The Character of Band Gaps in Transition Metal Compounds

Abstract

Perhaps the longest standing controversy in narrow band materials relates to the size and nature of the band gap in especially the late 3d transition metal compounds¹ which is of importance in understanding the systematics of band gaps², the closing of the gap in metallic systems3, the optical properties⁴ and superexchange interactions⁵ which involve virtual charge and spin excitations. Formally the band gap is determined by the minimum energy required to remove an electron from a system (E^N-1-E^N) plus the energy required to add one (E^N+1-E^N) where E^N is the ground state energy of the N electron system. This energy is equivalent to an electron-hole excitation in the N particle system to the lowest energy dissociative state i.e. the lowest energy of those states in which the electron and hole are uncorrelated. An important question then is what is the nature of the first ionized state and first electron affinity state in narrow band compounds? Obviously this is also an extremely relevant question in the new high temperature superconductors. For example the substitution of Ba for La in La₂CuO₄ or the addition of oxygen in YBa₂Cu₃O_6.5 must be charge compensated by holes in the valence band which then are the charge carriers. What is the nature of these holes — are they Cu 3d like or O2p like?