Intervalley Magnetotrions Tunable by Electric and Magnetic Fields in Buckled Two-Dimensional Materials

Abstract

We develop a theoretical framework for intervalley magnetotrions in buckled two-dimensional materials, including silicene, germanene, and stanene, subjected to perpendicular electric and magnetic fields. Within the effective-mass approximation, the three-particle Schrödinger equation is formulated with the Rytova--Keldysh interaction potential and analyzed in the high-magnetic-field regime. We demonstrate that intervalley trions with equal electron and hole effective masses constitute an exceptional case for which the center-of-mass and internal motions separate exactly. The center-of-mass motion is governed by a two-dimensional harmonic-oscillator Hamiltonian, leading to quantized Landau states whose energies form electrically tunable Landau surfaces controlled by the magnetic field and the electric-field dependence of the carrier effective masses. The internal motion is investigated by solving the three-body Schrödinger equation within the framework of the hyperspherical harmonics method. Numerical calculations reveal that the trion binding energy increases monotonically with both magnetic and electric fields owing to the combined effects of magnetic confinement and electric-field-induced enhancement of the effective masses. The strongest binding is obtained for silicene, followed by stanene and germanene. The present work provides a unified description of both the collective center-of-mass motion and the internal dynamics of magnetotrions in Xene monolayers, demonstrating that both degrees of freedom can be independently manipulated by external electric and magnetic fields.