Magnetoexcitons in phosphorene monolayers, bilayers, and van der Waals heterostructures

Roman Ya Kezerashvili,Anastasia Spiridonova,Andrew Dublin

doi:10.1103/physrevresearch.4.013154

Abstract

We study direct and indirect excitons in Rydberg states in phosphorene monolayers, bilayers, and van der Waals (vdW) heterostructure in an external magnetic field within the framework of the effective-mass approximation. The magnetic field is applied perpendicular to the monolayer or heterostructure and is varied between 0 and 60 T. Binding energies of magnetoexcitons are calculated by numerical integration of the Schr\"odinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect magnetoexcitons. The latter aids in the understanding of the role of screening in phosphorene. We report the magnetic field energy contribution to the binding energies and diamagnetic coefficients (DMCs) for magnetoexcitons, which depend strongly on the effective anisotropic masses of electrons and holes and can be tuned by the external magnetic field. We demonstrate that the vdW phosphorene heterostructure is a novel category of two-dimensional semiconductors with magnetoexcitonic binding energies tunable by means of the external magnetic field. The binding energies and DMCs are controlled by the number of hexagonal boron nitride layers separating two phosphorene sheets. Such tunability is potentially useful for the device design.

Highlights

Two-dimensional layered materials have been studied extensively in the past two decades
We report the dependence of the energy contribution of the external magnetic field on the binding energies of magnetoexcitons in Rydberg states (1s, 2s, 3s, and 4s) in FS [Fig. 1(a)] and hexagonal boron nitride (hBN)-encapsulated phosphorene [Fig. 1(b)], the FS bilayer phosphorene [Fig. 1(c)], and the van der Waals (vdW) heterostructure [Fig. 1(d)] on a magnetic field
Within the framework of the Mott-Wannier model, we study direct and indirect excitons in Rydberg states in phosphorene monolayers, bilayer, and vdW heterostructure in

Summary

INTRODUCTION

Two-dimensional layered materials have been studied extensively in the past two decades. Excitons in TMDC monolayers, bilayers, and vdW heterostructures in the presence of external magnetic fields have been studied extensively. There is, a lack of similar research on excitons in phosphorene This motivates us to study the effect of external magnetic fields on the binding energies of Rydberg states of magnetoexcitons in monolayer, bilayer, and vdW heterostructures composed of phosphorene, and to calculate the corresponding diamagnetic coefficients (DMCs). We report the diamagnetic coefficients (i) for the direct magnetoexcitons in freestanding (FS) and encapsulated phosphorene monolayers, (ii) for the indirect magnetoexciton in a bilayer composed of two phosphorene monolayers, and (iii) for the indirect magnetoexcitons in heterostructures formed by two phosphorene monolayers separated by N hexagonal boron nitride (hBN) monolayers. The remainder of this paper is organized as follows: In Sec. II a theoretical model is presented for the description of an electron-hole system in an external magnetic field with charge carrier effective-mass anisotropy.

THEORETICAL MODEL

RESULTS

Contribution of the external magnetic field to binding energies of magnetoexcitons in a monolayer

DIAMAGNETIC COEFFICIENTS

CONCLUSIONS