Hubbard U

Anisimov V i, Zaanen J and Andersen O K 1991 Band theory and Mott insuiators Hubbard U instead of Stoner / Phys. Rev. B 44 943... 

Anisimov VI, Zaanen J, Andersen OK (1991) Band theory and Mott insulators Hubbard U instead of Stoner I. Phys Rev B 44(3) 943... 

Figure 6.2 Variation of Hubbard U with band-width.

In materials in which a metal-insulator transition takes place the antiferromagnetic insulating state is not the only non-metallic one possible. Thus in V02 and its alloys, which in the metallic state have the rutile structure, at low temperatures the vanadium atoms form pairs along the c-axis and the moments disappear. This gives the possibility of describing the low-temperature phase by normal band theory, but this would certainly be a bad approximation the Hubbard U is still the major term in determining the band gap. One ought to describe each pair by a London-Heitler type of wave function... 

As U/I (or U/B) goes to infinity, then so does R/a. Moreover, the energy of the spin polaron at rest tends to —%B. It follows that the bandwidth is B and, in the limit when U/B is large, is unaffected by the Hubbard U. 

We emphasize that, in the insulating state, the gap is given by U- j(B1+ B2), and that it depends on the existence of moments and not on whether or not they are ordered. The gap is not related to the crystal structure. Indeed, if the crystal structure is such as to predict a gap, no antiferromagnetic lattice can form, unless the gap resulting from the Hubbard U is greater than that derived from the crystal structure. 

The second question that we discuss in this section is whether the Hubbard U determines the concentration at which the transition takes place—a possibility that could occur only in an impurity band—or whether the transition is purely of... 

In earlier work (see e.g. Mott 1987) the present author has attempted to combine the hypothesis that the Hubbard U determines the value of nc in doped semiconductors with the observation that the transition shows the properties of one of Anderson type (second order, cv = 0, quantum interference and interaction effects) by supposing that two Hubbard bands, separated by U, have small localized tails, as in Fig. 5.13, and that the transition occurs for a value of nc such... 

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

Electronic Structure Calculations. We have used first-principles electronic structure calculations as manifest in the (spin) density functional linearized muffin-tin orbital method to examine whether the asymmetry in properties is reflected in a corresponding asymmetry in the one-electron band structure. While in a more complete analysis explicit electron correlation of the Hubbard U type would be intrinsic to the calculation,17 we have taken the view that one-electron bandwidths point to the possible role that correlation might play and that correlation could be a consequence of the one-electron band structure rather than an integral part of the electronic structure. We have chosen the Lai- Ca,Mn03 system for our calculations to avoid complications due to 4f electrons in the corresponding Pr system. 

The cause or causes of the opening of a gap in the band structure of trans-PA has been the subject of many theoretical papers and of much debate (see Chapter 11, Section IV.A and reviews and discussions in [17,146,147,181]). It would seem that electron-phonon and electron-election interactions are of comparable importance. If electron correlations are treated by adding a Hubbard on-site interaction term to the SSH Hamiltonian, the available experimental results for tram-PA are best accounted for by taking about equal values for the electron-phonon coupling X and for the Hubbard U. It might be that in other CPs the importance of electron correlations is greater. Note, however, that a U term (on-site interactions) is not enough to treat the correlations correctly, especially if excitons are to be studied (see the discussion of the PDA case above). 

In contrast to the A4C60 salts, monomeric Na4C6o - stable above about 500 K -is a metal. The reason is that the shorter interfullerene distances of this compound reduce the Hubbard U and increase the bandwidth W, leading to an UAV value lying in the metallic domain [56]. Li4C6o also has a metallic monomer phase above 470 K [57,58]. The presence of distorted fulleride ions has not been investigated in these phases yet. 

An abundance of electron spectroscopic data has been reported for the high temperature superconductors. These include the valence band (VB), Cu 2p, and O Is photoelectron (UPS and XPS) data, the LuW and LasMiiV Auger (AES) data, the O K and Cu Lu x-ray emission (XES) data, and the O K and Cu Lta electron energy loss (EELS) and x-ray absorption near edge structure (XANES) data. These data reflect 1-, 2-, and 3-vaIence hole and core-hole density of states (DOS) and thertfore can provide direct measures of the Hubbard U and transfer parameters. Unfortunately, this data has proved to be difficult to interpret not surprisingly since the data for CuO is not even well understood. 

Most interestingly, we find that the Hubbard U decreases drastically the IBu exciton binding energy. We have shown the U-dependence of Eb in Figure 18. In fact, this result does clarify the... 

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