Theory of the excitonic fluctuation in a strong magnetic field. I. Development of the physical picture and a self-consistent Hartree theory

The physical picture of the appearance of the excitonic correlation in a strong magnetic field is developed in an electron-hole system which consists of one conduction band and one valence band. The field is assumed to be sufficiently strong that all the electrons and holes occupy their lowest Landau levels. Kinematical and dynamical aspects of such a truncated system are discussed in detail. The discussion does not deny the possibility of the excitonic phase transition in a strong magnetic field. The essence of the present physics is in the high degeneracy of the single-particle state and the strong shrinking of the electron wave function due to the magnetic field. In order to study the physics explicitly we construct a self-consistent Hartree theory. Further introducing static and local approximations for the excitonic fluctuation. We can determine the quasiparticle state and the fluctuation exactly near the transition point. We present the transition temperature in two limiting cases of the band configuration. We indicate the self-consistent Hartree theory combined with the static and local approximations is an unsatisfactory theory in the light of our physical picture. We also discuss possible improvements of the theory briefly.