| 1. |
|
|
| 2. |
- Moskalenko, S. A., et al.
(författare)
-
Coherence of two-dimensional electron-hole systems : Spontaneous breaking of continuous symmetries: A review
- 2013
-
Ingår i: Physics of the solid state. - 1063-7834 .- 1090-6460. ; 55:8, s. 1563-1595
-
Forskningsöversikt (refereegranskat)abstract
- The spontaneous breaking of the continuous symmetries of a two-dimensional electron-hole system in a strong magnetic field perpendicular to the plane leads to the formation of new ground states and determines the energy spectrum of collective elementary excitations that appear above these new ground states. In this review, the main attention is paid to the electron-hole system formed from coplanar magnetoexcitons under conditions of Bose-Einstein condensation in the ground state with the wave vector k = 0 taking into account the influence of excited Landau levels, when exciton-type elementary excitations coexist with plasmon-type oscillations. At the same time, the properties of a two-component system consisting of a two-dimensional electron gas and a two-dimensional hole gas spatially separated in a double quantum well under conditions of the fractional quantum Hall effect are of great interest, because these properties can affect the quantum states of magnetic excitons that are formed when the distance between the layers tends to zero. Bilayer electron systems are also considered under conditions of the fractional quantum Hall effect with the one-half filling factor for each layer and the total filling factor equal to unity for both layers. The coherence between the electron states in the two layers is equivalent to the formation of excitons in a macroscopic coherent state. This makes it possible to compare the energy spectrum of collective elementary excitations of Bose-Einstein condensed excitons under conditions of the quantum Hall effect and coplanar magnetoexcitons. The breaking of the global gauge symmetry or of the continuous rotational symmetry leads to the formation of a gapless spectrum of the Nambu-Goldstone type, whereas the breaking of the local gauge symmetry is accompanied by the appearance of a gap in the energy spectrum (Higgs phenomenon). These phenomena are equivalent to the formation of massless and massive particles in the relativistic physics. The application of the Nielsen-Chadha theorem, which determines the number of Nambu-Goldstone modes as a function of the number of broken symmetry operators, is demonstrated using the example of Bose-Einstein condensation of spinor atomic gases in an optical trap. This example is presented for a better understanding of the results obtained in the case of a Bose-Einstein condensation of coplanar magnetoexcitons. The Higgs phenomenon leads to the formation of composite particles under conditions of the fractional quantum Hall effect. Their description is given in terms of the Ginzburg-Landau theory. The possibilities for the appearance of spontaneous coherence in a system of indirect excitons in structures with a double quantum well are analyzed. The experimental attempts to create these conditions, the main results obtained in this field, and the accumulated knowledge are reviewed. The basic properties of the energy spectrum of magnetoexciton polaritons in a microcavity are formulated. A hypothesis is put forward about the possibility of forming two-dimensional magnetoexcitons and two-dimensional magnetoexciton polaritons of high density with attached point quantum vortices, i.e., about the possibility of forming new composite particles.
|
|
| 3. |
- Moskalenko, S. A., et al.
(författare)
-
Dispersion laws of the two-dimensional cavity magnetoexciton-polaritons
- 2016
-
Ingår i: Journal of Nanophotonics. - : SPIE - International Society for Optical Engineering. - 1934-2608. ; 10:3
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 4. |
- Moskalenko, S. A., et al.
(författare)
-
Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field
- 2006
-
Ingår i: Solid State Communications. - : Elsevier BV. - 0038-1098 .- 1879-2766. ; 140:5, s. 236-239
-
Tidskriftsartikel (refereegranskat)abstract
- The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.
|
|
| 5. |
- Moskalenko, S. A., et al.
(författare)
-
Landau quantization, Rashba spin-orbit coupling and Zeeman splitting of two-dimensional heavy-hole gases
- 2015
-
Ingår i: Physica status solidi. B, Basic research. - : Wiley. - 0370-1972 .- 1521-3951. ; 252:4, s. 730-742
-
Tidskriftsartikel (refereegranskat)abstract
- The origin of the g-factor of two-dimensional (2D) electrons and holes moving in the periodic crystal lattice potential with perpendicular magnetic and electric fields is discussed. The Pauli equation describing the Landau quantization accompanied by the Rashba spin-orbit coupling (RSOC) and Zeeman splitting (ZS) for 2D heavy holes with nonparabolic dispersion law is solved exactly. The solutions have the form of pairs of the Landau quantization levels due to the spinor-type wave functions. The energy levels depend on the amplitudes of the magnetic and electric fields, on the g-factor g(h), and on the parameter of nonparabolicity C. The dependences of two energy levels in any pair on the Zeeman parameter Z(h) = g(h)m(h) = 4m(0), where m(h) is the hole effective mass, are nonmonotonous and without intersections. The smallest distance between them at C = 0 takes place at the value Z(h) = n/2, where n is the order of the chirality terms determined by the RSOC and is the same for any quantum number of the Landau quantization.
|
|
| 6. |
- Dumanov, E. V., et al.
(författare)
-
Interaction of two-dimensional magnetoexcitons
- 2017
-
Ingår i: Physica. E, Low-Dimensional systems and nanostructures. - : Elsevier BV. - 1386-9477 .- 1873-1759. ; 88, s. 77-86
-
Tidskriftsartikel (refereegranskat)abstract
- We study interaction of the two-dimensional magnetoexcitons with in-plane wave vector (k) over right arrow (parallel to) = 0, taking into account the influence of the excited Landau levels (ELLS) and of the external electric field perpendicular to the surface of the quantum well and parallel to the external magnetic field., It is shown that the account of the ELLS gives rise to the repulsion between the spinless magnetoexcitons with (k) over right arrow (parallel to) = 0 in the Fock approximation, with the interaction constant g decreasing inverse proportional to the magnetic field strength B (g(0) similar to 1/B). In the presence of the perpendicular electric field the Rashba spin-orbit coupling (RSOC), Zeeman splitting (ZS) and nonparabolicity of the heavy-hole dispersion law affect the Landau quantization of the electrons and holes. They move along the new cyclotron orbits, change their Coulomb interactions and cause the interaction between 21) magnetoexcitons with (k) over right arrow (parallel to) = 0. The changes of the Coulomb interactions caused by the electrons and by the holes moving with new cyclotron orbits are characterized by some coefficients, which in the absence of the electric field turn to be unity. The differences between these coefficients of the electron-hole pairs forming the magnetoexcitons determine their affinities to the interactions. The interactions between the homogeneous, semihomogeneous and heterogeneous magnetoexcitons forming the symmetric states with the same signs of their affinities are attractive whereas in the case of different sign affinities are repulsive. In the heterogeneous asymmetric states the interactions have opposite signs in comparison with the symmetric states. In all these cases the interaction constant g have the dependence g(0) - 1/root B.
|
|
| 7. |
- Dumanov, E. V., et al.
(författare)
-
Mixed exciton-plasmon collective elementary excitations of the Bose-Einstein condensed two-dimensional magnetoexcitons with motional dipole moments
- 2013
-
Ingår i: Physica status solidi. B, Basic research. - : Wiley. - 0370-1972 .- 1521-3951. ; 250:1, s. 115-127
-
Tidskriftsartikel (refereegranskat)abstract
- The collective elementary excitations of the two-dimensional (2D) magnetoexcitons in the state of their BoseEinstein condensation (BEC) with nonzero wave vector k and inplane parallel oriented motional dipole moments are investigated in the HartreeFockBogoliubov approximation (HFBA). The breaking of the gauge symmetry is achieved using the Bogoliubov theory of quasiaverages and the KeldyshKozlovKopaev (KKK) method. The starting Hamiltonian and the Green's functions are determined using the integral two-particle operators instead of the single-particle Fermi operators. The infinite chains of equations of motion for the multioperator four- and six-particle Green-s functions are truncated following the Zubarev method and introducing a small parameter of the perturbation theory related with the lowest Landau levels (LLLs) filling factor and with the phase-space filling factor. The energy spectrum of the collective elementary excitations consists of the mixed excitonplasmon energy braches, mixed excitonplasmon quasienergy branches as well as the optical and acoustical plasmon energy branches. The exciton branches of the spectrum have gaps related with the negative values of the chemical potential and attractive interaction between the 2D megnetoexcitons with inplane, parallel oriented motional dipole moments. The slopes of the mixed excitonplasmon branches are determined by the group velocities of the moving condensed excitons in the laboratory reference frame. The acoustical and optical plasmon energy branches are gapless. Their dependence on the small wave vectors accounted from the condensate wave vector k is linear and quadratic, respectively, with saturation in the range of high values of the wave vectors.
|
|
| 8. |
- Moskalenko, S. A., et al.
(författare)
-
Effects of Rashba spin-orbit coupling, Zeeman splitting and gyrotropy in two-dimensional cavity polaritons under the influence of the Landau quantization
- 2015
-
Ingår i: European Physical Journal B. - : Springer. - 1434-6028 .- 1434-6036. ; 88:9
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the energy spectrum of the two-dimensional cavity polaritons under the influence of a strong magnetic and electric fields perpendicular to the surface of the GaAs-type quantum wells (QWs) with p-type valence band embedded into the resonators. As the first step in this direction the Landau quantization (LQ) of the electrons and heavy-holes (hh) was investigated taking into account the Rashba spin-orbit coupling (RSOC) with third-order chirality terms for hh and with nonparabolicity terms in their dispersion low including as well the Zeeman splitting (ZS) effects. The nonparabolicity term is proportional to the strength of the electric field and was introduced to avoid the collapse of the semiconductor energy gap under the influence of the third order chirality terms. The exact solutions for the eigenfunctions and eigenenergies were obtained using the Rashba method [E.I. Rashba, Fiz. Tverd. Tela 2, 1224 (1960) [Sov. Phys. Solid State 2, 1109 (1960)]]. On the second step we derive in the second quantization representation the Hamiltonians describing the Coulomb electron-electron and the electron-radiation interactions. This allow us to determine the magnetoexciton energy branches and to deduce the Hamiltonian of the magnetoexciton-photon interaction. On the third step the fifth order dispersion equation describing the energy spectrum of the cavity magnetoexciton-polariton is investigated. It takes into account the interaction of the cavity photons with two dipole-active and with two quadrupole-active 2D magnetoexciton energy branches. The cavity photons have the circular polarizations σk ± oriented along their wave vectors k, which has the quantized longitudinal component kz = ± π/Lc, where Lc is the resonator length and another small transverse component k∥ oriented in the plane of the QW. The 2D magnetoexcitons are characterized by the in-plane wave vectors k∥ and by circular polarizations σM arising in the p-type valence band with magnetic momentum projection M = ± 1 on the direction of the magnetic field. The selection rules of the exciton-photon interaction have two origins. The first one, of geometrical-type, is expressed through the scalar products of the two-types circular polarizations. They depend on the in-plane wave vectors k∥ even in the case of dipole-active transitions, because the cavity photons have an oblique incidence to the surface of the QW. Another origin is related with the numbers ne and nh of the LQ levels of electrons and heavy-holes taking part in the magnetoexciton formation. So, the dipole-active transitions take place for the condition ne = nh, whereas in the quadrupole-active transitions the relation is ne = nh ± 1. It was shown that the Rabi frequency ΩR of the polariton branches and the magnetoexciton oscillator strength fosc increase in dependence on the magnetic field strength B as ΩR ~ √B, and fosc ~ B. The optical gyrotropy effects may be revealed if changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection kz or equivalently changing the sign of the longitudinal projection kz at the same selected light circular polarization.
|
|
| 9. |
- Moskalenko, S. A., et al.
(författare)
-
Metastable bound states and spin structures of the two-dimensional bimagnetoexcitons
- 2018
-
Ingår i: Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IX. - : SPIE - International Society for Optical Engineering. - 9781510626140
-
Konferensbidrag (refereegranskat)abstract
- 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) over right arrow = 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 interconected 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) over right arrow not equal 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) over right arrow = 0 is composed from two antiparallel oriented electric dipoles moving with antiparallel wave vectors (k) over right arrow not equal 0 Their relative motion in the frame of the bound states is characterized by the variational wave functions phi(n) ((k) over right arrow) depending on the modulus vertical bar(k) over right arrow vertical bar. 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) over right arrow = 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.
|
|
| 10. |
- Moskalenko, S. A., et al.
(författare)
-
Metastable bound states of the interacting two-dimensional magnetoexcitons
- 2018
-
Ingår i: Solid State Communications. - : Elsevier. - 0038-1098 .- 1879-2766. ; 283, s. 14-21
-
Tidskriftsartikel (refereegranskat)abstract
- The possible formation of two-dimensional (2D) magnetic biexcitons composed of two 2D magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) with opposite center-of-mass wave vectors (k)over-right-arrow and -(k)over-right-arrow and with antiparallel electric dipole moments perpendicular to the corresponding wave vectors was investigated. Two spinor structures of two electrons and of two holes were considered. In the singlet-singlet state the spins of two electrons as well as the effective spins of two holes create the combinations with the total spin S = 0 and its projection on the magnetic field S-z = 0. The triplet-triplet state corresponds to S = 1 and S-z = 0. Two orbital Gaussian variational wave functions depending on vertical bar(k)over-right-arrow vertical bar and describing the relative motion of two magnetoexcitons inside the molecule were used. Analytical calculations show that in the LLLs approximation the stable bound states of bimagnetoexcitons do not exist, but there is a metastable bound state with the orbital wave function, having the maximum on the in-plane ring for the triplet-triplet spin configuration. The metastable bound state has an energy activation barrier comparable with the magnetoexciton ionization potential and gives rise to the new luminescence band due to the metastable biexciton-para exciton conversion with the frequencies higher than those of the para magnetoexciton luminescence line.
|
|
| 11. |
- Moskalenko, S. A., et al.
(författare)
-
Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation
- 2018
-
Ingår i: Semiconductors (Woodbury, N.Y.). - : PLEIADES PUBLISHING INC. - 1063-7826 .- 1090-6479. ; 52:14, s. 1801-1805
-
Tidskriftsartikel (refereegranskat)abstract
- The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector have opposite in-plane wave vectors and and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The bound state of two antiparallel dipoles moving with equal probability in any direction of the plane with equal but antiparallel wave vectors is characterized by the variational wave function of the relative motion depending on the modulus . The spins of two electrons and the effective spins of two holes forming the bound states were combined separately in the symmetric or in the antisymmetric forms with the same parameter for electrons and holes. In the case of the variational wave function the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring with the radius The stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with the ionization potential of the magnetoexciton with was revealed in the case and . In the case and only a shallow metastable bound state can appear.
|
|
| 12. |
- Moskalenko, S. A., et al.
(författare)
-
Spontaneous Symmetry Breaking and Coherence in Two-Dimensional Electron-Hole and Exciton Systems
- 2012
-
Ingår i: Journal of Nanoelectronics and Optoelectronics. - : American Scientific Publishers. - 1555-130X .- 1555-1318. ; 7:7, s. 640-670
-
Forskningsöversikt (refereegranskat)abstract
- The spontaneous breaking of the continuous symmetries of the two-dimensional (2D) electron-hole systems in a strong perpendicular magnetic field leads to the formation of new ground states and determines the energy spectra of the collective elementary excitations appearing over these ground states. In this review the main attention is given to the electron-hole systems forming coplanar magnetoexcitons in the Bose-Einstein condensation (BEC) ground state with the wave vector (k) over right arrow = 0, taking into account the excited Landau levels, when the exciton-type elementary excitations coexist with the plasmon-type oscillations. At the same time properties of the two-dimensional electron gas (2DEG) spatially separated as in the case of double quantum wells (DQWs) from the 2D hole gas under conditions of the fractional quantum Hall effect (FQHE) are of great interest because they can influence the quantum states of the coplanar magnetoexcitons when the distance between the DQW layers diminishes. We also consider in this review the bilayer electron systems under conditions of the FQHE with the one half filling factor for each layer and with the total filling factor for two layers equal to unity because the coherence between the electron states in two layers is equivalent to the formation of the quantum Hall excitons (QHExs) in a coherent macroscopic state. This makes it possible to compare the energy spectrum of the collective elementary excitations of the Bose-Einstein condensed QHExs and coplanar magnetoexcitons. The breaking of the global gauge symmetry as well as of the continuous rotational symmetries leads to the formation of the gapless Nambu-Goldstone (NG) modes while the breaking of the local gauge symmetry gives rise to the Higgs phenomenon characterized by the gapped branches of the energy spectrum. These phenomena are equivalent to the emergence of massless and of massive particles, correspondingly, in the relativistic physics. The application of the Nielsen-Chadha theorem establishing the number of the NG modes depending of the number of the broken symmetry operators and the elucidation when the quasi-NG modes appear are demonstrated using as an example related with the BEC of spinor atoms in an optical trap. They have the final aim to better understand the results obtained in the case of the coplanar Bose-Einstein condensed nnagnetoexcitons. The Higgs phenomenon results in the emergence of the composite particles under the conditions of the FQHE. Their description in terms of the Ginzburg-Landau theory is remembered. The formation of the high density 2D magnetoexcitons and magnetoexciton-polaritons with point quantum vortices attached is suggested. The conditions in which the spontaneous coherence could appear in a system of indirect excitons in a double quantum well structures are discussed. The experimental attempts to achieve these conditions, the main results and the accumulated knowledge are reviewed.
|
|
| 13. |
- Moskalenko, S. A., et al.
(författare)
-
Two-dimensional cavity polaritons under the influence of the landau quantization, Rashba spin-orbit coupling and Zeeman splitting
- 2016
-
Ingår i: IFMBE Proceedings. - Singapore : Springer. - 9789812877352 ; , s. 35-39
-
Konferensbidrag (refereegranskat)abstract
- The properties of the two-dimensional cavity polaritons subjected to the action of a strong perpendicular magnetic and electric fields, giving rise to the Landau quantization (LQ) of the 2D electrons and holes accompanied by the Rashba spinorbit coupling, by the Zeeman splitting and by the nonparabolicity of the heavy-hole dispersion law were investigated. Our results are based on the exact solutions for the eigenfunctions and for the eigenvalues of the Pauli- type Hamilonian with third order chirality terms for heavy-holes and with first order chirality terms for electrons. They were obtained using the method proposed by Rashba [1]. We predict the drastic changements of the optical properties of the cavity polaritons. The main of them are related with the existence of a multitude of the polariton energy levels nearly situated on the energy scale, their origin being related with the LQ of the electrons and holes. Most of these levels have the nonmonotonous dependences on the magnetic field strength B with overlapping and intersections.
|
|
| 14. |
- Moskalenko, S. A., et al.
(författare)
-
Two-dimensional cavity polaritons under the influence of the perpendicular strong magnetic and electric fields. The gyrotropy effects
- 2015
-
Ingår i: Solid State Communications. - : Pergamon Press. - 0038-1098 .- 1879-2766. ; 222, s. 58-64
-
Tidskriftsartikel (refereegranskat)abstract
- The properties of the two-dimensional cavity polaritons subjected to the action of a strong perpendicular magnetic and electric fields, giving rise to the Landau quantization (LQ) of the 2D electrons and holes accompanied by the Rashba spin-orbit coupling, by the Zeeman splitting and by the nonparabolicity of the heavy-hole dispersion law are investigated. We use the method proposed by Rashba (1960) [1] and the obtained results are based on the exact solutions for the eigenfunctions and for the eigenvalues of the Pauli-type Hamilonians with third order chirality terms and nonparabolic dispersion law for heavy-holes and with the first order chirality terms for electrons. The selection rules of the band-to-band optical quantum transitions as well as of the quantum transitions from the ground state of the crystal to the magnetoexciton states depend essentially on the numbers n(e) and n(h) of the LQ levels of the (e-h) pair forming the magnetoexciton. It is shown that the Rabi frequency Omega(R) of the polariton branches and the magnetoexciton oscillator strength f(osc), increase with the magnetic field strength B as Omega(R) similar to root B and f(osc) similar to B. The optical gyrotropy effects may be revealed changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection k(z) or equivalently changing the sign of k(z) at the same selected circular polarization.
|
|
| 15. |
- Moskalenko, S. A., et al.
(författare)
-
Collective Elementary Excitations of Two-Dimensional Magnetoexcitons in the Bose-Einstein Condensation State
- 2009
-
Ingår i: Journal of Nanoelectronics and Optoelectronics. - : American Scientific Publishers. - 1555-130X .- 1555-1318. ; 4:1, s. 52-75
-
Forskningsöversikt (refereegranskat)abstract
- The collective elementary excitations of a system of two-dimensional magnetoexcitons in a state of Bose-Einstein condensation (BEC) with arbitrary wave vector was investigated in Hartree-Fock-Bogoliubov approximation. The breaking of the gauge symmetry of the Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The equations of motion were written in the frame of the starting electron and hole creation and annihilation operators. The chains of equations of motion for a set of Green's functions describing the exciton-type excitations as well as the plasmon-type excitations were deduced. Their disconnections were introduced using the perturbation theory with a small parameter of the theory proportional to the filling factor multiplied by the phase space filling factor. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches, because the plasmon-type elementary excitations are gapless and are lying in the same spectral interval as the exciton-type elementary excitations.
|
|
| 16. |
- Moskalenko, S. A., et al.
(författare)
-
Exciton Condensation Under High Magnetic Field
- 2011
-
Ingår i: Journal of Nanoelectronics and Optoelectronics. - : American Scientific Publishers. - 1555-130X .- 1555-1318. ; 6:4, s. 393-419
-
Forskningsöversikt (refereegranskat)abstract
- The new results in the theory of Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexcitons formed by the high-density electron-hole (e-h) pairs created on the semiconductor mono-layer in a strong perpendicular magnetic field are reviewed. One of them is the metastable dielectric liquid phase (MDLP) formed by the 2D magnetoexcitons BEG-ed on the single-particle state with sufficiently large values of the wave vector k, so that its product kl with the magnetic length l equals about kl approximate to 3-4. This state was revealed in the conditions when the electrons and holes are situated on the lowest Landau levels (LLLs) and the polarizability of the Bose gas was calculated on the base of the Anderson-type coherent excited states. They give rise to correlation energy and to chemical potential displaying a nonmonotonous dependence on the filling factor v(2) with a relative minimum and with positive compressibility in its vicinity. The influence of the excited Landau levels (ELLs) on the quantum states of the e-h system is due to the virtual quantum transitions of particles from the LLLs to ELLs during the Coulomb scattering processes and to their subsequent return back. These quantum transitions were taken into account in the frame of the second order perturbation theory giving rise to an effective Hamiltonian describing the supplementary indirect interactions between the particles lying on the LLLs. This interaction is characterized by a small parameter equal to the ratio r of the magnetoexciton ionization potential l(ex)(0) to the Landau quantization energy (h) over bar omega(c). The parameter r = l(ex)(0)/(h) over bar omega(c), decreases as H-1/2 with the increasing the magnetic field strength H. The supplementary interaction is attractive, making the magnetoexcitons in the Hartree approximation more robust. Nevertheless its exchange, Fock terms as well as the Bogoliubov u-v transformation terms give rise to positive, repulsion-type contributions to the chemical potential. The Bose gas of magnetoexcitons with k = 0 becomes weakly nonideal when the ELLs are taken into account. The collective elementary excitations of two ground states corresponding to BEG-ed magnetoexcitons forming either a nonideal Bose gas with k = 0 or the MDLP with kl approximate to 3-4 were studied in the frame of the perturbation theory with the infinitesimal parameter v(2)(1 - v(2)), chosen as a product of the filling factor v(2) and of the phase space filling factor (1 - v(2)). The collective elementary excitations in both cases consist from the exciton and plasmon branches. Due to the presence of the condensate there are energy and quasi-energy branches. The self-energy parts containing the unknown frequency in denominators increase the degree of the dispersion equations and give rise to mixed exciton-plasmon and exciton-exciton elementary excitation branches.
|
|
| 17. |
- Moskalenko, S. A., et al.
(författare)
-
Nambu-Goldstone modes of the two-dimensional Bose-Einstein condensed magnetoexcitons
- 2012
-
Ingår i: European Physical Journal B. - : Springer Science and Business Media LLC. - 1434-6028 .- 1434-6036. ; 85:10, s. 359-
-
Tidskriftsartikel (refereegranskat)abstract
- The collective elementary excitations of two-dimensional magnetoexcitons in a Bose-Einstein condensate (BEC) with wave vector κ = 0 were investigated in the framework of the Bogoliubov theory of quasiaverages. The Hamiltonian of the electrons and holes lying in the lowest Landau levels (LLLs) contains supplementary interactions due to virtual quantum transitions of the particles to the excited Landau levels (ELLs) and back. As a result, the interaction between the magnetoexcitons with κ = 0 does not vanish and their BEC becomes stable. The equations of motion for the exciton operators d(P) and d†(P) are interconnected with equations of motion for the density operators ρ(P) and D(P). Instead of a set of two equations of motion, as in the case of usual Bose gas, corresponding to normal and abnormal Green's functions, we have a set of four equations of motion. This means we have to deal simultaneously with four branches of the energy spectrum, the two supplementary branches being the optical plasmon branch represented by the operator ρ(P) and the acoustical plasmon branch represented by the operator D(P). The perturbation theory on the small parameter v 2(1 - v 2), where v 2 is the filling factor and (1 - v 2) is the phase space filling factor was developed. The energy spectrum contains only one gapless, true Nambu-Goldstone (NG) mode of the second kind with dependence ω(κ) ≈ κ 2 at small values κ describing the optical-plasmon-type oscillations. There are two exciton-type branches corresponding to normal and abnormal Green's functions. Both modes are gapped with roton-type segments at intermediary values of the wave vectors and can be named as quasi-NG modes. The fourth branch is the acoustical plasmontype mode with absolute instability in the region of small and intermediary values of the wave vectors. All branches have a saturation-type dependencies at great values of the wave vectors. The number and the kind of the true NG modes is in accordance with the number of the broken symmetry operators. The comparison of the results concerning two Bose-Einstein condensates namely of the coplanar magnetoexcitons and of the quantum Hall excitons in the bilayer electron systems reveals their similarity.
|
|
| 18. |
- Moskalenko, S. A., et al.
(författare)
-
True, quasi and unstable Nambu-Goldstone modes of the two-dimensional Bose-Einstein condensed magnetoexcitons
- 2013
-
Ingår i: Solid State Communications. - : Elsevier BV. - 0038-1098 .- 1879-2766. ; 155, s. 57-61
-
Tidskriftsartikel (refereegranskat)abstract
- The collective elementary excitations of two-dimensional magnetoexcitons in a Bose-Einstein condensate (BEC) with wave vector k→=0 were investigated in the framework of the Bogoliubov theory of quasi-averages. The Hamiltonian of the electrons and holes lying in the lowest Landau levels (LLLs) contains supplementary interactions due to virtual quantum transitions of the particles to the excited Landau levels (ELLs) and back. As a result, the interaction between the magnetoexcitons with k→=0 does not vanish and their BEC becomes stable. The energy spectrum contains only one gapless, true Nambu-Goldstone (NG) mode of the second kind with dependence ω(k)≈k2 at small values k describing the optical-plasmon-type oscillations. There are two exciton-type branches corresponding to normal and abnormal Green's functions. Both modes are gapped with roton-type segments at intermediary values of the wave vectors and can be named as quasi-NG modes. The fourth branch is the acoustical plasmon-type mode with absolute instability in the region of small and intermediary values of the wave vectors. All branches have a saturation-type dependencies at great values of the wave vectors. The number and the kind of the true NG modes are in accordance with the number of the broken symmetry operators.
|
|
