Correlation energy and excitation spectra of two-dimensional electron-hole systems in high magnetic fields

Abstract

The correlation phenomena in two-dimensional semiconductors in high transverse magnetic fields are considered. A diagram expansion convergent at any temperatures T is obtained due to the special choice of an initial approximation. The expansion parameter appears equal to (E o/T)exp(-E o/2T) where E o is the exciton binding energy. The expansion parameter of the usual Matsubara diagram technique would be proportional to 1/T, if the noninteracting electron-hole system were choosen as the initial approximation, due to the infinite degree of degeneracy of the ground state. The system proves equivalent to the slightly non-ideal exciton gas with the same long-wave properties as the two-dimensional Bose gas. The Hartree-Fock approximation is exact at T = 0, but there is no phase transition with a long-range order creation at T≠0 in contrast to the HFA results (although there remain some properties of the transition such as the maximum of specific heat etc.). The Berezinsky-Kosterlitz-Thouless transition is predicted in the system for very low temperatures. The diagram technique developed may be employed to treat the thermodynamics of other infinitely-fold degenerated systems.