Peierls phase-transition temperature

Essential parts of the BCS theory can be taken over in the mean-field theory of the Peierls transition if one replaces the Debye energy tkoo in the superconductor by the Fermi energy Ep in the metal. Since Eplhrop, 10 -100, the Peierls phase transition temperatures are considerably higher than the critical temperatures of BCS superconductors, ii) The frequency of the phonons which are responsible for the Peierls transition has, for T > the temperature dependence... 

In the Cu(DCNQI)2 radical-anion salt in the neighbourhood of the Peierls phase-transition temperature, it was found that the insulating state can be switched optically on a time scale of less than 20 ps into the conducting state (F. O. Karutz, H. C. Wolf et al, Phys. Rev. Lett. 81,140 (1998)). This optical switching process was termed a reversed Peierls transition . From the current transients, it was found that the switched volume must be at least 100 times larger than the directly photo-... 

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) ... 

Structural correlations of Tc with chemical formula or structure type are limited. For the / -(ET)2X salts with linear anions there is a linear dependence of Tc on anion length (but this correlation fails for very long anions, as other phases form) [33]. The (TMTSF)2X salts with tetrahedral anions X show a linear dependence of the Peierls metal-to-insulator phase transition temperature with tetrahedral anion radius [33]. 

Depending on the crystal structure of the one-dimensional stacks and on whether a Peierls transition occurs or not (more on this subject wiU be given in Sect. 9.3), the states in the one-dimensional bands are wholly or partiaUy fUled. The CT crystals can therefore be semiconductors or metalHc conductors. If at high temperature metallic conductivity is present and at a lower temperature Tp a Peierls phase transition occurs, the metal becomes a semiconductor at T< Tp, or an insulator. 

In the mean-field approximation for the description of the Peierls transition, all the lattice fluctuations except those with the wavevector q = lkp are neglected. Fluctuations are however particularly effective in highly onedimensional systems in contrast to 3-d systems, phase transitions in 1-d systems are seriously influenced by fluctuations. The relation between the real phase-transition temperature Tp and the experimentally observable ground-state energy gap 2A(T = 0) is, taking the fluctuations in onedimensional metals into account ... 

At T = Tj, = 182 K, the Peierls transition takes place. The phase transition temperature Tp can be determined very precisely from the sudden jump in the slope of cr(T) at T= Tp [22]. From the results of variation of the counterion X" = PF, ... 

Fa)2PF6 crystal. Agff is the effective or pseudo-energy gap for T> Tp. A(T) was determined both from the magnetic susceptibility of the charge carriers (solid curve) and from the conductivity cr(T) (dashed curve). Tp is the transition temperature of the Peierls phase transition. From [24]. 

An important result of this analysis of the temperature dependence of the conductivity, cr(T), is the existence of an effechve energy gap for T> Ty, which can also be seen in the measurements of the magnetic suscephbility of the conduction electrons (cf. Sect. 9.6.4). It is characterishc of these highly-one-dimensional conductors and has its origin, as mentioned, in fluctuahons above the phase-transition temperature Tp for the Peierls transihon [26]. 

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... 

TTF-TCNQ is the first true organic metal ever prepared [32] (°ii3ook 300 to 500 S cm-1 o-1 S4K 104 S cm 1) [33]. This charge-transfer salt is well known for its quasi-one-dimensional electronic-transport properties and its sequence of Peierls (Tc = 54 K) and collective phase transitions at low temperature. Its physical properties have thus been the subject of detailed studies as a function of various physical conditions (for... 

Recently, the spectral study of DMTM(TCNQ)2 phase transition was performed [60]. The salt is a quarter-filled organic semiconductor containing segregated chains of TCNQ dimers and DMTM counterions. This material undergoes an inverted Peierls transition, which has tentatively been explained in terms of a crystal-field distortion. It was shown that the experimental values of unperturbed phonon frequencies and e-mv coupling constants are nearly independent of temperature. The dimer model fails to reproduce the phonon intensities and line shapes and underestimates the coupling constants, whereas the CDW model produces better results... 

When electron-phonon interactions are taken into account, the regular conducting chains are found to be unstable they undergo a low-temperature phase transition which results in both a modulation of the chains and the opening of an energy gap at the Fermi level. This is the so-called Peierls transition, at T = TP, a second-order symmetry-breaking transition that is characteristic of the quasi-one-dimensional conductors [2,3]. 

Mixed-chain charge-transfer complexes are characterized by a regular chain structure when in the quasi-neutral phase at high temperature. Often, but not always, the chains undergo dimerization in the low-temperature quasi-ionic phase, at Tc or below, as a possible consequence of one-dimensional spin-Peierls-like transition [74,76]. 

Further evidence for the relevance of EMV coupling to the Peierls transition of TTF-TCNQ is given in Fig. 25, which shows how the temperatures 7 and T3 of the two phase transitions are affected by various isotopic substitutions of the TTF or TCNQ molecules [110]. The resistive transitions do not all have the same widths A T, and as it is known that 7 and T3 can be suppressed and broadened by very small defect levels, in the figure Tx and T3 are plotted versus A T. This enables any shifts caused by defects to be distinguished from true isotope shifts. The observed isotope... 

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. 

A. TTF-TCNQ (x=o). I will show that two of the phase transitions of TTF-TCNQ are related to two different 3-dimensional ordering temperatures of the donor and acceptor stacks undergoing Peierls distortions. 

A/ - Below the Peierls transition taking place at 54 K, two addi-tionnal structural phase transitions are observed at 49 K and 38 K (figure 1). These 3 transitions correspond to a sequence of 3 different low temperature modulated phases which are thought... 

A Peierls distorsion at zero Kelvin on purely 1 D system is a second order phase transition. The observed transition (Figure 4) might be of weakly first order transition it is interesting to note that the specific heat anomaly increases with the transition temperature in the three considered compounds. We suppose that this critical temperature increases in relation with the 3-D and the disorder effects. 

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