Moldavian Journal of the Physical Sciences, Vol.1, N4, 2002 5 BOSE-EINSTEIN CONDENSATION OF EXCITONS IN IDEAL 2D SYSTEM IN STRONG MAGNETIC FIELD S. A. Moskalenko 1 , M. A. Liberman 2 , D. W. Snoke 3 and V. V. Boţan 2 1 Institute of Applied Physics of the Academy of Sciences of Moldova, Academic str. 5, Kishinev, MD2028, Republic of Moldova 2 Department of Physics, Uppsala University, Box 530, SE-751 21, Uppsala, Sweden 3 University of Pittsburgh, 405 Allen Hall, 3941 O’Hara, St., PA 15260, USA ABSTRACT We study ideal two-dimensional ( 2 D ) electron-hole system in a strong perpendicular magnetic field using the Keldysh-Kozlov-Kopaev method and generalized random phase approximation. The Bose-Einstein condensation of the correlated pairs takes place on a single particle state with an arbitrary wave vector k in a symmetric 2 D model. We show that the ground state energy per one exciton and the chemical potential at low exciton damping rates are nonmonotonous functions versus the value of the filling factor. They reveal the relative minima, so that the metastable states of the dielectric liquid phase with positive compressibility consisting of the Bose-Einstein condensate of magnetoexcitons and liquid drops can be formed by excitons with sufficiently high wave vectors and motional dipole moments. It is shown that the dielectric liquid phase of the Bose condensed excitons with low damping rate is more stable than the e h − metallic liquid phase. The observation of Bose-Einstein condensation ( BEC ) in atomic alkali and hydrogen gases using a laser and magnetic trapping [1,2] has greatly expanded the related research in recent years. As is well known, under certain conditions excitons, i.e. bound states of electron-hole pairs in semiconductors have bosonic properties [3]. Although theoretically recognized many years ago [3], experiments on BEC of excitons have made slow progress, because finite lifetime effects, strong interactions between excitons at high density, crystal imperfections and phonons in the crystal all act to complicate the system. In recent years, the system of coupled quantum wells in strong electric field has gained attention as a system with repulsive exciton-exciton interactions and long exciton lifetime, ideal for BEC of excitons. Another advantage of the two-dimensional ( 2 D ) system is a possibility of much faster cooling of hot photoexcited excitons compared with their bulk counterparts [4,5]. Another approach is to use strong magnetic field. It has been shown [6] that the properties of atoms and excitons are dramatically changed in a strong magnetic field such that the distance between Landau levels e eHmc / h exceeds the Rydberg energy. The diamagnetic excitons in bulk crystals were revealed in [7]. Their Bose-Einstein condensation was studied in [8]. Even more attractive and worth investigating is the electron-hole ( e h − ) system in two dimensions ( 2 D ) in the presence of a strong perpendicular magnetic field. In the latter case the energy spectrum of e-h system is completely discrete, is characterized by the number of the Landau levels, which are N -fold degenerated with 2 2 N S l π = / , where l is the magnetic length, 2 l c eH = / h , and S is the 2 D sample dimension. In the past two decades, a number of experimental [9,10,11,12] and theoretical [13,14,15] efforts have been dedicated to the study of 2D systems in a strong magnetic field. Lerner and Lozovik [13,14] studied the coherent pairing of electrons and holes resulting in the formation of the Bose-Einstein condensate of excitons in a single-particle state with wave vector 0 k = . In the Hartree-Fock approximation, when the coupling to the higher Landau levels and the correlation energy are neglected, the magnetoexcitons with 0 k = represent at 0 T = an ideal excitonic gas. A surprising