The metaldielectric transition in semimetals in extremely high magnetic fields. I
Abstract
An analysis is given of a model of a semimetal with isotropic electron and hole spectra, separated in momentum space. The applied magnetic field is assumed to be strong enough to ensure that only one quantum level participates in each spectrum. The overlapping of levels is such that the Fermi energy is greater than the binding energy of the particle pairs. Weak point interaction is assumed to operate between the particles, which is valid for fields and dielectric constants that are not too high. The sign of the interaction can be arbitrary. Since the analysis is concerned with spinless fermions (degeneracy removed by the field), the system exhibits interactions between electrons and holes, but there is no interaction between particles of the same kind. It is shown that Cooper pairing of particles with the same charge is absent, but electronhole excitons are formed, i.e., the transition to a dielectric takes place. The problem leads to “parquet” equations and is therefore solved only with logarithmic accuracy. A general method is developed for finding the “anomalous” averages corresponding to pairing, and the binding energies from “asymmetric” parquet vertices.
 Publication:

Journal of Low Temperature Physics
 Pub Date:
 February 1970
 DOI:
 10.1007/BF00628100
 Bibcode:
 1970JLTP....2...37A