The properties of the two-dimensional (2D) magnetoexcitons in the GaAs-type quantum wells subjected to the action of a strong perpendicular magnetic field and of the 2D Wannier-Mott excitons in the transition metal dichalcogenides with the binding energy determined by the direct Coulomb electron-hole (e-h) interaction and with the summary e-h spin projections F = ± 1 are compared. In both cases the exchange e-h Coulomb interaction leads to the creation of the symmetric and asymmetric superposition states formed by two bare exciton states with F = ± 1. The superposition states are characterized in different variants by the Dirac cone dispersion laws and with quantum interference effects in the optical quantum transitions from the ground state of the crystal.
The bound states of two interacting two-dimensional magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) moving in-plane of the layer with equal but opposite oriented wave vectors and forming a molecular-type structures with the resultant wave vector →k = 0 were investigated. Four possible spin structures of two electrons and of two holes forming the bound states were considered. Two of them lead to the formation of the para and ortho magnetoexcitons in the presence of the electron-hole (e-h) Coulomb exchange interaction. In this case we have studied the interaction of two para magnetoexcitons and of two ortho magnetoexcitons with the resultant spin equal to zero. Another two variant, are actual when the Coulomb exchange e-h interaction is negligible small and the spin of two electrons separately and the effective spin of two holes are interconnected and forms the singlet or the triplet states with zero spin projections on the magnetic field direction. The spin states of the four particles were constructed combining the singlet two electron state with the singlet two hole state as well as the triplet two electron state with the triplet two hole state. Only the bound states of two electrons and of two holes with singlet-singlet and with triplet-triplet spin structures were studied. It was shown that the spin structure of the type singlet-triplet and triplet-singlet do not exist due to the hidden symmetry of the magnetoexcitons. The orbital structure of the 2D magnetoexciton with wave vector →k ≠ 0 is similar with an in-plane electric dipole with the dipole moment perpendicularly oriented to the wave vector. The bimagnetoexciton with resultant wave vector →k = 0 is composed from two antiparallel oriented electric dipoles moving with antiparallel wave vectors →k ≠ 0. Their relative motion in the frame of the bound states is characterized by the variational wave functions φn(→k) depending on the modulus →k. It was shown that the stable bound state in the lowest Landau levels approximation do not exist in four investigated spin combinations. Instead of them a deep metastable bound state with an activation barrier comparable with the ionization potential of the magnetoexciton with →k = 0 was revealed in the triplet-triplet spin configuration. Its orbital structure in the momentum space representation is characterized by the maximal exciton density on the in-plane ring and with zero density in the center.
The energy spectrum of the two-dimensional cavity magnetoexciton-polaritons has been investigated previously, using exact solutions for the Landau quantization (LQ) of conduction electrons and heavy holes (hhs) provided by the Rashba method. Two lowest LQ levels for electrons and three lowest Landau levels for hhs lead to the construction of the six lowest magnetoexciton sates. They consist of two dipole-active, two quadrupole-active, and the two forbidden quantum transitions from the ground state of the crystal to the magnetoexciton states. The interaction of the four optical-active magnetoexciton states with the cavity-mode photons with a given circular polarization and with well-defined incidence direction leads to the creation of five magnetoexciton-polariton branches. The fifth-order dispersion equation is examined by using numerical calculations and the second-order dispersion equation is solved analytically, taking into account only one dipole-active magnetoexciton state in the point of the in-plane wave vector k→∥=0. The effective polariton mass on the lower polariton branch, the Rabi frequency, and the corresponding Hopfield coefficients are determined in dependence on the magnetic-field strength, the Rashba spin–orbit coupling parameters, and the electron and hole g-factors.
The Hamiltonian describing the interaction of the two-dimensional (2-D) magnetoexcitons with photons propagating with arbitrary-oriented wave vectors in the three-dimensional (3-D) space is deduced. The magnetoexcitons are characterized by the numbers ne and nh of the electron and hole Landau quantizations, by circular polarization σ⃗M of the holes in the p-type valence bands and by in-plane wave vectors k⃗‖. The photons are characterized by the wave vectors k⃗ with in-plane component k⃗‖ and perpendicular component kz, which is quantized in the case of microresonator. The interaction is governed by the conservation law of the in-plane components k⃗‖ of the magnetoexcitons and photons and by the rotational symmetry around the axis perpendicular to the layer, which leads to the alignment of the magnetoexcitons under the influence of the photons with circular polarization σ⃗±k⃗ and with probability proportional to |(σ⃗±k⃗⋅σ⃗∗M)|2.
The influence of the Rashba spin-orbit coupling on the two-dimensional (2D) electrons and holes in a strong
perpendicular magnetic field leads to different results of the Landau quantization in different spin projections. In Landau
gauge the unidimensional wave vector describing the free motion in one in-plane direction is the same for both spin
projections, whereas the numbers of the Landau quantization levels are different. For electron in s-type conduction band
they differ by one, as was established earlier by Rashba1, whereas for heavy holes in p-type valence band influenced by
the 2D symmetry of the layer they differ by three. There are two lowest spin-splitted Landau levels for electrons as well
as two lowest for holes. They give rise to four lowest energy levels of the 2D magnetoexcitons. It is shown that two of
them are dipole-active in band-to-band quantum transitions, one is quadrupole-active and the fourth is forbidden. The
optical orientation under the influence of the circularly polarized light leads to optical alignment of the magnetoexcitons
with different orbital momentum projections on the direction of the external magnetic field.
The energy spectrum of the collective elementary excitations of a 2D electrom-hole (e-h) system situated in a strong
perpendicular magnetic field in a state of Bose-Einstein condensation (BEC) with wave vector k=0 was investigated
in the frame of Bogoliubov theory of quasiaveraes. The starting Hamiltonian describing the e-h system contains not
only the Coulomb interaction between the particles lying on the lowest Landau levels(LLLs), but also the
supplementary interaction due to their virtual quantum transitions from the LLLs to the excited Landau levels and
return back. This supplementary interaction generates after the averaging on the ground BCS-type state wave
function the direct Hartree-type terms with attractive character, the exchange Fock-type terms giving rise to
repulsion as well as the similar terms arising after the Bogoliubov u - v transformation. The interplay of these three
parameters gives rise to the resulting different from zero interaction between the magnetoexcitons with wave vector
k=0 and to stability of their BEC as regards the collapse. It influences also on the single particle energy spectrum as
well as on the collective elementary excitations. It consists from six branches. Four of them are excitonic-type
branches, two of them being of exciton origin whereas the second two are the quasienergy branches representing the
mirror reflection of previous two branches. Another two branches are the optical and acoustical plasmon branches.
The carrier multiplication (CM) process generated from single photon absorption in spherical quantum dots is studied
theoretically taking into account as the perturbations the electron-radiation and the Coulomb electron-electron
interaction.
New aspects related with Raman scattering phenomena accompanying the light absorption were revealed. Side by side
with the creation of two or more electron-hole (e-h) pairs the Raman scattering photons can appear. A semiconductor
with simple parabolic e-h bands and impenetrable spherical symmetry quantum dots with strong size quantization were
considered. In these conditions the band-to-band quantum transitions lead to creation of e-h pairs with the same quantum
numbers l, n, m of the envelope functions. Only such type wave functions of the e-h pairs with the same quantum
numbers l, n, m were used as the real and virtual electron states in the frame of the perturbation theory. The photon states
are also introduced. First of all the probability to create two e-h pairs was studied in the scheme, when the first step is the
obligatory participation of electron-photon interaction followed by the second step involving the electron-electron
interaction. Side by side with this variant, the process of light absorption with the creation of two e-h pairs accompanied
by a Raman scattered photon was studied. In this case the second step of the perturbation theory is also based on the
electron-radiation interaction. In the first obligatory step the resonant part of the electron-radiation interaction is used,
whereas in the second step the antiresonant part is engaged. In difference on the first variant this second process leads to
smooth absorption band shape and can explain the existence of the threshold on the frequency dependence of the CM
quantum efficiency in the photon frequency region corresponding to creation of two e-h pairs.
Specific features of two-photon nutation in a system of coherent biexcitons in CuCl-type semiconductors are studied. It
is shown that, depending on the parameters of the system, nutation represents a process of periodic conversion of photon
pairs into biexcitons and vice versa. The possibility of phase control of optical nutation is predicted.
Taking into account the exciton-photon and elastic exciton-exciton interactions we investigated peculiarities of
transmission of supershort light pulses by thin semiconductor films. We predict the appearance of time dependent phase
modulation and dynamical red and blue shifts of transmitted pulse.
The Bose-Einstein Condensation (BEC) of the two-dimensional magnetoexcitons on the superposition state is studied.
The superposition of two excitonic states formed by electron and hole on the lowest Landau levels (0, 0) and on the first
excited Landau levels (1, 1) was considered. The generalized Bogoliubov u-v transformation was deduced. The criterion
on the exciton concentration was established. The influence of the BEC on the absorption band shape is discussed.
The indirect aftractive interaction between the electron and holes lying on the lowest Landau
levels on the surface of a two-dimensional structure in the presence of a strong perpendicular
magnetic field appears due to their virtual quantum transitions to excited Landau levels as a result
of the Coulomb scattering. The influence of this indirect interaction on the ground state energy and
on the chemical potential of the Bose-Einstein condensed magnetoexcitons is determined. The
corrections to the energy spectrum and to the wave function of the lowest magnetoexciton band due
to the influence of the first three excited exciton bands were investigated.
The generalized theory of the Hanle effect is developed for the case of propagation quantum beats. Time-integrated quantum beats of two polariton wave packets with the same group velocities and polarizations belonging to two different Zeeman components in Voigt geometry of the quadrupole-active ortho-exciton (Gamma) 5+ level in Cu2O crystal gives rise to the propagation Hanle effect. It is characterized by a quasiresonant dependence of the emitted light intensity on the magnetic field strength, as well as by a supplementary periodic dependence with the period inverse proportional to the sample thickness. The developed theory with the account of the effective propagation way explains recent experimental results published by Kono and Nagasawa.
The exciton absorption and emission bands in the presence of Bose-Einstein condensation (BEC) of excitons, induced by the coherent laser radiation is considered. The laser radiation creates the coherent macroscopic polarization of the crystal, which is described as a virtual BEC of excitons. The energy spectrum of the elementary excitations as well as the probabilities of the quantum transitions depend essentially on the frequency detuning (Delta) -. The nonequilibrium occupation numbers of out-of-condensate excitons nexq arising in the presence of virtual BEC influence on the forms of absorption and emission bands.
The renormalization of the energetic spectrum of paraexcitons in the presence of the Bose- Einstein condensate of orthoexcitons, or at least of their saturation, is studied. Due to the conversion of a pair of orthoexcitons into a pair of paraexcitons an absolute instability in the energy spectrum of paraexcitons appears. The paraexcitons that appeared can be downscattered by optical phonon (Gamma) 5-(88 cm-1) in a state above the bottom of the paraexciton band. This could be the reason for the observed peculiarities in the paraexciton luminescence band. On this basis a new explanation of the extra peak appearance in the luminescence spectrum of the uniaxially stressed Cu2O crystal is suggested. It has the same origin as the bump of the luminescence band in unstrained crystal. The spectral positions of the extra peak and of the bump differ due to the diminution of the ortho-para splitting in uniaxially stressed crystals. The difference of their widths is due to different densities of the condensed orthoexcitons in stressed and unstrained crystals.
The e-h plasma stimulated luminescence line A1 red-shifted (25 meV) due to band-gap renormalization is detected. The A1 emission lasts 100 ps. This peculiarity evidenced that a switching time of 100 ps can be achieved.
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