Pseudogap

For compositions with 50 and 57% sodium Ep lies within the tail of the partial DOS of the sp-band of tin, but Ep has still not reached the region where the partial DOS of sodium is large. This yields a small DOS (pseudogap) for these cases at the Fermi level. Therefore, one gets an explanation for the minimum of the conductivity (i.e. the maximum of the resistivity) near the equimolar composition, as can be seen in Table 1. (Analogously, for solid equimolar /3-NaSn even a indirect band gap at the Fermi level was reported in literature [16].)... 

As we saw in Section 3.2, in the absence of disorder (A(x)=Ao), the electron spectrum has a gap between the energies =-Aq and e=+Ao- Disorder gives rise to the appearance of electron states inside the gap, although for weak disorder a pseudogap still exists. Using the phase formalism [471, Ovchinnikov and Erikhman derived a losed expression for the integrated average density of states (J of the... 

FGM at arbitrary disorder strength [27]. The average density of states, p(c), that may be obtained from their result, is plotted in Fig. 3-5 for three values of the dimensionless disorder strength g = A/(vpAo). For small disorder, one clearly observes the pseudogap. Close to the center of this pseudogap ( c A0), the energy depen-... 

Here and below we assume e to be positive, which is sufficient in view of the symmetry of p(e) for the Hamiltonian Eq. (3.10). For g<2 the density of stales has a pseudogap (the Peierls gap filled with disorder-induced states). For g>2 the pseudogap disappears and the density of states becomes divergent at c=0. 

From Eq. (3.23) it is clear that at weak disorder (g 1) the density of states close to the middle of the pseudogap is strongly suppressed. The reason for this is that a large fluctuation of A(jc) is required in order to create an electron state with energy e < Aq. This makes it possible to apply a saddle-point approach to study the typ-... 

Comparing this result to Eq. (3.23), it is seen to give a good estimate for the shape of the density of states inside the pseudogap at g I. 

Fig. 12.3 DOSs (states/eV cell) for the MnuAlseGea compound from TB-LMTO-ASA calculations. The Fermi energy (Ef)=0 eV. The pseudogap region near the Ep is enlarged in the inset. The vertical dashed...

Furrer A (2005) Neutron Scattering Investigations of Charge Inhomogeneities and the Pseudogap State in High-Temperature Superconductors 114 171-204... 

Shortly after, we recognized that ScCu4Ga2 (Im3) [70] might also be tuned to a QC, but the correct stoichiometry and reaction conditions were not achieved in our limited experiments. Recently, Honma and Ishimasa [71] have reported that i-QC phase forms almost exclusively from a rapidly quenched ScisCu48Ga34 composition, emphasizing a very narrow phase width and its thermodynamic metastability at room temperature. However, the failure turned us to other Ga intermetallics, which led to the pseudogap tuning concepts that follow. 

In Sect. 4.2 we expand on pseudogap tuning concepts and illustrate these ideas and applications to the isotypic Mg2Cu6Ga5, Mg2Znn, and Na2Au6ln5. Because all the ACs we have obtained have very similar structural motifs, their structural regularities will be discussed together later in Sect. 5. 

Fig. 7 DOS and COOP data for Mg2Cu6Ga5 (EHTB). Note the pseudogap about 4 e/cell above EF. (Reproduced with permission from [75]. Copyright 2003 American Chemical Society)...

LMTO calculations on a hypothetical ScZn6 1/1 AC [82] revealed that Sc plays the same role here as in Sc-Mg-Cu-Ga 1/1 AC (Fig. 13). The Sc not only provides valence electrons to push into the pseudogap, but its d orbitals also afford mixing with Zn s, p orbitals to enhance the depth of the pseudogap. This may explain why no Mg-Zn binary or Mg-Cu-Ga ternary Tsai-type QCs exist, but the Sc-Cu-Zn i-QC [24,68] forms, although its discovery was not directed by the pseudogap tuning concept. 

As before, the DOS and COOP functions calculated for Na2 Auxins [84] exhibit a pseudogap and empty Au-In and In-In bonding states above F (Fig. 14). The... 

Mott NF (1969) Conduction in non-crystalline materials. 3. Localized states in a pseudogap and near extremities of conduction and valence bands. Phil Mag 19 835... 

Equation (39) shows that the conductivity is proportional to [iV(EF)]2, and N(Ef) is proportional to the effective mass. On the other hand, formulae such as (41) do not contain the effective mass. This is because the integral DE is inversely proportional to meff, as the analysis shows. However, if N E) is less than the free-electron value, as in a pseudogap (Section 16), no such cancellation occurs and the conductivity is proportional to [N(EF)]2. One may then write... 

If a conduction and valence band overlap slightly then a pseudogap or minimum in the density of states (Fig. 1.32) is expected, as first suggested by Mott (1966). As long as the overlap is small, one would expect the density of states, all... 

Fig. 132 (a) Overlapping bands forming a pseudogap, with localized states at the Fermi energy, (b) Total density of states, with localized states shaded. 

Pseudogaps in liquids are discussed in Chapter 10. Examples of pseudogaps in solids (Mg2 JBi2+x) are also described in Chapter 7. 

Hollinger et al (1985) have studied bronzes NaxW03 and Na2TayW1 y03 near the metal-insulator transition using photoelectron spectroscopy with synchrotron radiation. The results show that the transition is due to localization in an impurity band in a pseudogap. 

Throughout we make use of the pseudogap model outlined in Chapter 1, Section 16- A valence and conduction band overlap, forming a pseudogap (Fig. 10.1). States in the gap can be Anderson-localized. A transition of pure Anderson type to a metallic state (i.e. without interaction terms) can occur when electron states become delocalized at EF. If the bands are of Hubbard type, the transition can be discontinuous (a Mott transition). 

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