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Comment on "Size effects and charge-density-wave pinning in Nb1-xTixSe3: Evidence for weak pinning by a nonisoelectronic impurity"
Abstract
DiCarlo et al. have recently published experimental data on the effects of Ti impurity doping on threshold field ET for the sliding charge-density-wave (CDW) conductor NbSe3 at 77 K. They claim these data show that nonisoelectronic Ti impurities pin the CDW weakly, with a pinning strength 40 times greater than isoelectronic Ta atoms, and that size effects at small thicknesses support their three-dimensional–to–two-dimensional crossover model of weak pinning. Here I criticize their analysis, and offer an alternative interpretation.
Charge density-waves (CDW) have been the subject of intensive research for about twenty years. Most often they are found in synthetic compounds issuing from the assiduous efforts of chemists. These fascinating materials, inorganic and organic quasi-one-dimensional and quasi-two-dimensional conductors, have metallic properties that are unusual in many ways [1–4]. The key feature is the unstable metallic state, apt to spontaneously form a charge-density modulation ρ
CDW(r) and an associated lattice distortion. The modulation period is determined by the conduction electron density, i.e. related to the Fermi wave vector k
F, in 1D presentation. As a consequence of this instability there is a rich variety of low temperature phase transitions driven by the temperature dependence of the CDW amplitude ρο and the interaction of its phase φ with the underlying lattice. One can find metal-insulator transitions, incommensurate and commensurate modulated structures for example. A central and most intriguing ingredient is the collective sliding mode conductivity [5–9] where the CDW condensate moves as a whole under an applied field. In practice this sliding is hindered by defects, since the phase φ of the modulation will have preferred values at defect sites, opposing the ideally free choice of position of the modulated charge density. This strong connection to defects influences the whole physics of charge density-waves with consequences that are manifest in a wide space and time scale from microscopic to macroscopic. Nevertheless the initial effects are found at the spatial scale of the defects and of the CDW wavelength. This is the reason why microstructural characterization of the CDW is of primary importance for understanding the CDW physics and of course not only with regard to the sliding CDW but also in the full scope of CDW related features.
In this work, we present the numerical simulation results of the dynamics of charge density waves in one-dimensional systems. With a classical model, we show that the threshold field depends on the friction coefficient of the system. From the threshold field variation versus impurities concentration, we show the existence of three different pinning regimes and we prove that the pinning regime in witch Ec ∝ ni(4/3) is an intermediate regime between the weak pinning and the strong pinning one, in the sense of Fukuyama, Lee, Rice. We show also that the transition from one pinning regime to the other is continuous.
A model is proposed for the sliding charge density wave mechanism in the isostructural quasi-one-dimensional compounds NbSe3 and m-TaS3. It is based on an assumption that below either of the two onset temperatures T1 and T2 both modulation modes are present and form small statistically distributed domains along particular trigonal prismatic columns, i.e., along type III below T1 and in addition along type I below T2. Presuming the domains are of comparable sizes to the coherence lengths in the diffraction experiments, their disordered distribution results in a selective contribution to the reciprocal space in both temperature regions, which is in good accord with the diffraction experiments. The model might form the basis for a better explanation of the twinkling domains and low temperature tunneling microscopic images, which were not fully understood on basis of the old model with a selective occupation of the two column types by the two modulation modes.
An analysis of x-ray data from vanadium-doped blue bronze K,,(Mo, xVx)O, is presented for x =2.8% and 1.44%. 2k, satellite reflections are broadened in all the directions and exhibit a peculiar profile asymmetry in the chain direction We interpret this profile asymmetry by the presence of Friedel oscillations around the charged vanadium impurities. Pure low-dimensional (1D) systems undergo Peierls transitions, which leads to the formation of a periodic modulation of the electronic density called charge-density wave (CDW). Through electron-phonon coupling, this CDW is accompanied by a periodic distortion of same period, which is directly observable by x-ray diffraction. Below the transition, well-studied satellite reflections appear at a critical wave vector whose component along the ID direction is twice the Fermi wave vector 2kF. However, the structure of a CDW in presence of disorder is still a theoretical and experimental challenge. The only certainty is that all types of impurity destroy the CDW long range order, as experimentally observed in many cases [I]. This fact is interpreted by the pinning of the CDW-phase on the impurities. However, whether this pinning is collective or individual is still a matter of debate (see for example ref. [ 2 ]). An additional phenomena takes place when impurities are charged: the formation of Friedel oscillations in their vicinity, in order to screen their charge. These oscillations are a general phenomenon arising in any metal, but in 1D the electronic density p(x) is coupled to the lattice which makes their observation also possible by x-ray scattering. p(x) around an impurity of charge Z, located at x = 0, reads: where 5 is the damping length, and q the phase shift of the electron wave function at the Fermi level. q is related to Z by the Friedel sum rule Z = q(2h). Physically, this relation means that the charge Z is screened by the conduction electrons by bringing a charge of opposite sign into the vicinity of the impurity. A schematic representation of a Friedel oscillation is given in Fig. 1. It is noteworthy that the 2kF wave vector is characteristic of the FO and the CDW, which allows these density oscillations to match in some part of the crystal. To get a grasp of the physical meaning of the 1D Friedel sum rule, one can remember that there is two electrons per CDW-period (27~) and that bringing one electron around an impurity requires a shift of half a period (x), which corresponds to q= d 2 as required by eq. (I). We have performed experiments on BM2 (CRG D2AM beamline) at the ESRF, and on DW22 at LURE in Orsay, on heavily vanadium-doped (2.8 at.% and 1.44 at.% respectively) blue bronzes. We have carefully measured the profile of pairs of kq,-satellite reflections (qc = (1,0.748,0.5)) at low temperature along all directions including the chain direction b* (Fig. 2). The widths of these reflections are much larger that the experimental resolution, indicating the loss of the CDW long-range order. In both P(X) = exP(-lxY5)cos(2kFlxl+~)/lXl, (1)
This article reviews the static and dynamic properties of spontaneous
superstructures formed by electrons. Representations of such electronic
crystals are charge density waves and spin density waves in inorganic as well
as organic low dimensional materials. A special attention is paid to the
collective effects in pinning and sliding of these superstructures, and the
glassy properties at low temperature. Charge order and charge
disproportionation which occur in organic materials resulting from correlation
effects are analysed. Experiments under magnetic field, and more specifically
field-induced charge density waves are discussed. Properties of meso- and
nanostructures of charge density waves are also reviewed.
In this work, we present the numerical simulation results of the dynamics of charge density waves in one-dimensional systems. With a classical model, we show that the threshold field depends on the friction coefficient of the system. From the threshold field variation versus impurities concentration, we show the existence of three different pinning regimes and we prove that the pinning regime in witch Ec ∝ ni4/3 is an intermediate regime between the weak pinning and the strong pinning one, in the sense of Fukuyama, Lee, Rice. We show also that the transition from one pinning regime to the other is continuous.
A model is proposed for the sliding charge density wave mechanism in the isostructural quasi-one-dimensional compounds NbSe3 and m-TaS3. It is based on an assumption that below either of the two onset temperatures T1 and T2 both modulation modes are present and form small statistically distributed domains along particular trigonal prismatic columns, i.e., along type III below T1 and in addition along type I below T2. Presuming the domains are of comparable sizes to the coherence lengths in the diffraction experiments, their disordered distribution results in a selective contribution to the reciprocal space in both temperature regions, which is in good accord with the diffraction experiments. The model might form the basis for a better explanation of the twinkling domains and low temperature tunneling microscopic images, which were not fully understood on basis of the old model with a selective occupation of the two column types by the two modulation modes.
We present an x-ray diffuse scattering study of the perturbation of the charge-density-wave structure by impurities in doped NbSe3. Substitution of the transition-metal element niobium is performed either by an isoelectronic impurity, tantalum, or by a nonisoelectronic impurity, titanium, with the concentration equal to x=2% and x=1%, respectively. The nature of the pinning is determined for each type of doping, and we evaluate the size of the domains of coherence of the charge-density waves. [S0163-1829(99)03520-1].
We present an x-ray diffuse scattering study of the charge-density wave (CDW) structure in the doped blue bronzes K0.3(Mo1−xVx)O3 (x=2.8%), Rb0.3(Mo1−xVx)O3 (x=1.44% and 0.28%), and K0.3(Mo1−xWx)O3 (x=2%). At low temperature, the ±2kF satellite reflections are broadened in all four compounds, and shifted in V-doped compounds. Moreover, we have observed an intensity asymmetry of the ±2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that both effects, intensity and profile asymmetry, give access to the local properties of CDW in disordered systems, including the pinning and the phase shifts around impurities. This leads us to propose a complete scenario of the pinning in doped blue bronzes. In the V-doped compounds, we show that the profile asymmetry is due to Friedel oscillations around the charged V substituent and that the intensity asymmetry is related to the strong pinning of the CDW. In the W-doped crystal, the CDW is weakly pinned in regions containing a few tens of neutral W substituents and the CDW phase is slightly distorted around the W impurities. Exact calculations are presented to sustain these ideas.
NbSe3 is a quasi-low-dimensional compound with unique properties. Two incommensurate charge-density waves appear at low temperatures, which slide under the application of an electric field. The mechanism of sliding is not fully understood and it was speculated that precursor effects may be present above the onset temperatures. Scanning tunneling microscopy offers a unique tool to search for such charge instabilities and clear evidence is given for their existence at room temperature. © 1996 The American Physical Society.
The interplay between life-time and pinning effects is investigated for a strongly pinned CDW in the limit of low impurity concentration, treating the incoherent electron-impurity scattering in the single site approximation. In the very dilute limit, the correction to the thermodynamic potential found within this method is in good agreement with that obtained from the microscopic treatment of the Friedel oscillations for a single impurity. Contrary to the latter, the former could be extended to give a quantitative description in the range where the relevant CDW properties have a non-linear dependence on the impurity concentration.
An overview of numerical simulation and experimental works that contradict the Fukuyama-Lee-Rice (FLR) theory of weak pinning is presented. Within an alternative, analytic approach, we find a salomonic answer to the problem of three-dimensional weak pinning: short- and large-scale phase deformations coexist, but their role is different. The present results provide a unified picture of the CDW weakly pinned by impurities, and explain puzzling aspects of numerical simulations, disagreement between previous theories and experiments, e. g. in the case of NbSe, and the white line effect.
A simple variational approach is proposed to study the CDW pinning by individual impurities, relaxing the strong pinning condition. In three dimensions, the energy in the individual pinning régime is lower than that in the weak pinning régime in all situations compatible to a phase-only theory. The individual pinning mechanism is supported by the numerical simulation results and the “white-line effect” in the x-ray patterns.
To quantify the effects of human activities on atmospheric deposition of mercury in eastem Canada, an improved understanding of the natural variations of the concentrations, fluxes and sources of Hg over a long period of time is required. Peat cores from 3 sites in southern Ontario were used to reconstruct changes in atmospheric mercury accumulation rates for the past 10,000 years. The net mercury accumulation rates and excess mercury (mainly anthropogenic) were calculated using the long-terrn average Hg/Br and Hg/Se. The average background mercury accumulation rate during the pre-anthropogenic period was g m yr. An excess of Hg was observed only once during that period, probably reflecting a change in climat. Mercury contamination from anthropogenic sources began about AD 1475 at the Luther Bog, corresponding to extensive biomass burning for agricultural activities by Native North Americans. During the late 17 and 18 centuries, deposition of anthropogenic Hg was at least equal to that of Hg from natural sources. Hg pollution increased again at the beginning of the 19 century. The maximum increase (up to 30 times) compared to “background” occurred during the 1950s, when the anthropogenic component represented up to 85% ofthe total atmospheric mercury deposition.
A phenomenological model is proposed here to show that the pinning of the charge-density-wave (CDW) phase by individual impurities yields an energy gain even for very small values of the Fukuyama-Lee-Rice (FLR) parameter. In three-dimensional systems the individual pinning is energetically more favored than the collective (weak in the FLR sense) pinning in all situations that can be described within a phase-only theory. The present results agree well with those of numerical simulation. Unlike the collective pinning, the individual pinning can account for the +2kF/-2kF asymmetry of the x-ray satellite lines recently reported in many CDW compounds. In three dimensions, two regimes are found for the depinning by an applied electric field, characterized by a different dependence of the threshold field on the CDW gap and CDW-impurity coupling strength. The extension to the spin-density wave is straightforward.
We reexamine the problem of phase pinning of a three-dimensional charge-density wave (CDW) weakly coupled to impurities. Within an analytical approach, we find that the phase is adjusted both at the short scale, around individual impurity sites, and at the large scale, over extended domains containing many impurities. Both phase adjustments are important for the physical behavior and contribute to the understanding of experimental data as well as numerical simulation results in CDW systems. The former give the main contribution to energy and are responsible for the white-line effect observed in x-ray patterns. The latter determine the functional dependence of the threshold field Eth for nonlinear conduction. Unlike what was widely accepted, we find that Eth is not related to the total energy gained by phase spatial variations. This picture is consistent with that emerging from the recent experimental investigations of doped NbSe3 and could contribute to clarifying the controversy on the pinning type in this material.
We report measurements of the threshold electric field ET for charge-density-wave (CDW) depinning in Ti-doped NbSe3. In crystals with large cross-sectional dimensions, ET varies with the residual resistance ratio rR as ET∝rR-1.3. In small crystals, ET varies inversely with crystal thickness and rR. Because of pinning by residual defects, qualitatively different ET-rR relations may be obtained for different weak-pinning impurities. We show that the Ti-concentration, crystal-size, and CDW-transition dependence of ET are consistent with weak CDW pinning and with earlier results for Ta impurities, and indicate a Ti pinning strength roughly 40 times larger than that of Ta.
The conductivity σe due to sliding charge-density-wave (CDW) was measured in the T1-CDW regime of NbSe3. The measurements were also carried out on both crystals doped with Ti and with Ta. At high temperatures, where the CDW is considered in the impurity pinning regime, it is found that the field dependence of σe is independent both of depinning field and of the temperature, but it depends largely on a kind of the dominant impurity contained within the crystal. At low temperatures where the depinning field of the CDW is enhanced enormously, the field dependence of σe is different drastically from that observed at high temperatures.
Adiabatic potentials of a deformable charge density wave (CDW) coupled to impurities are studied in the classical Fukuyama-Lee model in three dimensions. Special attention is paid to the nature of phase slippage processes accompanying quasistatic translational motions of the CDW. Numerical experiments in the case of weak coupling elucidate the existence of phase slippage domains. The size of a single slippage domain has a broad distribution, typically over two orders of magnitude in volume. This distribution may be responsible for the experimentally observed glassy response of the CDW. Also it is shown that because of this distribution the CDW possesses memory of internal polarization which depends on the direction of its previous motion.
The consequences of the formation of two independent charge density waves on the physical properties of NbSe3 are reviewed. Particularly, it is shown that under pressure NbSe3 becomes a bulk superconductor. The non-linear properties of NbSe3 are described. Above a critical electric field, extra-conductivity and noise are measured. The extra-conductivity is associated with the depinning and the motion of the charge density waves. T'he noise is the superposition of broad band noise and periodic structures. These frequencies are described as due to the modulation of the current carried by the charge density wave in the anharmonic pinning potential. The number of condensed electrons under the gaps induced by the lattice distorsion is measured for each charge density wave.
The effect of Ta and Ti impurities on the anomalous transport properties (non-Ohmic dc conductivity and excess microwave absorption) of NbSe3 has been studied. Data from 22 samples show that the characteristic field E0 and the threshold field ET are very sensitive to doping. Both E0 and ET obey a c2 behavior where c is the Ta concentration. The anomalous microwave response is also suppressed by the presence of impurities. As in the dc case Ti is more effective than Ta in suppressing the anomalous behavior. These impurity studies lend strong support to the Fröhlich model in which the dc non-Ohmicity is ascribed to a sliding mode of the charge-density-wave condensate and the excess microwave absorption is ascribed to resonant oscillations of the condensate about pinning centers. The presence of impurities suppresses both the sliding and oscillatory modes. We also briefly describe the effect of the dynamic response of the massive condensate to very short pulses and its effect on non-Ohmic measurements.
The pinning of charge-density waves by impurities is considered in systems that exhibit at least short-range order in three dimensions. Impurities are classified into strong and weak with quite different pinning properties. The pinning of spin-density waves is weak and the phase values at impurity sites are almost random, in agreement with a recent experiment. The electric field required to depin the charge-density wave is estimated. The coupling between a drifting charge-density wave and carriers either from a remnant Fermi surface or thermal excitation is considered. Attention is focused on umklapp scattering of carriers by phasons as a coupling mechanism at finite temperature. The conductivity in the high-electric-field depinned limit can be large. Dislocations in the charge-density-wave lattice are examined with particular emphasis on the piecewise motion of the charge-density wave through the motion of dislocations. We also discuss the generation of dislocations by the analog of Frank-Read sources. The unusual nonlinear conductivity observed in NbSe3 is interpreted in terms of depinning of charge-density waves. The possibility of observing similar effects in other systems is briefly examined.
We have measured the nonlinear conductivity of Nb1−xTaxSe3 alloys in both charge density wave states. The threshold field ET for the onset of nonlinear conduction increases linearly with x. A large scatter for relatively pure samples suggests other pinning mechanisms, such as grain boundaries, for small impurity concentrations.
The interaction of a single impurity with a charge-density wave (CDW) cannot be described by Ginzburg-Landau theory. In the present paper a one-dimensional microscopic quantum theory is presented considering only the backward scattering of the electrons by the impurity at zero temperature. This theory considers the strong perturbation of the CDW inside the amplitude coherence length, which perturbation is dominated by the Friedel oscillations at short distances. It treats the CDW within the framework of the mean-field approximation, and sums up the backward scattering to all orders in perturbation theory. The main features of a self-consistent treatment of the mean field is briefly outlined and the modification can be embodied into the renormalization of the impurity scattering. The results obtained are sensitive to the impurity-scattering strength. In first order, the results of the rigid CDW are reproduced; in second order, the previous results by Barnes and Zawadowski are obtained. The largest effects are in the strong-scattering region. The following physical quantities are calculated: electron density, ground-state energy, density of states, and the force exerted by the impurity on the CDW as a function of the relative position of the impurity with respect to the CDW, and a solution of the equation of motion is found. Considering the electron density in the intermediate-coupling-strength case, the Friedel oscillations dominate at short distances well inside the amplitude coherence length. In the charge density, the Friedel oscillations and the CDW are additive to a good approximation. Outside the amplitude coherence length, the Friedel oscillations tunnel into the CDW gap. In the density of states at the impurity site, the singularity at the gap edge is smeared out and a pair of bound states appears in the gap if the CDW and the Friedel oscillations are out of phase. Further bound states appear also outside the conduction band. The effective potential describing the interaction of the CDW with the impurity is very nonsinusoidal in the intermediate-coupling-strength region, but becomes more sinusoidal for very weak and very strong coupling. The effect of this nonsinusoidal potential in the equation of motion is in the enhancement of higher harmonics appearing in the narrow-band noise, but their intensities remain monotonically decreasing. Among the observable effects predicted are the following: the temperature dependence of the ratios of the intensities of the harmonics in the narrow-band noise, the effect of the nonsinusoidal potential in the Shapiro steps, and the appearance of Friedel oscillations in NMR and diffraction experiments.
A theoretical model is developed to describe the polarization and depinning of charge-density waves (CDW’s) in the inorganic linear-chain compounds which exhibit Fröhlich sliding conduction. Each individual impurity within the crystal is assumed to pin the CDW phase very strongly at the impurity site, and dc CDW motion is made possible only by phase slip. Simple estimates are obtained for most observed properties of sliding CDW systems with use of a three-dimensional Ginzburg-Landau analysis. These predictions are found to be in excellent quantitative agreement with available experimental data characterizing virtually every aspect of CDW dynamics.
A complete theoretical model is constructed to characterize the pinning of charge-density waves (CDW's) to individual impurity sites. The model is based upon consistently incorporating the microscopic CDW-impurity interaction calculated by Tüttó and Zawadowski within the large-scale Ginzburg-Landau framework of Lee and Rice. This analysis shows that the local CDW pinning by impurities will always be strong for all realistic values of the scattering parameter. On the other hand, the large-scale average CDW phase away from the impurity sites will be weakly pinned over extended volumes containing a great many individual impurities, in nominally ``pure'' crystals. This interplay between ``weak'' and ``strong'' aspects of the impurity pinning is found to explain most features of the experimental phenomenology, including the remarkable behavior seen in the broadband 1/f-type noise spectrum above the depinning threshold.
We report measurements of the threshold electric field ET for charge-density-wave (CDW) depinning in Ti-doped NbSe3. In crystals with large cross-sectional dimensions, ET varies with the residual resistance ratio rR as ET∝rR-1.3. In small crystals, ET varies inversely with crystal thickness and rR. Because of pinning by residual defects, qualitatively different ET-rR relations may be obtained for different weak-pinning impurities. We show that the Ti-concentration, crystal-size, and CDW-transition dependence of ET are consistent with weak CDW pinning and with earlier results for Ta impurities, and indicate a Ti pinning strength roughly 40 times larger than that of Ta.
We report measurements of the impurity-concentration and crystal-size dependences of the threshold field ET for charge-density-wave (CDW) depinning in NbSe3. These measurements establish that CDW’s in Ta-doped NbSe3 are weakly pinned. Size dependence of ET occurs when the transverse crystal dimensions become comparable to the transverse CDW phase-phase correlation length, resulting in a crossover from 3D to 2D weak pinning. A divergence of the T=4.2-K Ohmic resistance with decreasing sample thickness is attributed to diffuse scattering by crystal surfaces.
A Comment on the Letter by McCarten, et al., Phys. Rev. Lett. 63, 2841 (1989).
A Comment on the Letter by McCarten et al., Phys. Rev. Lett. 63, 2841 (1989).
- S. Abe
- P. Monceau