Theory of internal transitions of charged excitons in quantum wells in magnetic fields

TL;DR

This paper develops an exact classification scheme for charged excitons in quantum wells under magnetic fields, revealing a new quantum number that governs magneto-optical transitions and enhances understanding of their internal transitions.

Contribution

It introduces a novel classification based on magnetic translations, including a new quantum number k, and explores its implications for magneto-optical transitions of charged excitons.

Findings

Identification of a new quantum number k related to cyclotron motion

Derivation of exact selection rules for magneto-optical transitions

Insights into internal transitions of charged excitons in magnetic fields

Abstract

For charged semiconductor complexes in magnetic fields B, we discuss an exact classification of states, which is based on magnetic translations. In this scheme, in addition to the total orbital angular momentum projection $M_z$ and electron and hole spins $S_e$, $S_h$, a new exact quantum number appears. This oscillator quantum number, k, is related physically to the center of the cyclotron motion of the complex as a whole. In the dipole approximation k is strictly conserved in magneto-optical transitions. We discuss implications of this new exact selection rule for internal intraband magneto-optical transitions of charged excitons $X^-$ in quantum wells in B.