Symmetry‐related motional enhancement of exciton magnetic moment

Abstract

A dramatic motional enhancement of heavy-and light-hole exciton magnetic moment in zinc-blende semiconductors under a magnetic field applied parallel to the [001] direction has been put into evidence when the exciton moves along the same direction [J. J. Davies et al., Phys. Rev. Lett. 97, 187403 (2006)]. The authors of the paper assigned the effect to a mixing between the 1S and 2P exciton states arising from the cubic term in the Luttinger Hamiltonian expansion in momentum. Such exciton states do not take into account the exact crystal structure since they are just eigenstates of the angular momentum. In addition, the Luttinger Hamiltonian does not take into account the full magnetic-field effect since it does not include the gauge transformations under the symmetry operations of the structure under the field. By determining the exact symmetry of the exciton states, it is shown here that, under a field parallel to the [001] direction, the Zeeman Splitting value vanishes at the G point and, due to accidental quasi-degeneracy in energy between dark and bright exciton states, becomes finite when the exciton moves parallel to the field. A perturbation model allows fitting experimental data and explains the exciton magnetic-moment enhancement with kinetic energy. On the contrary, under a field parallel to the [110] direction with the exciton moving parallel to the field, no accidental degeneracy probably takes place between exciton states. As a consequence, the concept of Zeeman Splitting is not relevant since no energy level is degenerate. In addition, a possible quasi-degeneracy between the excitons recombining with the s þ and s -4] have put into evidence a motional enhancement of exciton magnetic moments in zinc-blende semiconductors using wide quantum wells (QWs) with a magnetic field applied parallel to the [001] growth direction that was also the direction of the exciton motion. On the contrary, the QWs grown along the [110] direction that was also the applied magnetic field and exciton motion direction in the experiments do not exhibit noticeable enhancement. The effect along the [001] direction is present both for heavy-and light-hole excitons. It is clearly a bulk effect since the width of the QWs was in any case larger than the exciton Bohr radius by more than one order of magnitude. Just QWs allow knowing exact values of exciton momentum and separating in energy heavy-and light-hole exciton states. To find an approximated explanation of the results, Davies et al. proposed for the heavy-hole exciton a mixing between the 1S ground state and 2P excited states arising from the cubic term in the Luttinger Hamiltonian [5] expansion in momentum. They stated that their calculation is

Spin phenomena in asymmetrical [0 0 1] GaAs/AlxGa1−xAs quantum wells

“…the reduction of the structure symmetry. Therefore, the eigenstates from a pair do have the same energy and are transformed one into another by TRO [20].…”

“…For the latter group, light absorbed in the x (z ) polarization generates a couple of electron and heavy hole with the same 3 or 4 symmetry (with the 3 and 4 different symmetries). Note that the subduction procedure of the 5 IR of the C 2v group onto its σ v subgroup provides the following correspondence: With a magnetic field applied perpendicular to a symmetry plane, the electron Hamiltonian is invariant under TRO [20]. Indeed, under TRO, momentum and vector potential change sign, whereas the scalar product of spin and magnetic field as well as spin-orbit coupling term are invariant.…”

“…As a consequence, the populations of carriers (electrons or holes) with the 3 and 4 symmetries, respectively, are TRO conjugate and hence include the same numbers of carriers. Indeed, the matrix element modulus for an optical transition is invariant under TRO [20]. One therefore gets the following picture for electron (hole) spin orientation: the spins are perpendicular to the symmetry plane and the total spin of electron (hole) population is strictly equal to zero since the numbers of carriers with the 3 and 4 symmetries, respectively, are equal.…”