Effects of parallel electric and magnetic fields on Rydberg excitons in buckled two-dimensional materials

We study direct and indirect magnetoexcitons in Rydberg states in monolayers and double-layer heterostructures of Xenes (silicene, germanene, and stanene) in external parallel electric and magnetic fields applied perpendicular to the monolayer and heterostructure. We calculate binding energies of magnetoexcitons for the Rydberg states, $1s$, $2s$, $3s$, and $4s$ by numerical integration of the Schr\"odinger equation using the Rytova-Keldysh potential for direct and both the Rytova-Keldysh and Coulomb potentials for indirect magnetoexcitons, respectively. The latter allows understanding a role of screening in Xenes. In the external perpendicular electric field, the buckled structure of the Xene monolayers leads to the appearance of potential difference between sublattices allowing us to tune electron and hole masses and, therefore, the binding energies and diamagnetic coefficients (DMCs) of magnetoexcitons. We report the energy contribution from electric and magnetic fields to the binding energies and DMCs. The tunability of the energy contribution of direct and indirect magnetoexcitons by electric and magnetic fields is demonstrated. It is also shown that DMCs of direct excitons can be tuned by the electric field, and the DMCs of indirect magnetoexcitons can be tuned by the electric field and manipulated by the number of hBN layers, therefore allowing the possibility of electronic devices design that can be controlled by external electric and magnetic fields and the number of hBN layers. The calculations of the binding energies and DMCs of magnetoexcitons in Xenes monolayers and heterostructures can be compared with the experimental results when they are available.