StatusThe thesis was presented on the 12 December, 2008
Approved by NCAA on the 26 February, 2009
Abstract– 0.42 Mb / in russian
– 0.37 Mb / in romanian
ThesisCZU 538.94; 537.632/.636
1.15 Mb /
The dissertation is dedicated to the solution of two interdependent problems of the theory of high-density two-dimensional excitons and electron-hole pairs in a strong perpendicular magnetic field. One of them is the influence of the excited Landau levels (ELLs) on two ground states of these systems such as Bose-Einstein condensation of magnetoexcitons and another one is the metallic-type electron-hole liquid. The second problem is the determination of the energy spectrum of the collective elementary excitations arising in the presence of these two ground states, when the excitations of the quasiparticles take place in the frame of the lowest Landau levels (LLLs) and in the absence of their kinetic energy.
In the present work a supplementary Hamiltonian of indirect interaction was calculated. It describes the additional indirect interaction between particles existing in the frame of the LLL, brought about by influence of ELL, under which two particles in the process of Coulomb interaction make virtual transitions from LLL to heteronymous and homonymous ELL and return back. The indirect supplementary e-e and h-h interaction gives rise to direct pairing terms and exchanges pairing terms. The first terms being negative increase the binding energy of magnetoexcitons and energy per pair in the EHL phase, whereas the second terms are repulsive. They diminish the influence of the direct pairing terms, but do not surpass them, so that the resulting influence of both terms remains attractive. The supplementary e-h attraction after the u-v transformation in the case of BEC of magnetoexcitons on the state with wave vector k gives rise to repulsive-type Bogoliubov self-energy terms. They stabilize the BEC in the small region of wave vectors . The energy per one e-h pair inside the EHD happens to be situated on the energy scale very close to the value of the chemical potential of the Bose-Einstein condensed magnetoexcitons with wave vector . These two phases can coexist.
It was shown that in the electron-hole system exists a possibility of different virtual quasi-energy complexes with different free energies and rates damping formation, which in fact depend on their free energies. We have found out such equations of motion for operators of density fluctuations which permits obtain plasma oscillations without damping in our approximation for the Green function. The intra-Landau level excitations of the two-dimensional electron-hole liquid are characterized by two branches of the energy spectrum. One of them is the acoustical plasmon type branch with the linear dispersion law in the range of small wave vectors and monotonically increasing with saturation behavior at higher wave vectors. The second branch of the elementary excitations is an optical-plasmon branch with quadratic dispersion law at small wave vectors with a roton-type dispersion at intermediary wave vectors and with a similar behavior as the acoustical branch at higher wave vectors. It is essential that there exist density oscillations within the LLL, even though 2D system is under the influence of strong perpendicular magnetic field and quasi-particles have no kinetic energy.
Energy spectrum of collective elementary excitations in the ground state of the system, representing the Bose-Einstein condensation of magnetoexcitons, consists of excitonic energy branches accompanied by plasmon satellites and pure plasma branches. It is important to note, that concentration corrections of excitonic branches of spectrum appear in the form of plasmon satellites and actually the system has exciton-plasmon branches and pure plasma branches of spectrum. Excitonic component of exciton-plasmon branches has an energy gap defined by the value of chemical potential, which in conditions of metastable dielectric liquid phase has negative values, depending on the filling factor. An energy gap in the spectrum results from the energy required for detachment of magnetic exciton from the composition of dielectric liquid in the process of formation of elementary collective excitation.
Basic results of the dissertation paper were published in the form of 25 scientific works (8 articles and 17 abstracts). The dissertation paper consists of 105 pages, 15 illustrations and 68 bibliographical references.