Евгений Думанов » Публикация
Поделиться публикацией:
Опубликовано
2012-10-29
Опубликовано на SciPeople2013-08-23 15:27:05
ЖурналEDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag
Nambu-Goldstone modes of the two-dimensional Bose-Einstein condensed magnetoexcitons
Eur. Phys. J. B (2012) 85: 359
Аннотация
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
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 k = 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 v2(1 − v2), where v2 is the filling factor and (1 − v2)
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(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 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.