Charge Density Wave Model Research Articles

Theory of STM images of CDW in transition-metal dichalcogenides

Scanning tunneling microscopy (STM) images of charge density waves (CDW) in transition-metal dichalcogenides 2H-NbSe 2 and 1T-TaS 2 are theoretically simulated. The results of first-principles band calculations are applied to the mean-field approximation model for commensurate CDW in order to determine the electronic structure. The STM/STS spectrum is numerically simulated through the surface local density of states (LDOS) and the influence by the strength of the effective potential or the bias voltages is investigated. The obtained results suggest a sensitive bias voltage dependence of the STS spectrum of the CDW.

Mode-locking hysteresis in the globally coupled model of charge-density waves.

We study the response of a recently proposed global coupling model of charge-density waves to a joint ac+dc drive. The model is the standard Fukuyama-Lee-Rice model with an additional global coupling term to account for interaction with (uncondensed) quasi-particles. We find that traditional mode-locking is accompanied by hysteresis on mode-locked steps. The experimentally observed asymmetry in the size of hysteresis is reproduced and explained by drawing attention to the importance of the pinning force. For large values of global coupling, increased rigidity leads to vanishing of subharmonic steps consistent with experiments.

Avalanches and the renormalization group for pinned charge-density waves.

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization-group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization-group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an \ensuremath{\epsilon}=4-d expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions d=2,3 are in agreement with the analytical treatment. These results clarify the connections between the behavior above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.

Impulse response of switching NbSe 3

We present detailed measurements of the impulse response of the charge-density-wave (CDW) conductor NbSe 3 as a function of the pulse height, temperature, and initial configuration. We find that the average conduction delay τ has an activated temperature dependence for pulse heights sufficiently far above threshold: τ α exp ( E a k BT ), where E a =24.1±3.2 meV, comparable to the CDW gap. Numerical simulations of a model of CDWs which includes the interaction with normal carriers are in good qualitative agreement with experiments.

Factors governing the charge density wave patterns of layered transition-metal compounds of octahedral coordination with d2 and d3 electron counts

Two different charge density wave (CDW) patterns are observed for layered transition-metal compounds ML[sub 2] (e.g., M = transition metal, L = oxygen, chalcogen) of octahedral coordination with d[sup 2] and d[sup 3] electron counts. Tight-binding electronic band structure calculations were carried out for several d[sup 2] ML[sub 2] layers, and factors controlling these patterns were discussed. In general, the 1T-ML[sub 2] systems with short M-L bonds adopt a CDW pattern involving patterns were discussed. In general, the 1T-ML[sub 2] systems with short M-L bonds adopt a CDW pattern involving a weak distortion, while those with long M-L bonds adopt a CDW pattern involving a strong distortion. These calculations show that the metal-atom trimerization in LiVO[sub 2] is energetically favorable and opens a band gap for a small displacement of the metal atoms. This supports the CDW model of weak metal-atom trimerization proposed for the [radical]3 x [radical]3 superstructure of LiVO[sub 2].

ELECTRONIC STRUCTURE AND RECONSTRUCTION OF THE Mo(001) SURFACE

Recent developments in understanding the nature of surface electronic structure focused on illuminating the electronic origin of reconstruction of the Mo (001) surface have been reviewed. The long-standing disputes between two competing theoretical models, the charge density wave model and the local bonding model, for the driving mechanism of the reconstructional transition seem to be resolved by recent experimental evidences favoring the Peierls-type 2kF instabilities with significant matrix element effects. Details of recent experimental and theoretical findings for the surface electronic bands are discussed briefly with an emphasis placed on characterizing the surface states and their roles in the reconstruction.

The electrodynamics of the charge density wave condensate

The ac response of the charge density wave (CDW) condensate is reviewed, by discussing our detailed optical investigations on the CDW model compound K 0.3MoO 3. We are able to identify several features characterizing the CDW ground state (at T⪡T 3D, the CDW phase transition temperature) and the fluctuation regime (T ∼ T 3D).

Low-temperature charge-density-wave dynamics and switching in NbSe3.

We have studied charge-density-wave (CDW) transport in ${\mathrm{NbSe}}_{3}$ at temperatures below 45 K. Between the threshold electric field ${\mathit{E}}_{\mathit{T}}$ and a second characteristic field ${\mathit{E}}_{\mathit{T}}^{\mathrm{*}}$, the CDW conductivity varies as ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{CDW}}$\ensuremath{\propto}exp(-\ensuremath{\Delta}/${\mathit{k}}_{\mathit{B}}$T), with an activation energy \ensuremath{\Delta} comparable to the CDW gap. Above ${\mathit{E}}_{\mathit{T}}^{\mathrm{*}}$, the CDW conductivity increases, in many crystals via an abrupt ``switch,'' to a much larger, only weakly temperature-dependent value. Contrary to previous suggestions, we find that ${\mathit{E}}_{\mathit{T}}^{\mathrm{*}}$ is determined by bulk CDW pinning and dynamics, not by isolated defects. We show that this behavior has strong analogs in the semiconducting CDW materials, and compare it with predictions based upon a model of CDW--normal-carrier interactions proposed by Littlewood.

Lattice-induced modulation of a charge-density wave far from commensurability.

Using x-ray diffraction we have investigated whether the charge-density wave (CDW) is purely sinusoidal in the incommensurate (I) phase of 1T-TaS 2 . The second-order CDW satellite reflection is significantly more intense than a purely sinusoidal CDW model would predict. Our data suggest that the CDW is phase and amplitude modulated by the CDW-lattice interaction, despite the CDW system being far from commensurability

Spectrum of Third Harmonic Generation of MX Complex

The theory of third harmonic generation of MX complex is presented on the basis of charge density wave model. The recently observed spectrum χ(3) (ω) of Pt-Cl complex can be well interpreted by this theory, which shows that the experimental peak at 1.8eV is produced by the two-photon resonance between the bottom of valence band and the top of conduction band. Besides, our theory predicts that there exist another peak below the observed region.

Charge-density-wave phase elasticity of the blue bronze.

We report neutron inelastic scattering measurements of the dispersion of the phase mode of the charge-density-wave (CDW) collective excitations in the blue bronze. Anisotropy and temperature-dependence analysis yields phase elasticity parameters relevant for a classical deformable model of CDW. The considerable stiffening of the longitudinal phason velocity observed upon cooling clearly shows that Coulomb forces play a fundamental role in CDW deformation processes.

Vector Charge Density Wave Model of Metallic and Trigonal Te

High pressure metallic (m-) Te and pressure dependence of trigonal (t-)Te are studied by the vector charge density wave (VCDW) model, namely by coupled CDWs on vector p orbitals. Metallic Te comprising dimerized zigzag chains as well as semiconducting t-Te with helical chains can be described by VCDWs with the wave numbers (O, π/2, π/2) and (2π/3, 2π/3, 2π/3), respectively, on a simple cubic lattice. The VCDW model is improved to include all the first order change of the transfer interaction so that the effect of shear deformation can be taken into account

Vector Charge Density Wave Model of Metallic and Trigonal Te

Vector Charge Density Wave Model of Metallic and Trigonal Te

Theory of stretched exponential relaxation and critical behavior at depinning for charge density waves

We study analytically and numerically the critical behavior at the depinning transition and the stretched exponential relaxation in the pinned region of a charge density wave (CDW) under the influence of an applied field. The original model of an elastic string pinned by random sinusoidal impurity potentials is transformed, by a coarse graining operation, into a simpler model for which analytical expressions for the exponents corresponding to the critical behavior and to the stretched exponential relaxation can be derived in any dimension. In particular we can identify different correlation lenghts (static and dynamic) that diverge at the depinning transition with different exponents. Computer simulations on the coarse grained model and on the original CDW model turn out to be in very good agreement with our analytical expressions. These results clarify the nature of the critical behavior of the depinning transition and of the glassy-type relaxation in the pinned region. In addition our theoretical analysis may provide a new point of view for the description of other disordered and glassy systems.

Critical behavior of pinned charge-density waves below the threshold for sliding.

Numerical results on the static critical behavior of a collective-pinning model of charge-density waves are presented. Distinct critical behaviors are found for irreversible (typical) and reversible approaches to the threshold for sliding. From the size dependence of the threshold fields and polarizations, at least two distinct finite-size-scaling correlation-length exponents are identified. New analytic results on the general behavior of this model both above and below threshold are reported, including the uniqueness of the sliding state.

Phase slips and the instability of the Fukuyama-Lee-Rice model of charge-density waves.

Phase slips and the instability of the Fukuyama-Lee-Rice model of charge-density waves.

Critical dynamics of a pinned elastic medium in two and three dimensions: A model for charge-density waves.

We study numerically the dynamical equilibrium behavior for the uniformly driven, elastic model of Fukuyama, Lee, and Rice for pinned charge-density waves, in the critical region close to the threshold field for sliding, in two and three dimensions. We obtain a critical exponent for the mean velocity in good agreement with recent experiments, and scaling for the velocity correlation function, from which we extract a diverging correlation length. The correlation-length exponent \ensuremath{\nu} is found to be less than 2/d (d is dimension), suggesting unusual critical behavior for this model.

Vector charge density wave model of metallic Te and Se

High pressure metallic Te and Se are studied by the vector charge density wave (VCDW) model. They can be described by a VCDW state with the wave number (0, π/2, π/2) on a cubic lattice. In the VCDW state, Te or Se atoms make stacked zigzag chains. The period of orientational arrangement of p lone pairs in this state is two along a chain, four along two square edges including a chain plane and two along the stacking direction. The electronic and lattice structures of the metallic phases are calculated by the temperature-pressure Hartree-Fock (HF) method. The mixing between p x , p y and p z atomic orbitals is included so as to consider a general distortion including shearing displacements. This model can explain the characteristics features of the lattice structure such as the dimerization and staggered stacking of chains and the electronic energy band structure of metallic Te.

Density of states of quasi-one-dimensional charge-density and spin-density waves.

Making use of the quasi-two-dimensional model of charge-density waves, we analyze the electron density of states of ${\mathrm{NbSe}}_{3}$ observed by the electron tunneling technique. The model provides excellent description of both the observed density of states and the temperature dependence of the energy gap.

Glassy relaxation in the Fukuyama-Lee-Rice model of charge-density waves.

Glassy relaxation in the Fukuyama-Lee-Rice model of charge-density waves.