Collective properties of magnetobiexcitons in quantum wells and graphene superlattices

The Bose-Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field are considered. The two different Hamiltonians of a dilute gas of magnetoexcitons with a dipole-dipole repulsion in superlattices, consisting of both QWs and graphene layers (GLs) in the limit of high magnetic field, have been reduced to one effective Hamiltonian-a dilute gas of two-dimensional excitons with the renormalized effective mass of the magnetoexciton, which depends on the magnetic field. This Hamiltonian does not include the vector potential. Moreover, for N excitons we have reduced the problem of 2Nx2-dimensional space onto the problem of Nx2-dimensional space by integrating over the coordinates of the relative motion of an electron and a hole. The instability of the ground state of the system of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is found. The stable system of indirect quasi-two-dimensional magnetobiexcitons, consisting of a pair of indirect excitons with opposite dipole moments, is considered. The density of the superfluid component n(s)(T) and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both the QW and graphene realizations.