Electric-field-tuned binding energies of trions in silicene, germanene, and stanene monolayers

Abstract: We predict the formation of intravalley controllable trions in buckled two-dimensional (2D) materials such as silicene, germanene, and stanene monolayers in an external electric field. Performing a study within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH), the three-body Schr\"{o}dinger equation is solved with the Rytova-Keldysh potential by expanding the wave functions of a trion in terms of the HH. Then, we numerically solve a resultant system of coupled differential equations. The ground state energies of intravalley trions controlled by the external electric field are presented. The dependencies of the binding energy (BE) of trions in silicene, germanene, and stanene as a function of the electric field are shown to be qualitatively similar. BEs of trions formed by $A$ and $B$ excitons have a non-negligible difference that increases slightly as the electric field increases. We demonstrate that trion BEs can be controlled by the external electric field.