Periodic lattice distortion

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

Peierls pointed out in 1955 that a one-dimensional metallic chain is not stable at T = 0 K, against a periodic lattice distortion of wave vector 2kF, as the result of electron-phonon coupling, opening a gap 2A at the Fermi level. From this fact a collective electronic state results called a charge density wave (CDW). In the limit where U, the intrasite Coulomb repulsion, is infinite, since a given k state cannot be occupied by more than one... 

In the metallic state below about 150 K a set of diffuse streaks was found in X-ray studies as shown in Fig. 18 which suggests the onset of the periodic lattice distortion with = 0.295 b having no correlation among them perpendicular to the one-dimensional b-axis [55,56]. Corresponding to these x-ray streaks inelastic neutron scattering studies revealed the decrease in the phonon frequency for the wave vector = 0.295 b with decreasing temperature as shown in Fig. 19 [60]. This soft phonon is considered to be frozen out at the metal-insulator transition temperature 53 K causing the superstructure described above. This type... 

The Peierls transition, characteristic of one-dimensional metallic systems, is a static, periodic lattice distortion at its transition temperature Tp, which produces a semiconducting or insulating state for T < Tp. The lattice distortion is accompanied by a spatially periodic modulation of the density of the conduction electrons, a charge-density wave. The two periods are the same and depend only on the filling of the conduction band their lattice vector is given by 2kp, that is twice the Fermi wavevector kp. 

Fig. 17. (a) Schematic electron energy versus wavevector curve for a one-dimensional tight-binding band with a periodic lattice distortion of wavevector Tkf (Frohlich state) with no electrical current flow (F = 0). (b) Schematic electron energy versus wavevector curve for the FrShlich state with a finite current V, 0). The electron momentum distribution is displaced by an amount q (8). 

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