Electric and magnetic fields tunable energy levels in Xenes monolayers

We predict the formation of interavalley trions in Xenes monolayers, such as silicene, germanene, and stanene monolayers, controllable by external electric and magnetic fields perpendicular to the monolayer. Using a coordinate transformation, a trion Hamiltonian is split into the sum of a translational term describing Landau quantizations for the trion center-of-mass motion and a term describing three-particle relative motion. The trion eigenenergy and wavefunction are calculated efficiently within the formalism developed in [1,2]. The three-body Schrödinger equation is solved with the Rytova-Keldysh potential by expanding the wave functions of a trion in terms of the hyperspherical harmonics and then a numerical solution of a resultant system of coupled differential equations. We investigate the dependence of energy levels and binding energies of trions on the electric and magnetic fields strength and present trions’ binding energies (BE). The dependencies of the BEs of trions in silicene, germanene, and stanene as a function of the electric and magnetic fields are qualitatively similar.