Nanoscale physics

Two-dimensional magnetoexcitons under the influence of the quantum point vortices
Moskalenko S.A.1, Moskalenko V.A.1,†, Podlesny I.V.1, Zubac I.A.1
1Institute of Applied Physics. Academiei, 5, MD-2028, Republic of Moldova. 
E-mail: zubac_ion@mail.ru
1. The theory of the two-dimensional (2D) magnetoexcitons was completed taking into account the electron-hole (e-h) Coulomb exchange interaction in addition to the direct one. In difference on the direct Coulomb e-h interaction, which gives rise to the quadratic dispersion lawwith magnetic mass depending on the magnetic field strengththe exchange e-h Coulomb interaction gives rise to linear dispersion law known as Dirac conewith group velocity depending on the interband dipole moment in the way: where  is the magnetic length.
2. The thermodynamic properties of the ideal 2D Bose gas with linear dispersion law were discussed in the Ref[1]. The critical temperature of the Bose-Einstein condensation of the 2D magnetoexcitons is different from zero even at the infinite homogeneous surface area and following[1] is proportional to the group velocity: . In the case of the magnetoexcitons it increases with the increasing magnetic field strength B. 
3. It was shown that the Chern-Simons (C-S) gauge field created by the quantum point vortices in the conditions of the fractional quantum Hall effects (FQHEs) leads to the formation of the composite electrons and holes with equal integer numbers of the attached to each particle quantum point vortices. The coherent superposition of the velocities of these vortices leads to the formation of the C-S vector potential, which depends on the difference between the density operators  of the electrons andof the holes. The C-S vector potential generates the effective magnetic field acting on the particles in addition to the external magnetic field. In the mean field approximation, when the average densities of electrons and of the holes coincide the effective C-S magnetic and electric fields vanish and the Landau quantization of the composite particles with the bare electron and hole effective masses take place only under the influence of the external magnetic field.

1.	Moskalenko S.A., Snoke D. W. Bose-Einstein condensation of excitons and biexcitons and coherent nonlinear optics with excitons // Cambridge University Press.-2000. P. 189.