Charge Density Wave Dynamics Research Articles

Submicron charge-density-wave devices

We review our fabrication methods to producesubmicron charge-density-wave (CDW) structures and presentmeasurements of CDW dynamics on a microscopic scale. Ourdata show that mesoscopic CDW dynamics is different frombulk behavior. We have studied current-conversion and found asize-effect that can not be accounted for by existing models. Anexplanation might be that the removal and addition of wavefronts becomes correlated in time when probe spacing is reducedbelow a few µm. On small segments we occasionally observenegative differential resistance in the I(V) characteristics andsometimes the resistance may even become negative. We believethat the interplay between CDW deformations (strain) andquasi-particles may yield non-equilibrium effects that play acrucial role in this new phenomenon. No detailed theoreticalcalculations are available. Our measurements clearly show theneed of a microscopic model for CDW dynamics.

Dynamics of charge density waves in Q1D conductors:an approach based on broad-band noise analysis

The most direct manifestation of complexity of CDW dynamics and a possible clue to its understanding is a signal produced when CDW is brought to motion in electric fields. The signal produced by moving CDW in mesoscopic samples of ortho-TaS 3 studied by means of wavelet based methods with a special emphasis to a broad-band noise and its relation to narrow-band signal. It has been shown that the singularity points in the noise signal can be identified using wavelet transform modulus maxima method. These points are believed to correspond to moments when a strong scattering of CDW occurs.

Spatially resolved study of charge-density-wave strain inNbSe3:Evidence for a finite threshold for creep

We have used spatially resolved measurements of the low-field charge-density-wave (CDW) response in ${\mathrm{NbSe}}_{3}$ to obtain the CDW strain profile with single-wavelength resolution. Below $\ensuremath{\sim}35 \mathrm{K},$ the single-particle (linear) resistance R shows significant hysteresis with electric field E for E below a threshold field ${E}_{T}.$ The size of the local hysteresis loop $\ensuremath{\Delta}R(x)$ and thus of the CDW strain $\ensuremath{\epsilon}(x)$ varies linearly with position to within 20 $\ensuremath{\mu}\mathrm{m}$ of the current contacts. Our results confirm that slip boundary conditions at the current contacts are responsible for the single-particle resistance hysteresis, but not for the ``switching'' observed at a larger field ${E}_{T}^{*}.$ Although CDW motion is slow and creeplike between ${E}_{T}$ and ${E}_{T}^{*},$ extremely slow hysteresis relaxation below ${E}_{T}$ implies that the creep rate changes by at least several orders of magnitude at ${E}_{T}.$ This threshold behavior is inconsistent with existing predictions for thermal creep, and highlights the highly unusual character of CDW dynamics at low temperatures.

Convective terms and transversely driven charge-density waves

We derive the convective terms in the damping which determine the structure of the moving charge-density wave (CDW), and study the effect of a current flowing transverse to conducting chains on the CDW dynamics along the chains. In contrast to a recent prediction we find that the effect is orders of magnitude smaller, and that contributions from transverse currents of electron- and holelike quasiparticles to the force exerted on the CDW along the chains act in the opposite directions. We discuss recent experimental verification of the effect and demonstrate experimentally that geometry effects might mimic the transverse current effect.

Étude des effets de frottement sur la dynamique des ondes de densité de charge dans les systèmes unidimensionnels

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 E c ∝ n i 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.

Numerical simulation of the one-dimensional incommensurate charge density wave dynamics

The effect of impurities on the dynamic properties of the charge density wave (CDW) system is explored through numerical simulations based on the one-dimensional Fukuyama, Lee and Rice (FLR) elastic model of weakly pinned incommensurate CDW. In agreement with previous experimental work, the current density J CDW transported by the sliding CDW and the associated excess conductivity σ CDW are found to obey respectively the laws J CDW ∝ (E/E T−1) α and σ CDW ∝ (E T/E) (E/E T −1 α in a wide range of fields and impurity concentrations; α is an impurities dependent exponent and E T is the threshold field. The spatial mean velocity fluctuations present a pic which broadens with increasing field for E ⪢ E T.

Driven dynamics of periodic elastic media in disorder

We analyze the large-scale dynamics of vortex lattices and charge density waves driven in a disordered potential. Using a perturbative coarse-graining procedure we present an explicit derivation of non-equilibrium terms in the renormalized equation of motion, in particular Kardar-Parisi-Zhang non-linearities and dynamic strain terms. We demonstrate the absence of glassy features like diverging linear friction coefficients and transverse critical currents in the drifting state. We discuss the structure of the dynamical phase diagram containing different elastic phases very small and very large drive and plastic phases at intermediate velocity.

Transition to a highly conducting state in mesoscopic o-TaS 3 samples

The non-linear dynamics of charge density waves (CDW) has been studied in mesoscopically thin (transversal dimensions of order of the Lee-Rice coherence length) samples of o-TaS 3 under uniaxial stretch deformation. Electric field induced transition to a highly conducting state has been observed in the fields exceeding several times the threshold one for CDW motion. In a broad transitional region a negative differential resistance is observed in a current driven mode, while a bistability of I- V characteristics is found for voltage driven conditions. The transition is seen at T < 95 K under a reversible uniaxial stretch deformation in excess of some critical value ∼ 0.6%. The phenomena revealed are discussed within a model providing a transfer from a normal carrier screening current dissipative mechanism for CDW motion, dominating at low temperatures and low CDW velocities, to the phonon/phason one at high temperatures and high velocities. The most general result of this study is the recognition of the essential role of mesoscopic level processes for description of the dynamical behavior of CDW.

CDW dynamics in the quasi-one-dimensional molecular conductors (Per) 2M(mnt) 2, (M=Au and Pt)

A comparative study by pulsed current techniques of the Charge Density Wave (CDW) dynamics and the temperature dependence of the non-linear electrical transport threshold field, E t, for the quasi-one-dimensional molecular conductors (Per) 2M(mnt) 2, with M=Au and Pt, is presented. The voltage response to unipolar current pulse shows a similar regime in the two compounds with a quite rigid CDW. E t has a fast increase upon cooling in both compounds but has much larger values for M=Pt and presents a non universal temperature dependence.

Spatially resolved studies of charge-density-wave dynamics and phase slip in NbSe3.

We have performed spatially resolved measurements of the charge-density-wave (CDW) response to bipolar current pulses. These measurements directly yield the distribution of the CDW phase slip, the temporal evolution of the CDW elastic-force and strain profiles, and the local relationship between the phase-slip rate and strain. The steady-state elastic-force profile is strongly coupled to the phase-slip distribution. This coupling increases the CDW strain gradient near the current contacts, and reduces the size of the region in which significant phase slip occurs. Simulations of a model for CDW dynamics that includes the elastic-force--phase-slip coupling provide an excellent quantitative account of the complex spatiotemporal response. Our results imply a revised interpretation of the pulse-sign memory effect, establish the connection between CDW strains and the phase-slip voltage, provide insight into the processes underlying phase slip, and have broad implications for the understanding of previous transient and steady-state measurements in CDW systems. \textcopyright{} 1996 The American Physical Society.

Phase slip and the spatiotemporal response of charge-density waves in NbSe3.

We have performed spatially resolved measurements of the charge-density-wave (CDW) response to bipolar current pulses. These measurements directly yield the temporal evolution of the CDW elastic force profile and the distribution of CDW phase slip. The steady-state elastic force profile is strongly coupled to the phase-slip distribution. This coupling increases the CDW strain gradient near the current contacts, and reduces the size of the region in which significant phase slip occurs. We describe a model for CDW dynamics in the presence of phase slip that provides an excellent account of the complex spatiotemporal response.

Analysis of the 13C Knight shift and spin-lattice relaxation in A3C60 (A = Rb or K)

Abstract The density of states is derived from 13C Knight shift data to 8.6 eV−1 spin−1 C60 −1 for Rb3C60 and 6.8 eV−1 spin−1 C60 −1 for K3C60 at room temperature. It is shown that the simple Korringa relation does not hold for A3C60, that is density-of-states information cannot be obtained from T1 data. A modified Korringa relation must be applied instead by including a Korringa scaling factor S K, which is obtained as SK = 2.5 (Rb3C60) and 2.7 (K3C60) at room temperature. The anisotropic hyperfine interaction which is dominant here has been included. Non-exponential relaxation is predicted to occur from this anisotropy. The deviation from the Korringa value (S K = 1.0) may indicate appreciable electron-electron correlation or charge-density wave dynamics in A3C60.

Sub-domain scaling and asymmetry in NbSe 3

In the presence of a uniform temperature gradient, the charge density wave (CDW) conductor NbSe 3 breaks into a series of N “sub-domains” with independent CDW phase velocities. We experimentally find a scaling relation N ∼ (ΔT) 2 3 where ΔT is the temperature difference between the ends of the sample. Changing the relative directions of the temperature gradient and the electrical current through the sample leads to the same N - ΔT scaling relation but results in unusual transport asymmetries in the dynamic and static CDW configurations. Many of our observations are in accord with a simple phase strain model of CDW dynamics in a temperature gradient.

Transient charge density wave dynamics in pure, non-stoichiometric and V-doped blue bronzes A0.30MoO3 (A= K, Rb)

We report the observation of the transient voltage response to current pulses in pure, non-stoichiometric and V-doped blue bronzes A 0.30 MoO 3 (A=K, Rb) near threshold for depinning of the charge density wave. The transient response waveforms involve overshoot and sluggish behaviors at the leading edge of the pulse in pure samples, weak sluggish response in non-stoichiometric samples and strong sluggish behavior in V-doped blue bronzes. The time decays of the transient responses obey stretched exponential laws. The characteristic time for the overshoot obeys a power law as a function of the electric field and is divergent as threshold is approached from above, suggesting that depinning can be viewed as a dynamical critical phenomenon. The transient response has also been studied under inhomogeneous conditions when a current pulse is injected in a segment of the sample while a dc current is flowing in a neighboring segment the different regimes found in the transient response are analyzed in analogy with strain transient and plastic yielding of a crystal and in terms of combined motion of edge and screw charge density wave phase dislocations interacting with impurities

Transient charge density wave dynamics in A 0.30MoO 3 (A = K, Rb)

We have investigated the transient voltage response to current pulses in the blue bronzes A 0.30MoO 3 (A = K, Rb) near threshold for depinning of the charge density wave in the temperature range 40K–110K. The time dependence of the overshoot at the leading edge of the voltage response and of the tail at the trailing edge obey stretched exponential laws. The effect of a dc current superimposed on the current pulses on threshold values and voltage response is reported. The different regimes found for the transient response are discussed in terms of charge density wave phase dislocations and in analogy with strain transient and plastic yielding of a crystal.

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.

Charge-density-wave phase slip and current conversion inNbSe3

We report measurements of the phase-slip process by which charge-density-wave (CDW) current is converted to single-particle current at electrical contacts. An excess voltage ${\mathit{V}}_{\mathrm{ps}}$ produces a large static deformation of the CDW phase, which drives formation of dislocation loops. Measurements of the phase-slip rate as a function of the applied stress ${\mathit{V}}_{\mathrm{ps}}$ for both CDWs in ${\mathrm{NbSe}}_{3}$ reveal a diodelike relation, analogous to that for phase slip in superfluids. Our results are generally consistent with the predictions of Ramakrishna et al., and may have significant implications for study of CDW dynamics of temperatures well below the Peierls transition.

Two-mode model of charge-density-wave dynamics in quasi-one-dimensional conductors

The frequency dependent conductivity of quasi-one-dimensional inorganic conductors under Peierls transition experimentally observed is connected with collective transport of charge density wave (CDW). The dynamics of incommensurate CDW under impurity pinning has been described by two-mode model: low-frequency pinning mode and high-frequency phason one. The main feature of the model is that the modes are connected and displacements of CDW caused by both modes are sewn together at the pinning centers. The random distribution of model parameters is taken into consideration. Comparison between experimental data and calculated results based on the model proposed are in good quantitative agreement.

The complete frequency dependent response of charge density wave condensates

We have explored the frequency dependent conductivity in the charge density wave state of the model compound K 0.3MoO 3. We identify the pinned mode resonance, the contribution to single particle excitations and modes due to collective mode-phonon interactions. A detailed comparison is made with models of charge density wave dynamics.

Applicability of the ratchet model to the polarization of charge density waves below the threshold field

Abstract Using perturbation theory and computer simulations, it is shown that a simplified model for charge density wave dynamics, in which the sinusoidal potential of the Fukuyama-Lee model is replaced by a ratchet potential, is equivalent to that model in the large potential limit, at least for phenomena below threshold.