Comments on charge density waves

Abstract

Charge density waves (CDWs) in transition-metal compounds are shown to be a consequence of the first-order character of the crossover from localized to itinerant d-electron behavior; they are formed as this crossover is approached from either the localized-electron or the itinerant-electron side. Opening of a gap at the Fermi energy by changing the periodicity of the electron potential energy is a description that is only applicable on the approach from the itinerant-electron side. At crossover, single-valent transition-metal compounds with metal–metal d-electron bonding form cation clusters in which d-electrons are confined to molecular orbitals; normally, the individual bonds of a cluster are electron-pair bonds. However, in Zn[V₂]O₄, orbital ordering of a localized 3d-electron in an xy-orbital lowers the V–V separation in [011] and [101] chains sufficiently that the yz ± izx orbitals approach crossover from the localized-electron side. To resolve the magnetic frustration associated with the antiferromagnetic coupling between the localized spins in neighboring xy orbitals, the yz ± izx electrons become confined to one-electron bonds in a zigzag chain rather than an electron-pair bond within a dimer. The itinerant d-electrons of the zigzag chains are spin-polarized by intra-atomic exchange with xy-orbital spins. At crossover, compounds with cation–anion–cation bonding segregate into cations of an anion complex and cations with localized-electron spins; these segregations commonly result in a disproportionation electron transfer between cations that result in a static “negative-U” CDW in either single-valent or mixed-valent systems, but the perovskite HoNiO₃ demonstrates that this electron transfer does not always occur. The insertion of interstitial O_i atoms in the ${\hbox{L}}{{\hbox{a}}_2}{\hbox{Cu}}{{\hbox{O}}_{{\rm{4}} + \delta }}$ system allows monitoring of the formation of a dynamic phase segregation into mobile multihole polarons in a hole-free matrix that order into a thermodynamically distinct superconductive phase. The polarons may either order into pinned metallic stripes or as two-hole, two-electron bosonic polarons that become pinned to phonons in a superconductive phase that masks a quantum critical point.