Peierls mechanism

The resulting band is only half-filled (metallic regime) because each of the carbon atoms offers one electron, and the number of COs is equal to the number of carbon atoms (each CO can accommodate two electrons). Therefore, the Peierls mechanism (Fig. 9.11) is bound to enter into play, and in the middle of the band, a gap will open. The system is, therefore, predicted... 

In this chapter we describe the consequences of electron-phonon coupling in the absence of electron-electron interactions. The celebrated model for studying this limit is the so-called Su-Schrieffer-Heeger model (Su et al. 1979, 1980), defined in Section 2.8.2. In the absence of lattice dynamics this model is known as the Peierls model. We begin by describing the predictions of this model, namely the Peierls mechanism for bond alternation in the ground state and bond defects in the excited states. Finally, we reintroduce lattice dynamics classically and briefly describe amplitude-breathers. 

We seek a solution of H for arbitrary A . In Section 4.4 we discuss the Hellmann-Feynman theorem, which gives us a general solution for any eigenstate. For now, however, we describe the Peierls mechanism, which gives us the dimerized, broken-symmetry ground state. 

In the continuum models of Brazovskii and Kirova [35] and Fesser et al. [36] (the FBC model), the preferred sense of bond alternation is introduced through an extrinsic contribution to the gap parameter A. sls A = zlo + Je. where Aq is the contribution to the gap due to the Peierls mechanism and Je is the extrinsic contribution. It is useful to define a confinement parameter y, as y = AJ2 A, where A is the effective electron-phonon coupling constant such that A = exp[y]. 

TAK 88] TAKEUCHI S. and SUZUKI T., Deformation of crystals controlled by the Peierls mechanism , in Strength of metals and alloys, p. 161-166, Ed. Kettunen P.O., Lepisto T.K. and Lehtonen M.E., Pergamon Press, Oxford, New York, Tokyo, 1988. 

Since some earlier work based on anisotropic elasticity theory had not been successful in describing the observed mechanical behaviour of NiAl (for an overview see [11]), several studies have addressed dislocation processes on the atomic length scale [6, 7, 8]. Their findings are encouraging for the use of atomistic methods, since they could explain several of the experimental observations. Nevertheless, most of the quantitative data they obtained are somewhat suspicious. For example, the Peierls stresses of the (100) and (111) dislocations are rather similar [6] and far too low to explain the measured yield stresses in hard oriented crystals. 

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... 

Semiempirical methods which involve an explicit quantum mechanical treatment of the -electrons by PPP-type theories, coupled with a classical a-com-pression energy, have been employed by Paldus et al. to investigate the general question of Peierls distortion in polyenes and in large [n]-annulenes.22-25 The results show that the r-energy tends to be... 

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. 

The conductivity of Ni(tmp)I at room temperature is high (o 100 Q 1cm 1) and metal-like, increasing until it reaches a rounded maximum at T 115 °K, then decreasing in an activated manner. The spin susceptibility is temperature independent down to a transition temperature of 28 °K, well below the conductivity maximum. At temperatures below the transition, the susceptibility decreases in an activated fashion, with A/k = 60 °K. Similar observations with organic conductors (TMTTF)2Y, Y = CIO4, BF4, have been attributed to a Peierls transition212, but in the present instance the mechanism has yet to be elucidated. 

The origin of these transformations is very difficult to investigate. Yet it appears that the optical study should be very helpful for this purpose. An analysis of T dependence of the phase phonon absorptions at 317 and 253 cm -1 show that the 54 K metal-insulator transition is driven by the Peierls distortion on the TCNQ sublattice, whereas the distortion on the TTF chains increases markedly around 49-K phase transition [100]. It is a typical example of a close relationship between the optical properties of organic conductors and a molecular mechanism of the phenomena that occur in the material. 

One of the initial motivations for pressure studies was to suppress the CDW transitions in TTF-TCNQ and its derivatives and thereby stabilize a metallic, and possibly superconducting, state at low temperatures [2]. Experiments on TTF-TCNQ and TSeF-TCNQ [27] showed an increase in the CDW or Peierls transition temperatures (Tp) with pressure, as shown in Fig. 12 [80], Later work on materials such as HMTTF-TCNQ showed that the transitions could be suppressed by pressure, but a true metallic state was not obtained up to about 30 kbar [81]. Instead, the ground state was very reminiscent of the semimetallic behavior observed for HMTSF-TCNQ, as shown by the resistivity data in Fig. 13. One possible mechanism for the formation of a semimetallic state is that, as proposed by Weger [82], it arises simply from hybridization of donor and acceptor wave functions. However, diffuse x-ray scattering lines [34] and reasonably sharp conductivity anomalies are often observed, so in many cases incommensurate lattice distortions must play a role. In other words, a semimetallic state can also arise when the Q vector of the CDW does not destroy the whole Fermi surface (FS) but leaves small pockets of holes and electrons. Such a situation is particularly likely in two-chain materials, where the direction of Q is determined not just by the FS nesting properties but by the Coulomb interaction between CDWs on the two chains [10]. 

A CDW is a periodic modulation of the conduction electron density within a material. It is brought about when an applied electric field induces a symmetry-lowering lattice modulation in which the ions cluster periodically. The modulation mechanism involves the coupling of degenerate electron states to a vibrational normal mode of the atom chain, which causes a concomitant modulation in the electron density that lowers the total electronic energy. In one-dimensional systems, this is the classic Peierls distortion (Peierls, 1930, 1955). It is analogous to the JT distortion observed in molecules. 

Extensive studies have revealed the mechanism for these novel properties. It is the interplay among many mechanisms the Peierls instability characteristic of one-dimensional system, the Mott transition in Coulomb interacting system, the mixed valence of Cu, the Jahn-Teller effect of Cu ions, and the Curie-Weiss paramagnetism of the 1/2-spin of Cu. The key role in showing the variety of properties was played by the structural deformation which causes a shift in the energy level of d-electrons of Cu. 

The structure and properties of C2o (8,8) CNT system are explored by quantum chemical and molecular mechanic calculations. The change of the barrier for relative motion of fullerene along the carbon nanotube axis at the Peierls transition is found. The changes of dynamical behavior of the system C2o (8,8) CNT at the transition are discussed. 

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