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We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Mobius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z2 topology of the Mobius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.

When a C60 film is irradiated with a 3-kV electron-beam (EB), a peanut-shaped C60 polymer with metallic properties is formed. Valence photoelectron spectra of the polymer indicated that the density-of-states (DOS) of the polymer clearly comes across the Fermi edge in a manner similar to that of Au film used as a reference. Interestingly, the spectral function of the peanut-shaped polymer around the Fermi edge resembles that of quasi one-dimensional (1D) materials such as K0.3MO3 with its metallic phase. This suggests that the peanut-shaped polymer has also a quasi 1D structure and may exhibit the Peierls transition at a given temperature. If the polymer shows the metal-insulator transition at the given temperature, the transition would change the electron-transport mechanism of the polymer. Then, we examined the temperature-dependence of the electrical conductivity of the polymer in the range of 9K-400K. It is found that the electron transport mechanism was changed at approximately 90 K, suggesting that the valence electronic structure around the Fermi edge was changed at this temperature.

The fine structure of magnetic nanoparticle periodic chains is studied by considering the competition between magnetic dipolar interaction and elastic interaction. A Peierls phase with a doubled unit cell length can be formed under proper conditions and a Peierls transition can be induced by temperature and by external magnetic field. Due to the coupling between the magnetic state and the structural state, the nanoparticle chains would possess distinct properties and exhibit interesting behaviour.

The structural transformation of the quasi-one-dimensional charge-density-wave (CDW) conductor K0.3MoO3 blue bronze upon electron irradiation is reported. Evidence of the disappearance of Bragg spots corresponding to the C-centre symmetry is clearly demonstrated by the in situ recorded selected area electron diffraction (SAED) patterns in the transmission electron microscope, which acts as the electron irradiation facility as well as the structural analysis and recording instrument. Based on the experimental results and the crystal structure of K0.3MoO3 (Graham and Wadsley 1966 Acta Crystallogr. 20 93), a hypothetical atomic model is proposed to interpret this kind of disordering. The simulated SAED patterns on the basis of the proposed atomic model agree with the experimental ones very well. This strong disorder may break both the coherence of the CDW along the chain direction and the phase order of the CDW in the transverse directions, and furthermore it may suppress the Peierls transition.

Transport and low-frequency optical reflection measurements (180-380 GHz) are reported for the quasi-three-dimensional conducting alloy Cu[(2, 5(CH3)2-DCNQI)0.70(2, 5(CD3)2-DCNQI)0.30]2 between room temperature and 35 K. The optical properties of the system are strongly anisotropic. It is metallic down to 60 K where a Mott-Peierls phase transition occurs. While the transverse conductivity remains practically unchanged, the longitudinal conductivity abruptly drops at the phase transition. Comparing our latest results with previous dc data and measurements of the microwave conductivity also reported here, we find indications of an ageing effect in these samples.

The electron spin resonance line-width anisotropy and intensity are analysed for the quasi-one-dimensional organic conductors (fluoranthene)2PF6 and (perylene)2PF62/3 tetrahydrofurane in the metallic phase above the Peierls transition temperature. Based on the bottleneck model of relaxation, the temperature dependence of the intra-stack exchange constant between conduction-electron spins and localized defect spins is derived and discussed.

The magnetic susceptibility of the prototype of quasi-one-dimensionally conducting arene radical cation salts, the naphthalene salt (C10H8)2AsF6, is analysed. The Peierls transition is characterized by a molecular field temperature TMF of about 570 K and an actual three-dimensional transition temperature TP of 234 ± 4 K. The low-temperature gap is extrapolated to 2Δ(0)/kB = 1950 ± 75 K. The naphthalene salt thus has the highest Peierls transition temperature among the arene radical cation salts analysed so far.

We have carried out a 93 Nb nuclear magnetic resonance (NMR) study on a quasi-one-dimensional superconductor, Nb3Te4, and the isostructural intercalated compounds AxNb3Te4 (A = In and Zn), to understand the varied impact of metal–atom intercalations into the hexagonal infinite tunnels on the charge density wave and superconductivity formations. Below the Peierls transition temperature TC for each of the compounds, the nuclear spin–lattice relaxation rate (T1 T)−1 exhibited a significant decrease which originates from the partial Fermi surface quenching associated with the Peierls transition. With x 0.1 introductions of In and Zn, (T1 T)−1 was greatly enhanced from 10 s−1K−1 to 20 and 18 s−1K−1, respectively. On the other hand, the nuclear quadrupole frequency νQ was diminished from 0.98 MHz to 0.63 and 0.74 MHz, respectively. A remarkable difference between the In and Zn intercalations was found in the extent of decrease in the isotropic Knight shift Kiso: from 0.237 to 0.216% for In; and to 0.166% for Zn. Based upon the d band structures predicted theoretically, we have indicated that the variations in the NMR parameters can be explained consistently, if the extent of hole doping by a Zn atom is much larger than that by an In atom. The heavy hole doping by Zn intercalation changes the dominant subband at EF from dyz,zx to dx2 −y2, giving rise to a distinct nesting condition of the Fermi surface.

Electronic structures for several neutral and anionic one-dimensional (1D) C36 polymers are investigated by using the ab initio self-consistent-field crystal orbital method based on the B3LYP (Becke–Lee–Yang–Parr) density functional theory. Calculations show that all the neutral polymers are semiconductors with energy gaps in the range from 0.55 to 2.04 eV. The possibilities of superconducting and Peierls phase transitions are also explored for these metallic anionic polymers at the same time. It is found that the intramolecular electron–phonon (e–p) coupling in metallic 1D C36 polymers plays an important role in producing high superconducting transition temperatures (Tc). The estimated Peierls phase transition temperatures (Tp) are very small due to the very weak intermolecular e–p interactions.

The research on spin-Peierls transition and impurity-induced antiferromagnetic state(s) in CuGeO3 is reviewed. In particular the recent progress of the studies of the compositional phase diagram will be discussed. The discovery of two antiferromagnetic phases in Mg-doped CuGeO3 (Masuda T et al 1998 Phys. Rev. Lett. 80 4566) opened a new aspect of this kind of research. The transition between dimerized antiferromagnetic and uniform antiferromagnetic phases is of the first order as a function of the impurity concentration. This phenomenon was studied in detail by the susceptibility, neutron diffraction, synchrotron x-ray diffraction and other methods. The existence of this transition was firmly confirmed and it was revealed that the impurity-induced phase diagram of CuGeO3 is very complex. Another important problem is whether the impurity-induced ordered phase in the spin-gap system is unique to the S = ½ spin-gap system or not. As to this problem a new Haldane-gap compound PbNi2V2O8 was found (Uchiyama Y et al 1999 Phys. Rev. Lett. 83 632). This compound has relatively strong inter-chain interaction. It was also found that the substitution of Mg2+ ions (S = 0) for Ni2+ ions (S = 1) induces antiferromagnetic phase in PbNi2V2O8. From these experimental results it was shown that the occurrence of the impurity-induced ordered phase is a common feature of quasi-one-dimensional spin systems with relatively strong inter-chain interaction.

The theoretical possibility of obtaining cavityless optical bistability in quasi-one-dimensional Peierls semiconductors is demonstrated. The nonlinear interaction of the system with an electromagnetic field is caused by the red shift of the lower edge of an optical transition in the semiconductor with increasing concentration of nonequilibrium electron - hole pairs. (nonlinear optical phenomena and devices)

We report results from a systematic strong-coupling expansion of a spin-1/2 Heisenberg chain coupled to Einstein phonons. In the non-adiabatic regime this model is used to describe zero temperature properties of CuGeO3. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. In particular, the spin gap and the dispersion of the elementary triplet excitation are calculated up to 10th order in a dimer expansion. The magnetic structure factor of the ground state is evaluated up to 6th order. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO3. The ground state magnetic correlations are found to be hardly effected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO3., revtex, 4 pages, 3 eps-figures, see also http://brahms.physik.uni-bonn.de/ClusterExpansion/DOC/Intro.html

We report a comparative study of the electrical resistivity under hydrostatic pressure up to 18?kbar of the quasi-two-dimensional conductors (PO2)4(WO3)2m (m = 4, 5, 6) and ?-Mo4O11, which show Peierls transitions towards a charge density wave state. The pressure dependences of the transition temperatures are discussed in relation with the hidden nesting properties of these oxides. The results for ?-Mo4O11 are compared with previous works.

Magnetotransport properties of quasi-two-dimensional thallium purple bronze were measured at different magnetic fields for H∥c. Huge positive magnetoresistance below the Peierls transition TP and Shubnikov-de Haas oscillation in the high-field range were found. In the charge-density-wave (CDW) state below TP, nonlinearity of the voltage-current characteristics due to the depinning of a CDW was also observed at 2 K and 14 T. These results supported the suggestion that the CDW gap opening below TP still leaves small electron and/or hole pockets, but an applied magnetic field can remove these pockets to a great extent, thus leading to an enhanced gap.

Brillouin scattering measurements have been carried out for the first time on K 0.3 MoO 3 . The spectrum reveals two bulk modes at 18 and 27 GHz and a Rayleigh surface mode at 6 GHz. Both the bulk modes and the surface mode exhibit changes at the Peierls transition (180 K). Interestingly, the 18 GHz mode also shows softening at the incommensurate-commensurate transition around 100 K, suggesting the important role of phasons.

We present an analysis of experimental specific heat data measured in the vicinity of the spin-Peierls transition of a CuGeO3 single crystal. The aim of the investigation was to analyse the type of the transition, including the character of the fluctuations, and to give a proper determination of the critical temperature. We used and successively compared the Gaussian and critical fluctuations models to fit the experimental points detected in magnetic fields up to 21 T. Our results present new information about the influence of a magnetic field on fluctuations in the CuGeO3 compound. Within the framework of the Gaussian fluctuations model, there is no significant magnetic field dependence of the fluctuations. Using this model, the critical region is estimated to be as small as 10 mK in zero field, which excludes the possibility of observation of critical fluctuations in the present experiments. In spite of this, a critical fluctuations type of analysis can also be carried out, with a critical exponent value lying between the three-dimensional XY and the Heisenberg universality classes. We also note the absence of broadening of the fluctuations regime under magnetic field. Taking into account the scatter of the data, the two models are equally suitable in the fitting process.

Quasi-one-dimensional conductors which undergo a Peierls transition to a charge-density-wave state at a temperature show a region of one-dimensional fluctuations above . The Ginzburg-Landau-Langevin theory for the frequency-dependent collective conductivity from conductive fluctuations into the charge-density-wave state is developed. By inclusion of a phase-breaking term the effect of local pinning due to random impurities is simulated. It is found that the spectral weight of the unpinned fluctuations is partly redistributed into a pinned mode around a pinning frequency in the far-infrared region. In addition, selection rule breaking by the impurities makes the fluctuating amplitude mode visible in the optical response.

Measurements of the elastic constant of the 2% Zn-doped spin - Peierls system under high magnetic fields up to 20 T are reported. The successive magnetic ordering and the spin - Peierls transition are confirmed. The magnetic phase diagram has been determined. A transition line between the magnetic ordered phase and the uniform phase is observed at very high magnetic fields above 15 T.

Using an extension of the Jordan - Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin - Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin - lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.

We report the first muon-spin relaxation study of an organic spin - Peierls system, the linear-chain compound MEM(TCNQ). Our results show a crossover from a Gaussian relaxation to an exponential relaxation as the temperature is lowered below the spin - Peierls transition. We associate this behaviour with the slowing down of the electronic fluctuations resulting from the opening of a gap in the magnetic excitation spectrum.

Frequency-dependent complex conductivity measurements on the organic quasi–one-dimensional CDW system (Fa)2PF6 between 10−4 Hz and 3·109 Hz at temperatures ranging from 20 K to 290 K are reported. Below the temperature of the Peierls transition (TP = 182 K) the real part of the conductivity exhibits two structures, which can be attributed to two modes of the charge density wave (CDW): a temperature-dependent low-frequency relaxational mode of local oscillating deformations and a high-frequency resonant mode of the pinned CDW as a whole. The measurements indicate that the damping of the relaxational mode is dominated by free carriers in the covered temperature range. At low temperatures the dynamics of the CDW in (Fa)2PF6 shows features characteristic of the transition into a glass-like state.

By means of high-resolution x-ray scattering, we have studied the temperature dependence of the critical scattering associated with the Peierls transition in . From a careful intensity and line shape analysis the critical exponents , and were derived. , and are the critical exponents of the temperature dependence of the order parameter, the susceptibility and the correlation length of the order parameter fluctuations, respectively. Though this incommensurate structural phase transition is reported to be continuous, an unusual exponent value is obtained: . The small value of suggests a blurred first-order transition. We also report on the anisotropy of the correlation in the basal plane perpendicular to the -chain direction.

We report ultrasonic and thermal expansion measurements on quasi-one-dimensional . The elastic constant exhibits strong anomalies over a wide temperature range around the Peierls transition. Anisotropic behaviour of the slow shear mode propagating along and perpendicular to the chain direction is observed around . Elastic constants, like electrical resistance, are very sensitive to a small Nb content substituted for Ta. Anomalous behaviour of at low temperatures is reported. We also present measurements of the anisotropic thermal expansion coefficients.

We present and analyse microwave dielectric response data under magnetic field in the Peierls ordered state of the quasi-one-dimensional two-chain organic conductor (Per)2[Pt(S2C2(CN)2)2]. The data are shown to provide a unique opportunity to extract the full-temperature profile of the Peierls gap under field. Quantitative agreement with the fluctuation-free mean-field theory is found.

The non-linear transport properties of sliding charge-density waves (CDWS) in pure Tl0.3MoO3 and impurity-doped (Tl0.2K0.8)0.3MoO3 blue bronzes are measured in the temperature range 80-150 K. It is found that the analytical form of non-linear current in a moderate field range fits the power-law relation, i.e. ICDW varies as (V/Vr-1)alpha , where the exponent alpha is temperature dependent and not a constant 1.5. Such a relation seems to be universal for blue bronzes over the temperature range below the Peierls transition temperature and does not depend on the quality of samples. The results are in agreement with those observed by Mihaly et al for pure K0.3MoO3 blue bronze in the low-temperature range and suggest that the dominant damping of the collective mode arises from the dissipative normal current induced by dynamical deformation of the CDWS, not only in the low-temperature range, but also in the high-temperature range.

We have investigated the stability of the antiferromagnetic order in the ground state of the two-dimensional Heisenberg model against a lattice dimerization produced by the electron-lattice interaction. Unlike the one-dimensional case, we found that a critical coupling is required to form a dimerized state via a first-order phase transition. We have also considered the combined effects of frustrating second-neighbour interactions and lattice dimerization in destroying the Neel order. Our approach is based on the Schwinger representation of spin operators, and is in excellent quantitative agreement with exact numerical results on finite lattices.

Due to its simple molecular and crystalline structure, the organic conductor (FA)2X (X = PF6, AsF6, SbF6) can be regarded as a model system to study the Peierls instability and charge density wave transport phenomena. In this contribution we give a short introduction to the field of low-dimensional conductors and compare our experimental data with theoretical predictions for quasi-one-dimensional conductors with a Peierls transition to a charge density wave ground state.

A quasi-two-dimensional Peierls-Hubbard model with the typical two types of anharmonic phonons has been studied, so as to clarify both the enhancement and reduction of isotope shifts of superconducting (SP) transition temperature Tc, as well as the competition between the metallic state and the charge-density-wave (CDW) or spin-density-wave (SDW) state. The first type is a sextic anharmonicity like a hard-core repulsion, and the second type is a small negative quartic anharmonicity in addition to the sextic one, just like a mixture of a hardcore and a soft one. This theory is based on the mean-field approximation for electrons and a variational method for phonons. In the first type, the Peierls distortion is excessively suppressed, and the SP state becomes more stable than the CDW, even when electron-phonon (e-ph) coupling is very strong. Thus, Tc of this case is enhanced, but has no isotope effect. In the second type, in contrast, the SP state is suppressed by the CDW when e-ph coupling is strong. The Tc of this case is reduced, but shows a strongly enhanced isotope shift. In both cases, the SDW is always suppressed.

Measurements of the thermopower in the charge density wave compound (NbSe4)10I3 show a large hysteresis between the cooling and heating cycles below and above the Peierls transition temperature. The magnitude of the observed hysteresis depends on the lowest temperature reached in the cooling regime. This effect is attributed to the interaction between charge density wave deformations and a quasi-periodic structure of lattice defects.

The breakdown of translational symmetry of a polyethylene chain, associated with a Peierls-like phase transition, has been analysed using the general principles of 'action of a group on a set'. All possible phase transitions (dimerization, trimerization, or, in general, p-merization) are classified and the corresponding driving modes are derived.

The E-k dispersion of the 6p derived valence band of Tl chains adsorbed on Cu(100) has been measured as a function of density and temperature using high-resolution angle-resolved photoelectron spectroscopy. The most dense chain structure, at a coverage of theta =0.67 undergoes a Peierls distortion with a corresponding band gap at the Fermi level estimated to be 0.25 eV. At temperatures below about 225 K, LEED shows two-dimensional order with an alignment of the distortion between neighbouring chains. The measured dispersion at room temperature indicates that the overlayer still retains a distorted chain structure and the observed loss of overlayer spots in the LEED pattern is due to the loss of inter-chain registry. At the lower coverage, theta =0.6, a less dense chain structure occurs which shows no evidence for a Peierls distortion. The suppression of any superstructure is ascribed to the greater commensurability between the overlayer and the substrate.

The nonlinear conductivity in orthorhombic and monoclinic TaS3 has been measured as a function of temperature from the Peierls transition temperature down to 4.2 K in the electric field range 10-2-500 V cm-1. At liquid-helium temperature a sharp increase in conductivity is measured in a very limited variation range of voltages. A general description based on phase-slip processes is given to explain these nonlinear properties in the whole temperature range.

The effects of deviation from the half-filling of the conduction band ( mu not=0) and magnetic field on the coexistence of superconductivity (SC) and the charge-density wave (CDW) in a quasi-one-dimensional system are investigated. The behavior of the superconducting order parameter Delta s and dielectric order parameter Delta p as functions of temperature essentially depends on the theory parameters p=Ts0/TP0, mu and the external magnetic field H0. In particular, it is possible to increase the superconducting transition temperature Ts as the magnetic field grows. The spin magnetic susceptibility and penetration depth are calculated in the mixed SC+CDW phase and it is shown that their temperature dependences essentially differ from the BCS theory both qualitatively and quantitatively.

In a recent letter [1], the magnetic-field dependence of the metal-insulator (MI) transition temperature in the Per2[Pt(mnt)]2 compound (Per = perylene,mnt = S2C2(CN)2) was presented and was found in agreement (fig. 1) with the theoretical prediction for the Peierls transition temperature, Tp(B), obtained by Dieterich and Fulde [2]: ln[Tp(0)/Tp(B)] = Re {ψ(1/2+iμBB/2πkTp(B))} − ψ(1/2), (1) where ψ(x) is the digamma-function. For low fields (μBB << 2πkT(0)), this gives a B2-dependence [2], [3]: ΔTp(B)/Tp(0) = [Tp(B) − Tp(0)]/Tp(0) = − γ(μBB/kBTp(0))2, with γ ≈ 0.21 .(2) The authors used this agreement to simultaneously validate two different assertions: equation (1) describes well the magnetic-field dependence of the Peierls transition temperature and the transition occurring in this compound is driven only by the electron-phonon interaction (Peierls transition). In this comment, we would like to show that equation (1) is not completely satisfactory and that the MI transition mechanism involved in this compound is more complicated than claimed by the authors.

Non-equilibrium electronic transport through a polymer chain is investigated by the scattering state operator method. The polymer chain is described by an electron-lattice coupling model and its two ends are connected with metal electrodes of different chemical potentials. The scattering states are shown to be a set of complete eigenstates of electrons in the system at non-equilibrium steady state. With this method, we show that the non-equilibrium Peierls transition (NEPT) does not survive the lattice relaxation and the soliton-antisoliton pair excitations. Furthermore the electronic transport is shown to be accomplished through the soliton-lattice energy band.

We have studied Jahn-Teller effects in Cs2Au2Br6, ACu3Co4O12(A=Ca or Y), and IrTe2 in which the ligand p-to-transition-metal d charge-transfer energy is small or negative. The Au+/Au3+ charge disproportionation of Cs2Au2Br6 manifests in Au 4f photoemission spectra. In Cs2Au2Br6 with negative Δ and intermediate U, the charge disproportionation can be described using effective d orbitals constructed from the Au 5d and Br 4p orbitals and is stabilized by the Jahn-Teller distortion of the Au3+ site with low-spin d8 configuration. In ACu3Co4O12, Δs for Cu3+ and Co4+ are negative and Us are very large. The Zhang-Rice picture is valid to describe the electronic state, and the valence change from Cu2+/Co4+ to Cu3+/Co3+ can be viewed as the O 2p hole transfer from Co to Cu or d9 + d6L → d9L + d6. In IrTe2, both Δ and U are small and the Ir 5d and Te 5p electrons are itinerant to form the multi-band Fermi surfaces. The ideas of band Jahn-Teller transition and Peierls transition are useful to describe the structural instabilities.

A quasi-one-dimensional spin-1/2 Heisenberg antiferromagnet coupled with optical phonons is numerically studied by the quantum Monte Carlo method. We have implemented the stochastic series expansion method for the spin part of the Hamiltonian and the path-integral quantization method for the phonon part. Keeping the spin-phonon coupling strength unchanged, we have calculated the spin-Peierls transition temperature as a function of the frequency of optical phonons. It is found that the transition temperature decreases as the phonon frequency increases. Above a critical frequency, the spin-Peierls transition does not occur all the way down to zero temperature due to quantum fluctuations. We have determined the universality class of the spin-Peierls transition by the phenomenological finite-size scaling analysis. The transitions at low frequencies belong to the universality class of the two-dimensional Ising model while that at a high frequency is found to be characterized by the tricritical exponents of the two-dimensional spin-1 Blume-Capel model.

The combined influence of electron irradiation-induced defects, substrate-induced strain and finite size effects on the electronic transport properties of individual micron-sized thin film growth domains of the organic charge transfer compound tetrathiafulvalene– tetracyanoquinodimethane (TTF–TCNQ) have been studied. The TTF–TCNQ domains have been isolated and electrically contacted by focused ion beam etching and focused ion and electron-beam-induced deposition, respectively. This allowed us to measure the temperature-dependent resistivity and the current–voltage characteristics of individual domains. The dependence of the resistivity on temperature follows a variable-range hopping behaviour which shows a crossover of the exponents as the Peierls transition is approached. The low temperature behaviour is analysed within the segmented rod model of Fogler, Teber and Shklovskii which was developed for charge-ordered quasi one-dimensional electron crystals (Fogler et al 2004 Phys. Rev. B 69 035413). The effect of substrate-induced biaxial strain on the Peierls transition temperature is discussed with regard to its interplay with the defect-induced changes.

We report the growth of nanowires of the charge transfer complex tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) with diameters as low as 130 nm and show that such nanowires can show Peierls transitions at low temperatures. The wires of sub-micron length were grown between two prefabricated electrodes (with sub-micron gap) by vapor phase growth from a single source by applying an electric field between the electrodes during the growth process. The nanowires so grown show a charge transfer ratio approximately 0.57, which is close to that seen in bulk crystals. Below the transition the transport is strongly nonlinear and can be interpreted as originating from de-pinning of CDW that forms at the Peierls transition.

The structural and electronic properties of self-lacing atomic chains on Pt modified Ge(001) surfaces have been studied using low-temperature scanning tunnelling microscopy and spectroscopy. The self-lacing chains have a cross section of only one atom, are perfectly straight, thousands of atoms long and virtually defect free. The atomic chains are composed of dimers that have their bonds aligned in a direction parallel to the chain direction. At low temperatures the atomic chains undergo a Peierls transition: the periodicity of the chains doubles from a 2 × to a 4 × periodicity and an energy gap opens up. Furthermore, at low temperatures (T80 K) novel quasi-one-dimensional electronic states are found. These quasi-one-dimensional electronic states originate from an electronic state of the underlying terrace that is confined between the atomic chains.

In this viewpoint article we analyse recent crucial structural, optical and transport experiments on Fe(3)O(4) magnetite across the Verwey transition at T(V)∼120-125 K. We find that all the relevant experimental data are consistent with a model of a Peierls distortion in the cubic spinel lattice, and likewise, some of them evidence against the original and still distributed hypothesis of the long range charge ordering origin of the Verwey transition. An estimated Peierls transition temperature (T(P)) is comparable with T(V). The Peierls model provides new insight into the electronic properties of magnetite. Application of the Peierls model to some other systems is briefly discussed also.

The stability of the multimode Peierls (MMP) state, which has been predicted for the 2D square-lattice electron system with the Su-Schrieffer-Heeger (SSH) type electron-lattice (e-l) coupling and with a half-filled electronic band, is discussed in the presence of a dilation-type e-l interaction. To understand the role of the latter interaction, the ground state for the model with only the latter interaction is numerically investigated for the 1D chain and the 2D square lattice. The results indicate that this interaction favors a phase separation into two regions, one with sites doubly occupied by electrons and the other with sites having no electron. Detailed numerical analyses show that the MMP state in the 2D system can survive even in the presence of the dilation-type interaction as long as its coupling strength is weak compared to that of the SSH-type interaction.

The magnetic susceptibility measurements in the temperature range from 2 K to 300 K have been performed on a novel genuine organic TCNQ salt (N-Me-2,5-di-Me-Pz)(TCNQ)2. Based on previous study of similiar material spin-ladder like behaviour was expected. However, obtained experimental data are analyzed in terms of the Heisenberg linear chain model. Transition with spin-Peierls features occurs due to the peculiarities of crystalline structure.

Temperature, T, variations of the tunnel conductance G(V) were calculated for junctions between a normal metal and a spatially inhomogeneous superconductor with a dielectric gap on the nested sections of the Fermi surface or between two such superconductors. The dielectric gapping was considered to be a consequence of the charge density wave (CDW) appearance due to the electron–phonon (for a Peierls insulator) or a Coulomb (for an excitonic insulator) interactions. Spatial averaging was carried out over random domains with varying parameters of the CDW superconductor (CDWS). The calculated tunnel spectra demonstrate a smooth transformation from asymmetric patterns with a pronounced dip–hump structure at low T into those with a pseudogap depletion of the electron densities of states at higher T in the vicinity or above the actual critical temperatures of the superconducting transition for any of the CDWS domains. Thus, it is demonstrated that both the dip-hump structure and pseudogapping are manifestations of the same phenomenon. A possible CDW-induced asymmetry of the background contribution to G(V) is also touched upon. The results explain the peculiar features of G(V) for Bi2Sr2CaCu2O8+δ and other related high-Tc cuprates.

The physical and electronic properties of atomic chains formed on various surfaces have become one of the most popular fields of study in surface science. Due to the inherent one-dimensional nature of these chains, various exotic physical phenomena specific to one-dimensional systems have been observed. Among them are Peierls instability and Luttinger liquid behavior. This topical review briefly introduces the physics of these one-dimensional atomic chains and gives some examples from the recently published literature.

The structural properties associated with the orbitally induced Peierls transition in MgTi(2)O(4) are characterized by in situ cooling TEM observations. A distinctive structural modulation with the wavevector of q(1) = 1/4 (0, 0, 4) has been well demonstrated below a critical temperature of about 260 K for MgTi(2)O(4). Systematic analysis demonstrates that this structural modulation can be well explained by an orbital order existing in the low-temperature insulating phase. It is also noted that the nonstoichiometric feature commonly appearing in the present system could yield visible changes in both physical and structural properties. A low-temperature study of the microstructure of Mg[Ti(1.9)Mg(0.1)]O(4) reveals that a little substitution of Mg(2+) for Ti(3+) ions on the octahedral sites can disrupt the long-range order of the t(2g) orbitals, resulting in complex tweed structures in the superstructure phase.

The resistivity and magnetism for the Cu1−x−yAgxIr2S4 (x = 0, y = 0, 0.05, 0.1, 0.15; y = 0, x = 0, 0.05, 0.1, 0.15) system were investigated. A Peierls-like phase transition occurs at TMI~226 K for CuIr2S4. The transition is suppressed in the Cu1−xAgxIr2S4 system, which is attributed to that the substitution of Ag, with its larger radius, for Cu releases the pressure of Ir–Ir. The transition temperature TMI increases slightly with vacancies increasing in the Cu1−yIr2S4, which corresponds to the increase of pressure. Our explanation about the pressure release and increase can also be applied to clarifying the pressure effect which is still an open question. The magnetization rises at low temperatures below TMI. We suggest that it is attributed to remnant localized electrons, which do not participate in the Peierls-like phase transition, accompanied by spin-dimerization in this system. By fitting the experimental curves, we find that about 0.7% of the Ir4+ ions do not participate in the Peierls-like transition. The contributions of Pauli paramagnetism, Landau diamagnetism, Larmor diamagnetism and Curie magnetism can be distinguished.

The In-adsorbed Si(111) 4×1 reconstructed surface is known to undergo a phase transition to an 8×2 structure at approximately 130 K. This structural transition accompanies a metal-insulator transition known as the Peierls transition or charge density wave (CDW) transition. We construct a continuous displacement model and discuss the surface electronic states using a tight-binding model based on the first principles calculations. We performed Monte Carlo simulations, estimated the atomic displacement, and calculated the surface electronic properties around the transition temperatures, in terms of the density of states projected into the reciprocal space (RDOS). The results show that the nature of the transition can be understood as the order-disorder transition of an Ising system.

The experimental data on incommensurate phase versus temperature, as they have been obtained by high resolution inelastic neutron scattering, are compared to theoretical models. In the experiments reported we have set out to examine the phonon dispersion surface to verify that the charge-density wave (CDW) state is present continuously at temperature even above TCDW. The position of the phonon minimum (qmin = qCDW), as well as the detailed shape of the dispersion surface of phonon modes over an extended areas in the (E, q) space, is important in view of the debate on the origin of the CDW at the Peierls transition (2nd_order phase) and gives rise to a further modulation of the structure. This work confirms that the CDW state has precursor effects before the phase transition, there is a strong coupling between phonon and electronic states and that a 'soft-mode transition' occurs at TCDW. This result is compared to theories discussing the origin of the CDW state.