Simple treatment of the metal-insulator transition: Effects of degeneracy, temperature, and applied magnetic field

Abstract

A simple slave-boson representation combined with the Hartree-Fock approximation for Hund's rule coupling is introduced for a doubly degenerate narrow band, which bears a direct relation to that introduced previously in the nondegenerate case. Namely, one keeps the fermion representation of the spin operator to recover properly the energy of fermionic quasiparticles in the presence of an applied magnetic field. A simple two-parameter mean-field analysis of the metamagnetism is provided, with the emphasis on the role of Hund's rule coupling. We also analyze the appearance of the spin-split effective masses in the applied field and for the non-half-filled band situation. The Mott-Hubbard boundary is determined at nonzero temperature $(T>0)$; it shifts towards lower interactions with increasing $T$ and the field signaling the precursory localization effects, explicitly exhibited in the behavior of the magnetic susceptibility calculated in the Appendix. We also formulate a more general two-parameter rotationally invariant approach for an arbitrary degeneracy $d$ of equivalent orbitals and show that the Mott-Hubbard transition at zero temperature and at any integer filling $n>~1$ is always discontinuous. A brief overview of the experimental situation is also given.