A high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, gives an opportunity to create various new states of matter, i.e. exciton crystal, molecular compexes, Bose–Einstein condensation an exciton gas in a semiconductor, depending on the dimensionality of the system. We consider the problem of excitonic interaction in a semiconductor in its multi-electron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. A system of excitons in its ground state in a high magnetic field is similar to a weakly non-ideal Bose gas; whereas the excited states may be strongly bounded. It is shown that different types of exciton complexes in a quasi-one-dimensional semiconductor quantum wire, from crystals to molecular chains, can be obtained both by varying the direction and intensity of the magnetic field and by changing the exciton density. The existence and the stability of the Bose condensate in a bulk semiconductor due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons. Existence of the built-in condensate of excitons in a broad density range significantly changes the excitation spectrum of coupled excitons and photons in a high magnetic field and results in a number of interesting optical phenomena.
Magnon Bose-Einstein condensation and various phases of three-dimensonal quantum helimagnets under high magnetic field