Variational method for solving the Bethe-Salpeter equation for excitons in GaAs-(Ga,Al)As quantum wells in perpendicular magnetic fields

Abstract

The Bethe-Salpeter (BS) formalism is used to study the effect of the coupling between the center of mass and the relative internal motions of quantum-well excitons in a constant magnetic field. The BS equation in the case of an in-plane magnetic field is reduced to the well-known Schr\odinger equation for magnetoexcitons. In a perpendicular magnetic field, the BS equation has an extra term (BS term) that does not exist in the Schr\odinger equation. Within the framework of the variational method, it is shown that (i) the ground-state energy of a heavy-hole magnetoexciton with a zero wave vector in GaAs-(Ga,Al)As quantum wells, which is calculated by means of the BS formalism, is very close to the ground-state energy obtained from the Schr\odinger equation by using the same trial function; and (ii) in a strong perpendicular magnetic field, the magnetoexciton dispersion (in-plane magnetoexciton mass) is determined mainly by the BS term rather than the term that describes the electron-hole Coulomb interaction in the Schr\odinger equation.