Motion of a 3D exciton in a magnetic field: Exciton-magnetoexciton “phase” transition

Abstract

A rearrangement of the ground state of a Wannier-Mott exciton upon an increase in its momentum is considered. The phase diagram of the electron and the hole experiencing the Coulomb interaction on the magnetic momentum-external magnetic field plane is investigated. A jumplike exciton-magnetoexciton “phase” transition is observed upon an increase in the momentum in fields B weaker than a certain value B<B _tr1. As momentum P increases above a certain critical value P _tr(B), the ground state of the system changes from the hydrogen-like state polarized by the Lorentz force to the magnetoexciton state in which the average distance 〈 r〉 between the electron and the hole increases jumpwise in the transverse direction relative to the field. As the exciton momentum increases, its wave function is extended along the magnetic field, acquiring the shape of a strongly prolate ellipsoid. It is interesting that the momentum of the transition tends to a finite value P ₀>0 even for B→0. At the point of transition, the exciton energy-momentum relation changes jumpwise from a quadratic law to a relation virtually independent of the momentum. For B<B _tr1, the exciton-magnetoexciton transition becomes blurred.