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Опубликовано
2011-12-01
Опубликовано на SciPeople2013-08-23 15:23:41
ЖурналAmerican Scientific Publishers
Exciton Condensation Under High Magnetic Field
Journal of Nanoelectronics and Optoelectronics, Volume 6, Number 4, pp. 393-419(27)
Аннотация
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 BEC-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 ≈ 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 v2
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 Iex0 to the Landau
quantization energy c. The parameter r = Iex0/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
BEC-ed magnetoexcitons forming either a nonideal Bose gas with k =0 or the MDLP with kl ≈3−4
were studied in the frame of the perturbation theory with the infinitesimal parameter v21−v2, chosen
as a product of the filling factor v2 and of the phase space filling factor 1−v2. 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.