Mott gap

Another famous hopping model is Mott s variable range hopping [23], in which it is assumed that the localized sites are spread over the entire gap. At low temperatures, the probability to find a phonon of sufficient energy to induce a jump to the nearest neighbor is low, and hops over larger distances may be more favorable. In that case, the conductivity is given by... 

First we consider the origin of band gaps and characters of the valence and conduction electron states in 3d transition-metal compounds [104]. Band structure calculations using effective one-particle potentials predict often either metallic behavior or gaps which are much too small. This is due to the fact that the electron-electron interactions are underestimated. In the Mott-Hubbard theory excited states which are essentially MMCT states are taken into account dfd -y The subscripts i and] label the transition-metal sites. These... 

Semiconductors that are used in electrochemical systems often do not meet the ideal conditions on which the Mott-Schottky equation is based. This is particularly true if the semiconductor is an oxide film formed in situ by oxidizing a metal such as Fe or Ti. Such semiconducting films are often amorphous, and contain localized states in the band gap that are spread over a whole range of energies. This may give rise... 

Table 4.4 The gap Eg) and binding (Ej) energies of (Mott-Wannier and Frenkel) excitons in different materials...

Figure 5-47 shows the Mott-Schottky plot of n-type and p-type semiconductor electrodes of gallium phosphide in an acidic solution. The Mott-Schottl plot can be used to estimate the flat band potential and the effective Debye length I D. . The flat band potential of p-type electrode is more anodic (positive) than that of n-type electrode this difference in the flat band potential between the two types of the same semiconductor electrode is nearly equivalent to the band gap (2.3 eV) of the semiconductor (gallium phosphide). 

Figure 12. Mott-Schottky plots as in Figure 11 but for p-type GaP in 0.5M HgSO. Symbols have the same meaning as in Figure 11 (IQ).

HOMO of DBTTF and the LUMO of TCNQ, respectively (Fig. 4b). Source and drain electrodes are several organic metals of the TTF TCNQ type having different chemical potentials predicted using Fig. 4c which is the same as Fig. 2a. For the electrodes whose chemical potentials are set within the conduction band of the channel material, FET exhibited n-type behavior (A in Fig. 4d). When the chemical potentials of organic metals are allocated within or near the valence band of the channel, p-type behaviors were observed (E, F in Fig. 4d). When the chemical potentials of the electrodes are within the gap of the channel, FET exhibited ambipolar-type behavior (B-D in Fig. 4d). Since the channel material is the alternating CT solid, the drain current is not excellent and a Mott type insulator of DA type or almost neutral CT solid having segregated stacks is much preferable in this context. 

Kezsmarki I, Shimizu Y, Mihaly G, Tokura Y, Kanoda K, Saito G (2006) Depressed charge gap in the triangular-lattice Mott insulator k-(ET)2Cu2(CN)3. Phys Rev B74 201101/1-4... 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

Hubbard (13) elucidated a mathematical description of the change from one situation to another for the simplest case of a half-filled s band of a solid. His result is shown in Figure 11. For ratios of W/U greater than the critical value of 2/ /3 then a Fermi surface should be found and the system can be a metal. This critical point is associated with the Mott transition from metal to insulator. At smaller values than this parameter, then, a correlation, or Hubbard, gap exists and the system is an antiferromagnetic insulator. Both the undoped 2-1 -4 compound and the nickel analog of the one dimensional platinum chain are systems of this type. At the far left-hand side of Figure 11 we show pictorially the orbital occupancy of the upper and lower Hubbard bands. 

The important feature of magnetic insulators is that, being nonmetallic, they have a band gap and possess unpaired electrons. They show crystal-field transitions due to the presence of open-shell (d") ions. Mott proposed that electron repulsion can be responsible for the breakdown of the normal band properties of transition-metal... 

In transitional and noble metals the s-band crosses the d-band and is hybridized with it. The situation is discussed in a number of papers (cf. Mott 1964, Heine 1969, p. 25). Figure 1.7, taken from Heine (1969), shows the band structure of copper in the (111) direction. 2y is the hybridization gap where the 4s-band crosses the d-band. ... 

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,... 

Other experimental evidence that the index for is unity is scanty. If we are right in thinking that hopping conduction near the transition is not affected by a Coulomb gap (Chapter 1, Section 15), evidence can be obtained from this phenomenon Castner s group (Shafarman et ai 1986) give evidence for v = 1 in Si P. For early work in a two-dimensional system see Pollitt (1976) and Mott and Davis (1979, p. 138), which give evidence that v = 1. In two-dimensional systems there is evidence (Timp et ai 1986) that the Coulomb gap has little effect on hopping conduction. 

Anderson type (though affected of course by long-range interaction). Until recently it was supposed by the present author that the former is the case. We must now favour, however, the latter assumption for many-valley materials (e.g. Si and Ge), the Hubbard gap opening up only for a value of the concentration n below nc. The first piece of evidence comes from a calculation of Bhatt and Rice (1981), who found that for many-valley materials this must be so. The second comes from the observations of Hirsch and Holcomb (1987) that compensation in Si P leads to localization for a smaller value of nc than in its absence. As pointed out by Mott (1988), a Mott transition occurs when B = U (B is the bandwidth, U the Hubbard intra-atomic interaction), while an Anderson transition should be found when B 2 V, where V is some disorder parameter. Since U e2/jcuH, where aH is the hydrogen radius, and K e2/jca, and since at the transition a 4aH, if the transition were of Mott type then it should be the other way round. 

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