Thirring model interpretation of incommensurate charge density wave. I

It is shown that the one-dimensional incommensurate charge density wave system is equivalent to the Thirring model. Its static classical solutions are kink solutions of the phonon phase and localized electron sollutions. Impurity effects on the solutions are also discussed.     

Possible evidence for an incommensurate spin density wave in the stanford electron tunneling studies into LaSrCuO

The Stanford studies include a remarkable dI/dV versus voltage curve with not just one BCS-like peak on each of the positive and negative voltage curves, but with three peaks on the positive-V side, and almost the same structure on the negative-V side. This structure may be caused by an incommensurate spin density wave (SDW) with T_CSCW comparable to 125 K. Incommensurability of the SDW would replicate the usual structure at E_F with two peaks at the edges of a 2Δ gap centred not at E_F, but at displaced positions ± 2v_FδQ away from E_F, where δQ is the incommensurability of the SDW wave vector.     

Dynamic properties of an incommensurate charge density wave in monoclinic TaS3 at low temperatures

The permittivity of monoclinic TaS₃, a quasi-one-dimensional conductor with an incommensurate charge density wave (CDW), as a function of frequency and temperature has been studied. At low temperatures and at frequencies below 1 MHz, the temperature dependence of the real part of the permittivity shows a maximum shift to lower temperatures with decreasing frequency. The temperature dependence of the relaxation time consists of two branches corresponding to macroscopic regions of CDWs with long and short relaxation times τ on the microscopic scale. With decreasing temperature, the growth of τ for large CDW regions is faster than thermal activation and shows a tendency to diverge at a finite temperature while the growth of τ due to the relaxation on the microscopic scale is slower than the activation rate. Our results show that with decreasing temperature the m-TaS₃ quasi-one-dimensional conductor goes over to a glasslike state due to the strong pinning of CDWs by randomly distributed impurities and the formation of mutually interacting solitary CDW collective excitations. Zh. éksp. Teor. Fiz. 111, 988–1000 (March 1997)     

Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

Phonon anomalies observed in various high T_c cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary.     

Polaron defects in a charge density wave: a model for lightly doped BaBiO3

A model for BaBiO₃ was introduced by Rice and Sneddon, which treats this material as a simple three-dimensional version of a Peierls insulator, where the insulating gap is a consequence of the ordered distortion of the oxygen atoms. Charge accumulates on half the atoms and depletes from the other half. Experimentally, when holes are added to BaBiO₃ by doping, it remains insulating until a very large hole concentration is reached, at which point it becomes superconducting. In the Rice-Sneddon model, at large enough electron-phonon coupling, a mechanism for insulating behavior of doped samples is formation of small polarons or bipolarons which trap carriers in bound states in the Peierls gap. A variational calculation of the polaron binding in this model is given, and compared with “exact” numerical results on large clusters with periodic boundary conditions.     

The 2D-electric-field gradient profile in the incommensurate charge density wave state of 1T-TaS2

Using time differential perturbed angular correlation we probed the incommensurate 2D-plane wave charge density wave in 1T-TaS₂ via the¹⁸¹Ta nuclear quadrupole interaction. For the interpretation of the observed line profiles a non-local treatment of the ICDW-perturbation is required. Taking the tensorial character of the electric field gradient into account the wavelength of the CDW-modulation can be derived from the line profiles within an accuracy of better than 5%.     

Tunable charge density wave in TiS_3 nanoribbons

Recently, modifications of charge density wave(CDW) in two-dimensional(2D) show intriguing properties in quasi-2D materials such as layered transition metal dichalcogenides(TMDCs). Optical, electrical transport measurements and scanning tunneling microscopy uncover the enormous difference on the many-body states when the thickness is reduced down to monolayer. However, the CDW in quasi-one-dimensional(1D) materials like transition metal trichalcogenides(TMTCs) is yet to be explored in low dimension whose mechanism is likely distinct from their quasi-2D counterparts.Here, we report a systematic study on the CDW properties of titanium trisulfide(TiS_3). Two phase transition temperatures were observed to decrease from 53 K(103 K) to 46 K(85 K) for the bulk and 15-nm thick nanoribbon, respectively,which arises from the increased fluctuation effect across the chain in the nanoribbon structure, thereby destroying the CDW coherence. It also suggests a strong anisotropy of CDW states in quasi-1D TMTCs which is different from that in TMDCs.Remarkably, by using back gate of-30 V ～ 70 V in 15-nm device, we can tune the second transition temperature from110 K(at-30 V) to 93 K(at 70 V) owing to the altered electron concentration. Finally, the optical approach through the impinging of laser beams on the sample surface is exploited to manipulate the CDW transition, where the melting of the CDW states shows a strong dependence on the excitation energy. Our results demonstrate TiS_3 as a promising quasi-1D CDW material and open up a new window for the study of collective phases in TMTCs.     

Pseudogaps in incommensurate charge density waves and one-dimensional semiconductors

We consider pseudogap effects for electrons interacting with gapless modes. We study generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of photoelectron or tunneling spectroscopy. Within the formalism of functional integration and adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by the presence of gapless phonons that change the usual dynamics to the quantum dissipation regime. Below the free-particle edge, the pseudogap starts with an exponential (stretched exponential for gapful phonons) decrease of the transition rates. Deeply within the pseudogap, they are dominated by a power law, in contrast to a nearly exponential law for gapful modes.     

Distinct current-carrying charge density wave states in NbSe3

We have performed detailed measurements of the dc current-voltage (I–V) characteristics of NbSe₃ in the hysteretic switching regime. Within the hysteresis loop, we observe a series of well-defined and quasi-stable current-carrying states, each with a unique I–V relationship. Transitions between the states, induced by both the applied electric field and thermal fluctuations, are observed. Rapid and random transitions between closely spaced levels are suggested to result in excessive current or voltage noise for the depinned charge density wave condensate.     

Search for a sliding charge density wave in layered compounds

Non-linear voltage-current behavior is observed in the quasi one dimensional compound NbSe₃, due to the contribution of a sliding Charge Density Wave (CDW) to the conductivity. We have looked for a non-linear voltage-current characteristics in the incommensurate CDW state of the layered compounds 2H-TaSe₂ and 1T-TaS₂ and find no evidence for such up to $\text{1.0V}\text{cm}$ and $\text{10V}\text{cm}$, respectively. These values are several orders of magnitude higher than the minimum depinning field observed in NbSe₃.     

Mesoscopic charge density wave in a magnetic flux

The stability of a Charge Density Wave (CDW) in a one-dimensional ring pierced by a Aharonov-Bohm flux is studied in a mean-field picture. It is found that the stability depends on the parity of the number N of electrons. When the size of the ring becomes as small as the coherence length , the CDW gap increases for even N and decreases for odd N. Then when N is even, the CDW gap decreases with flux but it increases when N is odd. The variation of the BCS ratio with size and flux is also calculated. We derive the harmonics expansion of the persistent current in a presence of a finite gap. Received: 16 September 1997 / Received in final form: 12 November 1997 / Accepted: 13 November 1997     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.     

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe₃. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour.     

Phase and amplitude collective modes of an incommensurate spin density wave

We examine the collective modes of an incommensurate quasi-one-dimensional spin density wave associated with oscillations in the phase and amplitude of its complex order parameter. Using a linear response formalism that ensures gauge- and translational-invariance the effects of the Coulomb repulsion in the particle-particle channel are shown to simply renormalise the velocity of the massless phase mode to a value higher than the Fermi velocity. Analytic results for the frequency and damping of the massive amplitude mode are presented. These two longitudinal collective modes remain decoupled for arbitrary wavevector q.     

Measurement of the shear strength of a charge density wave

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.     

Non-linear conductivity of one-dimensional charge density wave

A pure system with one-dimensional CDW placed in a homogeneous electric field is considered. Non-linear effects are found to appear due to motion of a soliton superstructure. The dependence of the differential conductivity on the electric field is calculated.     

The angular magnetothermoelectric power of a charge density wave system

The angular dependence of the magnetothermopower of a charge transfer organic salt α-(ET)(2)KHg(SCN)(4) below (4 K) and above (9 K) the phase transition temperature, T(p) = 8 K, and under fields of 15 T and 25 T, below and above the 'kinkfield', has been studied. We find that for a longitudinal thermoelectric measurement both an interlayer thermopower (the Seebeck effect), S(zz), and a transverse thermopower (the Nernst effect), S(yz), exist in all three different B-T phases (the CDW (0), CDW (x) and metallic states) with large amplitude. Both thermoelectric effects display a resonant-like behavior without a sign reversal at the angles corresponding to angular magnetoresistance oscillation minima and maxima in this compound. The resonant behavior is most evident in the CDW(0) state, indicating a mechanism involving the Fermi surface nesting. Angular dependences reveal different behaviors of the thermopower and Nernst effect in the high magnetic field (CDW(x)) state.     

Nonthermal melting of a charge density wave in TiSe2

We use time-resolved optical reflectivity and x-ray diffraction with femtosecond resolution to study the dynamics of the structural order parameter of the charge density wave phase in TiSe2. We find that the energy density required to melt the charge density wave nonthermally is substantially lower than that required for thermal suppression and is comparable to the charge density wave condensation energy. This observation, together with the fact that the structural dynamics take place on an extremely fast time scale, supports the exciton condensation mechanism for the charge density wave in TiSe2.