bulk states are not.

Magnetic field increases layer polarization of edge states.

Bias potential induces layer polarization in both edge and bulk states.

Abstract

Using the tight-binding approach, we investigate the electronic properties of bilayer phosphorene (BLP) quantum dots (QDs) in the presence of perpendicular electric and magnetic fields. Since BLP consists of two coupled phosphorene layers, it is of interest to examine the layer-dependent electronic properties of BLP QDs, such as the electronic distributions over the two layers and the so-produced layer-polarization features, and to see how these properties are affected by the magnetic field and the bias potential. We find that in the absence of a bias potential only edge states are layer-polarized while the bulk states are not, and the layer-polarization degree (LPD) of the unbiased edge states increases with increasing magnetic field. However, in the presence of a bias potential both the edge and bulk states are layer-polarized, and the LPD of the bulk (edge) states depends strongly (weakly) on the interplay of the bias potential and the interlayer coupling. At high magnetic fields, applying a bias potential renders the bulk electrons in a BLP QD to be mainly distributed over the top or bottom layer, resulting in layer-polarized bulk Landau levels (LLs). In the presence of a large bias potential that can drive a semiconductor-to-semimetal transition in BLP, these bulk LLs exhibit different magnetic-field dependences, i.e., the zeroth LLs exhibit a linear-like dependence on the magnetic field while the other LLs exhibit a square-root-like dependence.