The properties of the two-dimensional (2D) magnetoexcitons in the GaAs-type quantum wells subjected to the
action of a strong perpendicular magnetic field with the binding energy determined by the direct Coulomb electronhole
(e-h) interaction and with the summary e-h spin projections are discussed.
A new property of the 2D magnetoexciton is the interdependence between the center-of-mass and the relative e-h
motions induced by the action of the Lorentz force. This interdependence happens to play an important role promoting
to the formation of the Dirac cone dispersion law under the influence of the exchange e-h Coulomb interaction.
The symmetric magnetoexciton state due to the exchange e-h Coulomb interaction acquires a Dirac cone dispersion
law in the range of small in-plane wave vectors with the group velocity vg proportional to the magnetic field strength
B, with equal probabilities of the quantum transitions from the ground state of the crystal in both light circular
polarizations but with maximum probability in the Faraday geometry of the light propagation and vanishing probability
in the Voigt one. In difference on it, the asymmetric superposition state remains with the usual dispersion law
inherited from the bare magnetoexciton states and has a dipole-active quantum transitions in both circular polarizations,
indifferent on the direction of the light propagation. When the light is arbitrary propagating in 3D space, the
symmetric superposition state is dipole active in the case of the linear polarization vector
−→
s−→k with the longitudinal
projection on the 2D exciton in-plane wave vector
−→
k|| and is forbidden in the linear light polarization with the vector
−→
t−→k , which has a transverse projection on
−→
k||.
In the case of the circular polarizations the probability of quantum transition is proportional to k2
z/|
−→k |2, and the
probability is different from zero when the incident light has perpendicular projection to the layer. The asymmetric
superposition state is dipole active in the linear polarization vector
−→
t−→k with transverse projection as regards the
in-plane exciton wave vector, is forbidden in the
−→
s−→k polarization vector and does not depend on the light orientation.
The case of 2D magnetoexcitons [1] is similar with the quantum transitions in the excitons states of the transition
metal dichalcogenides monolayers [2]. This marvelous property was firstly discussed and underlined by the authors of
theoretical and experimental investigations published in the Ref. [2].
The both symmetric and asymmetric superposition states with the interference effects in the case of the light
with two linear polarizations, which have different parities as regards the inversion of the light wave vector
−→k were
revealed. The result was obtained by applying the perturbation theory of a degenerate energy level [3]. In such a
way the symmetric (asymmetric) state is allowed in the case of linear polarization with positive (negative) parity and
is forbidden in the case of linear polarization with negative (positive) parity. The obtained optical results open the
possibility to investigate the thermodynamic properties of the 2D Bose gas with Dirac cone dispersion law.
Bibliography:
[1] S.A. Moskalenko, I.V. Podlesny, I.A. Zubac, and B.V. Novikov, Two-dimensional magnetoexciton superposition
states with Dirac cone dispersion law and quantum interference effects in optical transitions. Solid State Communications
306, 113714 (2020).
[2] Y. Hongyi, L. Gui-Bin, G. Pu, X. Xiaodong and Y. Wang. Nature Communications 5, 3876 (2014).
[3] L.D. Landau and E.M. Lifshitz, Quantum Mechanics Non-Relativistic Theory. Volume 3 of Course of Theoretical
Physics. Translated from the Russian by J.B. Sykes and J.S. Bell. Second edition, revised and enlarged. (Oxford,
Pergamon Press, 1965).