Semiconductor Mott-Hubbard

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

Matsumoto [98] tried to summarize the work done on the electronic structure of iron oxides and concluded that the about 2 eV in the bandgap of the hematite semiconductor measured in photoelectrochemistry indeed is based on the 3d band transition between the Fe3+ ions, which supports a Mott-Hubbard insulator. 

Figure 5. The metal-insulator transition in the doped semiconductor (Si P) and a divided metal. Here t/jc is the Mott-Hubbard correlation energy in the doped semiconductor, and t/dus is the corresponding charging energy of the divided metal.

Though the Mott-Hubbard picture is still under theoretical and experimental investigation, it is clear that materials with an odd number of electrons per repeat unit may be either metals or semiconductors, depending on the relative size of the bandwidth ( 4l) and the effective on-site electron-electron... 

If the on-site repulsion is large (U>4t), then two electrons cannot be accommodated on the same site, and the band fills up to 7c/b (Fig. 5c). The magnetic lattice period is twice the normal period, and one has a Mott-Hubbard semiconductor, in which Bragg or Umklapp scattering occurs at 4kp. 

Fig. 5. Band structure for full charge transfer (four electrons on four sites Z=l) (a) metal (b) Peierls semiconductor (c) Mott-Hubbard semiconductor...

It can be seen that e2 drops linearly at first, but has lower slope near the transition. There is no discontinuity, as would be expected for a Mott transition in a crystal (Chapter 4), and, as we believe, occurs (though broadened by temperature) in liquids such as fluid caesium (Chapter 10). The disorder here is greater than in a liquid metal because the orbitals of the electrons in the donors can overlap strongly. The present author (Mott 1978) has given conditions under which disorder can remove the discontinuity but this may not be relevant to such materials as Si P, because (Section 12) the Hubbard gap has disappeared, at any rate in many-valley semiconductors, at a concentration well below the transition,... 

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... 

It is interesting that superconductivity appears for T < Tq in doped cuprates, since ordinary cnprates are insulators, lacking conductivity at T = 0. Similar systems remain insnlators or semiconductors. Doped CuO is semiconducting with a quite low activation barrier. NiO and nickelates with Ni in the +2 valence state are semiconductors, thus insulators at T = 0. In the Mott insulators, the Hubbard U parameter, already discussed in Chapters 10 and 16, is necessary to explain the spectra and the lack of conductivity. Is this phenomenological parameter hiding some important physics ... 

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