Mott-Hubbard insulators for systems with orbital degeneracy
Olle Gunnarsson(1), Erik Koch(2), Richard M. Martin(2) ((1), Max-Planck-Institut f\"ur Festk\"orperforschung, Stuttgart, Germany, (2), Department of Physics, University of Illinios, Urbana)
TL;DR
This paper investigates how electron hopping influences the Mott-Hubbard band gap in systems with orbital degeneracy, revealing a growth pattern of the hopping contribution with respect to the degeneracy N.
Contribution
It provides a theoretical analysis of the dependence of the Mott-Hubbard gap on orbital degeneracy and identifies a crossover in the hopping behavior at large N.
Findings
Hopping contribution scales as approximately rac12; \, \\sqrt{N}W
Crossover to linear N dependence occurs at large N
Results support the rac12; \, \\sqrt{N}W growth in certain models
Abstract
We study how the electron hopping reduces the Mott-Hubbard band gap in the limit of a large Coulomb interaction U and as a function of the orbital degeneracy N. The results support the conclusion that the hopping contribution grows as roughly \sqrt{N}W, where W is the one-particle band width, but in certain models a crossover to a \sim NW behavior is found for a sufficiently large N.
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