Dimensionality of Density Fluctuations and the Excitonic Phase of Electron-Hole Systems in Strong Magnetic Fields

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Abstract
Dimensionality of the density fluctuation of electron-hole systems in strong magnetic fields is examined in connection with the possibility of the excitonic phase. Our system consists of one conduction and one valence band. Even in extremely strong fields where only one Landau level of each carrier is taken into consideration and the energy spectrum is purely one-dimensional, the density fluctuations are three-dimensional as far as magnetic field strength is finite. This is due to the motion of carriers which is perpendicular to the field and caused by interactions. Thus the phase transition with the excitonic order parameter may occur at a finite temperature. However, as the field is increased, fluctuations acquire one-dimensional characteristics and critical temperature should be reduced.