A Simple Treatment of Metal-Insulator Transition: Effects of Degeneracy, Temperature and Applied Magnetic Field

TL;DR

This paper introduces a simplified slave-boson approach to study the metal-insulator transition in degenerate bands, analyzing effects of temperature, magnetic field, and Hund's coupling, revealing discontinuous transitions and localization precursors.

Contribution

It develops a new two-parameter mean-field method for degenerate bands, extending previous nondegenerate models, and analyzes the impact of Hund's rule coupling and magnetic field on the transition.

Findings

Mott-Hubbard boundary shifts to lower interactions with increasing temperature and magnetic field.

Discontinuous Mott-Hubbard transition at zero temperature for integer fillings greater than one.

Presence of spin-split effective masses in applied magnetic fields.

Abstract

A simple slave-boson representation combined with the Hartree-Fock approximation for the 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 the Hund's rule coupling. We also analyse the appearance of the spin-split effective masses in the applied field and for nonhalf-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 signalling 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 experimental situation is also made.