1. The exchange e-h Coulomb scattering takes place with the annihilation and the creation of the e-h pairs with the resultant electronic charges equal to zero. During the direct Coulomb scattering the electron and a hole remain in the same energy bands interacting as a charged particles. They have dipole-dipole interaction, when the interband dipole moments c v r − are different from zero. It happens when the crystals have the dipole active optical quantum transitions. We have considered the semiconductor layers of the type GaAs with s-type h 32. z j = ± The Lorentz force in the Landau gauge description determines the positions of the Landau quantization oscillations of the electrons and holes and their distances in the frame of the magnetoexcitons. Their relative and center of mass motions are interconnected. In difference on the direct Coulomb e-h interaction, which gives rise to the quadratic dispersion lawh2k 2 2M(B) with magnetic mass M (B) depending on the magnetic field strength B, the exchange e-h Coulomb interaction gives rise to linear dispersion law known as Dirac cone g hv k with group velocity g v depending on the interband dipole moment in the way: 2 g 0 v , c v r l B − » » where 0 l 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 (BEC) 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. The new possibilities to study the BEC phenomenon of the 2D magnetoexcitons appeared. But it takes place only at the filling factors v of the lowest Landau levels smaller than unity (v <1) [2].

References

[1] S. A. Moskalenko, D. W. Snoke, Bose-Einstein condensation of excitons and biexcitons and coherent nonlinear optics with excitons, Cambridge University Press, New York (2000), p. 189. [2] S. A. Moskalenko, M.A. Liberman, D. W. Snoke, V.V. Botan, Phys. Rev. B 66, 245316 (2002).