Peierls GAP

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

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. 

Figure 8 Temperature dependence of (a) BCS-like Peierls gap AP [29] and (b) integrated half-gap A of TEA(TCNQ)2 [15]. The gaps are normalized to their 0 K values and the temperatures to Tc = 210 K.

The effects of an external periodic potential VQ with Q = 2kP on an electronic-Peierls transition at T = TP have been investigated in detail by Hansen and Carneiro [51] within a mean-field theory. They have found in this case that the Peierls transition is somewhat smeared out around TP, but not depressed. The modified gap 2A(7) is larger than the original Peierls gap 2AP(7) below TP and it does not vanishes above TP. Thus only a change in the slope of A(7) at TP recalls in this case the underlying transition [28,51]. If VQ is small enough [V"Q < 0.1AP(0)], then A(T) varies dramatically around TP with dMdl maximum, at TP. One also gets in this case the two limits... 

It is useful to recall here the example of Fig. 8, which reports, for the special case of TEA(TCNQ)2, both the experimental gap 2A(7) = EC(T) (curve a) and the BCS-like Peierls gap 2AP(T) (curve b), on normalized scales. In this figure the temperature T0 = 210 K at which dNdT is maximum has been identified simply with TP, as in the small yQ limit. 

Fig. 2.4. (a) Schematic representation of a quasi ID Fermi surface with nesting vector fcp = (2A F,7r/6,0). The dash-dotted line is the resulting new Brillouin zone, (b) Opening of the Peierls gap 2A at ifep in the dispersion relation... 

Figure 16 A band picture and a classical particle one for the Peierls transition, (a) metallic band, (b) particle picture of metal, (c) band with the Peierls gap, (d) particle picture of the insulating state for the electron density n = /a.

In the weak-coupling limit becomes much larger than the length of the unit cell a for rrani -polyacetylene) and the Peierls gap has a strong effect... 

In this section we will illustrate the gap concept by some explicit applications. We exclude applications to small molecules as well as spin-polarized band calculations, which fall outside the scope of this article. Several of the examples to be discussed are related to the concepts of Mott and Peierls gaps,21 28 but we will not discuss these very interesting aspects here. A number of—direct or indirect—applications on polyenes have been carried out these have been treated in another paper.29... 

The one-dimensional Frohlich model is investigated for kgT S0 Eg with the mean field Peierls gap at T = 0. Treating the ions classically... 

This effect is distinct frcm the stabilization of the Peierls gap by the softening of intramolecular optical modes suggested by M. J. Rice, C. B. Duke, and N. O. Lipari [Sol. St. Ccran., 17, 1089 (1975)]. In fact, their calculation is flawed in its assumption that the phases of the intramolecular and inter-molecular soft inodes are arbitrary. The correct theory [a. Madhukar, Chem. 

An interesting feature that is common to all the quasi-one-dimensional organic conductors exhibiting metallic conductivity down to low temperatures is the existence of two partially filled bands of donor and acceptor stacks. The metal-to-insulator transition is usually associated with the opening of Peierls gap in at least one of these bands. Therefore it is of utmost interest to study alloys created by selective doping of different stacks in order to evaluate the effects of the two stacks on various physical properties and on the metal-insulator phase transition. Conclusions with regard to stabilization of the metallic phase to low temperatures will be presented. 

The structure of (5,5) carbon nanotube has been calculated for its quasistatic expansion up to the elongation of 20 %. Two first order structural phase transitions with the change of the atomic structure symmetry were revealed as the result of the nanotube expansion. For the elongation greater than 13 % the structure of nanotube corresponds to the metallic phase without the Peierls gap. The considered phenomena can be observed experimentally at ultra low temperatures. 

J.-L. Calais, Mott and Peierls Gaps, Technical Note No. 603, Quantum Chemistry Group, Uppsala University, 1979. 

The parameters should be compared with the bandwidth, i.e. with the longitudinal transfer integral t in pseudo-1-D systems. Since, in the presence of a weak dimerization, the Peierls gap is negligible (compared to the Hubbard gap), therefore, for regular or pseudo-regular stacking, the following requirement appears to be necessary ... 

These three conclusions are not consistent with the excitation spectrum of the simple metal which would result if the Peierls gap had been reduced to zero (there would be no gap and no IRAV modes). 

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