Phase Peierls

The smectic A phase is a liquid in two dimensions, i.e. in tire layer planes, but behaves elastically as a solid in the remaining direction. However, tme long-range order in tliis one-dimensional solid is suppressed by logaritlimic growth of tliennal layer fluctuations, an effect known as tire Landau-Peierls instability [H, 12 and 13]... 

The octet principle, primitive as it may appear, has not only been applied very successfully to the half-metallic Zintl phases, but it is also theoretically well founded (requiring a lot of computational expenditure). Evading the purely metallic state with delocalized electrons in favor of electrons more localized in the anionic partial structure can be understood as the Peierls distortion (cf. Section 10.5). 

The structure of MnP is a distorted variant of the NiAs type the metal atoms also have close contacts with each other in zigzag lines parallel to the a-b plane, which amounts to a total of four close metal atoms (Fig. 17.5). Simultaneously, the P atoms have moved up to a zigzag line this can be interpreted as a (P-) chain in the same manner as in Zintl phases. In NiP the distortion is different, allowing for the presence of P2 pairs (P ). These distortions are to be taken as Peierls distortions. Calculations of the electronic band structures can be summarized in short 9-10 valence electrons per metal atom favor the NiAs structure, 11-14 the MnP structure, and more than 14 the NiP structure (phosphorus contributes 5 valence electrons per metal atom) this is valid for phosphides. Arsenides and especially antimonides prefer the NiAs structure also for the larger electron counts. 

Figure 9 (Top) schematic of bistability in 1,3,2-dithiazolyl radicals arising from a solid-solid phase transition between regular and Peierls distorted n-stacks (bottom) free energy diagram of the two structural phases present...

Figure 1.19. Generic T-P phase diagram for BFS. The origin on the pressure axis is arbitrarily set for (TMTTF)2PF6. MH, Mott-Hubbard M, Metal SP, Spin-Peierls AF, Antiferromagnetic SDW, Spin-Density-Wave SC, Superconductor. Adapted from Auban-Senzier J6rome, 2003.

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

Fig. 13 Generalized phase diagram for the (TMTSF)2X and (TMTTF)2X by Jerome [195]. CL, SP, SDW, and SC refer to charge-localized (which corresponds to charge-ordered state), sprn-Peierls, spin density wave, and superconducting states, respectively, (a) (TlVrrTF)2PF6, (b) (TMTTF>2Br, (c) (TMTSF)2PF6, (d) (TMTSF)2C104...

In conducting solids, the conduction electron density is spatially modulated, forming charge density waves (CDW) the periodic distortion accompanying the CDW (due to interaction between the conduction electron and the lattice) is responsible for the incommensurate phase (Overhauser, 1962 Di Salvo Rice, 1979 Riste, 1977). The occurrence of CDW and the periodic distortion can be understood in terms of the model proposed by Peierls and Frdhlich for one-dimensional metals. Let us consider a row of uniformly spaced chain of ions (spacing = a) associated with conduction electrons of energy E k) and a wave vector k. At 0 K, all the states are filled up to the Fermi energy, = E(kp). If the electron density is sinusoidally modulated as in Fig. 4.15 such that... 

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. 

The trisulphides (and triselenides) of Ti, Zr, Hf, Nb and Ta crystallize in onedimensional structures formed by MSg trigonal prisms that share opposite faces. Metal atoms in these sulphides are formally in the quadrivalent state, and part of the sulphur exists as molecular anions, M S2 S . TaSj shows a metal-insulator transition of the Peierls type at low temperatures (Section 4.9). NbSj adopts a Peierls distorted insulating structure suggesting the possibility of a transformation to a metallic phase at high temperatures, but does not transform completely to the undistorted structure. Electronic properties and structural transitions of these sulphides have been reviewed (Rouxel et al, 1982 Meerschaut, 1982 Rouxel, 1992). 

In CoOP above 300 K the compound exists in the Cccm space group, but with characteristic diffuse X-ray lines indicative of the Peierls modulation and no evidence of superstructure formation. Below 300 K a superstructure develops as shown by the appearance of satellite reflections on the X-ray diffraction photographs. At 280 K a phase transition to the Pccn space group occurs and associated with this are changes in the satellite pattern.78 74 Superstructure development which is commensurate with the Peierls modulation is completed about 250 K. 

Competing ground states and quantum criticality present a special interest of modem physics of strongly correlated systems and most of emergent materials [1, 2], The lightly doped Cu xMxGeO has demonstrated a competition of a dimerized spin-Peierls (SP) phase and a 3D AFM phase, which replace each other under temperature decrease [3-5], The microscopic mechanism of this replacement and phase coexistence (phase separation) could be a subject of magnetic resonance spectroscopy. 

Peierls showed 74 [41,42] that an instability in a one-dimensional chain, with one electron per site, driven by electron-phonon interactions, can lead to a subtle structural distortion and to a first-order Peierls phase transition, at and below a finite temperature TP (the Peierls temperature) [42], For instance, at and below Tp either a dimerization into two sets of unequal interparticle distances d and d" (such that d + d" = 2d) or some other structural distortion must occur. The electronic energy of the metallic chain may also be lowered by the formation of a charge-density wave (CDW) of amplitude p(x) ... 

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