Magnetoexcitons in phosphorene monolayer, bilayer, and van der Waals heterostructure

We study direct and indirect magnetoexcitons in Rydberg states in phosphorene monolayers, bilayer, and van der Waals heterostructure in an external magnetic field applied perpendicular to the monolayer or heterostructure within the framework of the effective mass approximation. Binding energies of magnetoexcitons are calculated by numerical integration of the Schrödinger equation using the Rytova-Keldysh potential for direct magnetoexcitons and both the Rytova-Keldysh and Coulomb potentials for indirect one. We report the magnetic field energy contribution to the binding energies and diamagnetic coefficients (DMCs) for magnetoexcitons and show their strong depends on the effective masses of electron and hole. We demonstrate theoretically that phosphorene is a novel category of 2D semiconductors offering a tunability of the binding energies of magnetoexcitons by means of external magnetic field and control of the binding energies and DMCs by the number of hBN layers separating two phosphorene sheets. Such tunability is potentially useful for the design of the device.