Charge Density Wave Amplitude Research Articles

ChemInform Abstract: Scanning Tunneling Microscopy (STM) Investigations of a New Charge Density Wave (CDW) Phase in Niobium‐Doped Tantalum Disulfide.

AbstractThe CDW amplitude, wavelength, and domain structure are characterized by STM for a new discommensurate CDW phase in NbxTa1‐xS2 materials as a function of the Nb concentration.

Hexagonal Domain-Like Charge Density Wave Phase of TaS 2 Determined by Scanning Tunneling Microscopy

The structure of the room-temperature charge density wave (CDW) phase in octahedrally coordinated tantalum disulfide, 1T-TaS2, has been a controversial issue for over 15 years. Large-scale scanning tunneling microscope images of the intralayer structure of this phase exhibit a domain-like pattern defined by a variation in the maximum CDW amplitude. The circular domains, consisting of high-amplitude CDWs, are arranged in a regular hexagonal lattice (period 73+/-3 angstroms) that is rotated relative to the CDWs. In addition, from the analysis of atomic resolution images it was determined that there is a well-defined phase shift between the CDWs in adjacent domains, and that within a domain the CDW superlattice is commensurate with the atomic lattice. These results provide evidence for the hexagonal discommensurate CDW phase in 1T-TaS2 and also suggest an explanation for the long-standing controversy concerning the structure of this phase.

Energy-loss image formation in scanning transmission ion microscopy

We derive and study equations for dissipative transient processes in a constraint incommensurate charge density wave (CDW) with remnant pockets or a thermal population of normal carriers. The attention was paid to give the correct conservation of condensed and normal electrons, which was problematic at presence of moving dislocation cores if working within an intuitive Ginzburg–Landau like model. We performed a numeric modeling for stationary and transient states in a rectangular geometry when the voltage V or the normal current are applied across the conducting chains. We observe creation of an array of electronic vortices, the dislocations, at or close to the junction surface; their number increases stepwise with increasing V. The dislocation core strongly concentrates the normal carriers but the CDW phase distortions almost neutralize the total charge. At other regimes, the lines of the zero CDW amplitude flash across the sample working as phase slips. The studies were inspired by, and can be applied to experiments on mesa-junctions in NbSe3 and TaS3.

Applications of scanning tunneling microscopy to the study of charge density waves

Scanning tunneling microscopy (STM) studies of the surfaces of transition metal di- and tri-chalcogenides have been used to detect a variety of charge-density-wave (CDW) contributions to the surface charge modulation at 77 and 4.2K. In the 1T phases of TaSe2 and TaS2 strong charge maxima are observed which correspond to the √13 a0 × √13 a0 superlattice generated by the CDWs formed as standing waves from the conduction electrons. The charge-density contours located between the charge maxima show major contributions from the detailed arrangement of surface Se or S atom. The z-deflection observed from the total surface charge-density modulation in the 1T phases is extremely large in the range 1.0 to 2.5Å. The STM scans show the same general structure for the 1T phases at both 77 and 4.2K, but variations in the z-deflection suggest some temperature dependence of the CDW amplitude. The observations are consistent with band structure considerations and the large electron transfer associated with the CDWs. In 2H-TaSe2 at 77K and in 2H-NbSe2 at 4.2K the CDWs are much weaker than in the 1T phases and contribute only small deflections to the STM scans which are mainly dominated by the atomic modulation of the surface charge-density. The linear chain compound NbSe3 has two CDW transitions, one at 144K and one at 59K. The STM scans at 77K with only one CDW present and only 20% of the Fermi surface gapped show no detectable contribution to the surface charge modulation at the CDW wavelength. The z-deflection shows a large surface modulation and resolves the three chains per surface unit cell, but the STM pattern can be matched to the expected height and charge variations of the surface Se atoms. At 4.2K the two CDWs present in NbSe3 gap approximately 80% of the Fermi surface and a modulation at the CDW wavelength of ∼ 4b0 along the chain axis can be analyzed in terms of the band structure and CDW formation. Initial STM scans have also been performed at 77K on the linear chain compound TaS3. The CDW onset occurs at 216K with gapping of the entire Fermi surface and formation of a semiconducting phase at low temperatures. A clear CDW modulation has not yet been observed, but reasonable STM scans can be obtained and improved resolution should make it possible to detect the CDW structure. Technical problems associated with operation of the STMs at both 77 and 4.2K will also be discussed.

Detection of atomic surface structure on NbSe2 and NbSe3 at 77 and 4.2 K using scanning tunneling microscopy

Scanning tunneling microscopy (STM) studies have been performed on NbSe2 and NbSe3 at 77 and 4.2 K. The surface atomic structure has been clearly resolved, but evidence of charge-density wave (CDW) modulation has only been observed at 4.2 K in NbSe3. CDW’s exist in NbSe2 at 4.2 K and in NbSe3 at 77 K, but the CDW amplitude is either too small or is screened by the remaining conduction electrons. The linear chain structure in NbSe3 has been clearly resolved and the STM profiles are dominated by the heights and effective charges of the surface Se atoms. Improved sensitivity and resolution will be required to study any details of the CDW structure in both compounds.

Charge density wave fluctuations in one dimensional metals

The magnetic susceptibility χ( T) for several quasi one-dimensional (1-D) inorganic metals was recently found to agree quantitatively with that predicted in 1973 by Lee, Rice and Anderson for 1-D chains exhibiting charge density wave amplitude fluctuations. We derive here a physical interpretation of their predicted pseudogap in the electronic density-of-states (from which they derived χ( T)) and examine applications of the theory to the electronic heat capacity.

Raman scattering of light from a charge-density-wave (CDW) phonon in an anisotropic CDW superconductor.

The probability of Raman scattering of light by a charge-density-wave (CDW) phonon is calculated for a model anisotropic system which exhibits coexistent CDW and superconducting characteristics. It is pointed out that in such a system both ordinary electron-phonon interactions and the modified Balseiro-Falicov interaction contribute to the Raman activity of the CDW phonon. The Raman spectrum obtained has features qualitatively similar to that of the renormalized spectral function of the CDW phonon previously discussed. However, the inclusion of the electron-photon vertices may considerably enhance the weight of the superconducting gap peak relative to the CDW amplitude mode. The polarizations of the incident and scattered light enter the expressions of the scattering probability, thus giving a natural explanation for the intensity difference of the gap peaks in the A and E modes observed in experiments by Sooryakumar and Klein on 2H-${\mathrm{NbSe}}_{2}$.

Influence of charge density wave fluctuations on the magnetic susceptibility of the quasi one-dimensional conductor (TaSe4)2I

The results of magnetic susceptibility (χ) measurements from 4 K to 430 K are reported for the quasi one-dimensional (1-D) conductor (TaSe4)2I. The long range charge density wave (CDW) transition at Tc = 265 K is manifested in the data via a small (20%) slope change in χ(T). By comparison with the 1973 theoretical prediction of Lee, Rice and Anderson for χ(T) of isolated 1-D chains, CDW amplitude fluctuations are found to be responsible for the strong continuing increase of χ observed above Tc. Comparison with χ(T) previously reported for the quasi 1-D conductors o-TaS3 and K0.3MoO3 reveals the universal behavior of χ(T) above Tc for these compounds.

Transient nonlinear conduction and switching due to charge-density waves in Fe-doped NbSe3

Measurements of hysteresis, switching, and overshoot in the non-Ohmic conductivity of Fe-doped Nb${\mathrm{Se}}_{3}$ single crystals have been made in the temperature range 20-120 K. Crystals of ${\mathrm{Fe}}_{0.03}$Nb${\mathrm{Se}}_{3}$ show two nonlinear thresholds in the $I$ vs $V$ curve with substantial hysteresis centered on each nonlinear threshold. Fast-pulse experiments also show two nonlinear thresholds, both producing an initially slow-rising nonlinear pulse followed by squaring of the pulse at input amplitudes substantially above threshold. Application of successive negative and positive pulses gives rise to overshoot phenomena as observed in pure Nb${\mathrm{Se}}_{3}$, except that two separate overshoot responses are observed corresponding to each separate threshold. Both the overshoot phenomena and hysteresis reach maximum amplitude in the range 45-50 K, and substantial thermal activation is indicated. The higher threshold shows the largest and most complex hysteresis, with multiple nonlinear transitions and intermediate states. The nonlinear response is characteristic of domain-wall motion in the presence of impurities and two distinct charge-density-wave (CDW) pinning strengths or domain structures are indicated. At Fe concentrations below 3 at.%, a variable combination of the two separate thresholds and hysteresis loops is observed, often leading to a distribution of multiple thresholds and a spread of hysteretic segments in the $I$ vs $V$ curve. The complex nonlinear phenomena observed are associated with the low-temperature CDW and decrease rapidly between 54 and 59 K as the CDW amplitude decreases close to the transition. The lifetime of the metastable nonlinear conducting states shows a rapid temperature dependence and gives rise to complex excitation and decay modes. Between 59 and 144 K, where only the high-temperature CDW is present, the Fe-doped Nb${\mathrm{Se}}_{3}$ does not show nonlinear response up to at least 200 mV/cm and no metastable effects have yet been observed.

Collective modes in charge-density-wave superconductors

We investigate the coupling of the collective modes of a coexistent incommensurate charge-density-wave (CDW) superconductor (SC). We use a gauge-invariant random-phase approximation that correctly includes screening to treat both the amplitude and phase modes of the coupled system. Unlike previous work, the SC and CDW orderings are treated fully self-consistently, on an equal footing, and it is found that the only significant coupling is between the CDW and SC amplitude modes. We obtain qualitative agreement with Raman scattering data on Nb${\mathrm{Se}}_{2}$. The phase modes should not display any new structure in addition to that corresponding to pure CDW and pure superconducting order.

NMR study of the charge‐density‐wave state in VSe2

AbstractThe 51V NMR lineshape, Knight shift, quadrupole interaction, spin—lattice relaxation time and magnetic susceptibility in a single‐crystalline VSe2 are studied in the temperature range 4.2 to 300 K. Above the charge‐density‐wave (CDW) onset temperature T0 ≈ 110 K the linear temperature dependence of the quadrupole coupling constant and the pretransitional line broadening are found. The temperature dependence of the CDW amplitude is determined from the width of electric‐field‐gradient distribution at nuclear sites below T0. Combining the experimental data on NMR properties and magnetic susceptibility the effective electron—electron interaction parameter, J = 0.29 eV, is estimated and the density of electron states at the Fermi level. The latter is found to decrease from 2.05 to 1.60 states/eV spin V at the phase transition into the CDW state.

Charge transfer effects in X-ray core level photoemission from layered transition metal intercalates

The authors report X-ray photoemission measurements of core level shifts in TaS2, Fe13/TaS2, Mn14/TaS2 and Ni13/TaS2. The shifts are related to charge transfer from the intercalate 3d ions to the host band structure, and have implications concerning observations of charge density wave amplitudes.

A Theory of the Onset and the Pinning of Charge Density Wave in a Quasi One-Dimensional Conductor

Two kinds of functions of the impurity are studied for the charge density wave (CDW) in a Quasi one·dimensional conductor, by considering the case of a single impurity. We formulate our problem in the self-consistent field approximation and near the transition point to the CDW state. It is pointed out that the impurity·induced Friedel oscillation of electron density as well as the symmetry-breaking effect of impurity in the usual sense governs the processes of the onset and the pinning of CDW below the transition point. They are described in terms of the effective local Fermi wavenumber and the local amplitude of CDW. Both the functions work cooperatively, S0 that the effective local Fermi wavenumber remains uniform in a range as wide as possible. Concerning the amplitude they work destructively in an important range of distance from the impurity. The distortion above the transition point is expressed by the effective local Fermi wavenumber and a localized amplitude. It is essentially a long-ranged reproduction of the Friedel oscillation, as the Friedel oscillation is the sole source of distortion.

The onset and the pinning of charge density wave in a quasi one-dimensional conductor

he recently proposed idea by the authors about the onset and the pinning of charge density wave around an impurity is applied to the case of a quasi one-dimensional conductor. The process is described in terns of the local Fermi wave- number and the local amplitude of charge density wave.

X-ray scattering and electric field studies of the sliding mode conductor NbSe3

X-ray scattering studies of Nb${\mathrm{Se}}_{3}$ show the formation of two independent, incommensurate charge-density waves (CDW) with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{1}=(0, 0.243, 0)$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{2}=(0.5, 0.263, 0.5)$ at ${T}_{1}=144$ K and ${T}_{2}=59$ K, respectively. Electric fields that suppress the resistive anomaly associated with the lower-temperature CDW have no measurable effect on either the CDW amplitude or wave vector. The field required for suppression appears to scale roughly with the defect concentration as measured by the residual-resistance ratio. These results are consistent with the Fr\"ohlich sliding-CDW model with impurity pinning.

Charge-density waves in TSeF-TCNQ — an x-ray study

In an X-ray study of TSeF-TCNQ, two- and three-dimensional short-range ordering of the charge-density waves were found below ∼100 K and ∼50 K, respectively. The periodicity of the short-range order along the a -axis developing below ∼50 K is a, although that of the superlattice below 29 K is 2 a From this behavior it is concluded that charge-density wave amplitudes on both kinds of stacks are comparable and that fourth-order interaction terms are important near as well as below the phase transition. Evidence is also given that it is a 2k F-CDW, not a 4k F-CDW, that is seen in TSeF-TCNQ. The differences between the roles of the fulvalene CDWs in TSeF-TCNQ and in TTF-TCNQ are discussed.

NMR measurements of phenomena related to charge density waves in NbSe2

NMR techniques have been used to investigate the charge density wave (CDW) state in NbSe2. Above the transition temperature T0, the Knight shift and electric field gradient (EFG) tensors have been measured. Broadening of quadrupolar transitions above T0 has been attributed to fluctuations in the EFG which are a precursor to the formation of CDW's. Below T0, a Knight shift distribution is observed whose width can be correlated with the amplitude of an incommensurate CDW which shows a temperature dependence characteristic of BCS type order parameter. The width of the distribution extrapolated to T=0 is shown to be proportional to T0, a fact which supports the hypothesis of a BCS model for the CDW state.

Coupling of the CDW and the water mode in K 2Pt(CN) 4Br 0.3⋯3.2H 2O

In previous work we have observed the amplitude mode of the charge density wave (CDW) in K 2Pt(CN) 4Br 0.3⋯3.2H 2O (KCP) by means of Raman scattering. New measurements made on deuterated material, K 2Pt(CN) 4Br 0.3⋯3.2D 2O (KCP∗), show the same mode but shifted from 44 to 38 cm −1, maintaining the symmetry properties and temperature dependence of frequency and linewidth. This considerable isotope effect is interpreted in terms of a coupling of the CDW with the water stretching mode, which by the deuteration is shifted from 3494 cm −1 in KCP to 2560 cm −1 in KCP∗ according to the change in atomic mass. Both of these modes exhibit A 1(z) symmetry. At 5 K the resulting decoupled frequency of the CDW amplitude mode is 57 cm −1, and the coupling energy about 140 cm −1. A discussion of the temperature dependence of various important quantities is given. The present results show that the water molecules, which are located in between the Pt chains are strongly involved in the eigenvector of the CDW amplitude mode.

Sign and amplitude of charge density waves in 1T-TaS 2 and TaSe 2

The effect of charge density waves has been observed in X-ray photoelectron spectra of 1T-TaS 2 and TaSe 2 as a perturbation of the core-electron binding energies. In the commensurate CDW range the Ta 4f levels show a marked splitting; in the quasi-commensurate and incommensurate states they show broadening of magnitude comparable to this splitting.