Transient non-linear phenomena and metastable states of charge-density waves in niobium triselenide

Details are given of the transient response of NbSe₃ at 42 K to currents I(t) of various repetitive pulsed waveforms. Nonlinear conduction, due supposedly to motion of one of the two charge-density waves (CDWs) present, was measured as U(t) = IR₀ ? V, where V(t) is the voltage developed across the specimen and R₀ is its resistance in the Ohmic regime.With unidirectional pulses two threshold currents for nonlinearity were observed. On passing the lower threshold, a gradual rise (time-constant 50 μs) of U towards the d.c. value was seen; this behaviour was shown not to originate in the inertia of the CDW, and probably arose thermally. Only after the second threshold was passed did U appear to rise immediately current was applied. The existence of two thresholds accounts for a discrepancy between pulsed and d.c. measurements of conductivity noted by Brill et al. (1981), and also for a phenomenon previously attributed to “locking” between the two CDWs [6].When the pulses were alternately negative- and positive-going, |U| rose beyond its eventual (d.c.) value, towards which it subsequently decayed. A study of this “overshoot” phenomenon has shown the speciment to be left, after a current pulse, in a long-lived metastable state in which pinning stabilises some distortion of the CDW, presumably similar to that of which recent electron micrographs [11] appear to be evidence.A simple model, associating the overshoot with transitions between metastable states, adequately describes the conditions for its occurrence. However, the origin of the conduction associated with the moving CDW remains uncertain, both the Frohlich mechanism and a single-electron alternative finding some experimental support.     

Bistability of non-linear conductivity in insulators with sliding charge density waves

At low temperatures in semiconducting compounds with a sliding charge density wave (CDW), it is shown that the nonlinear d.c current voltage characteristic should be bistable. The high velocity branch describes free sliding of the CDW, motion which becomes undamped at zero temperature (“Fröhlich superconductivity”). In the low-velocity branch the CDW is highly deformed, with a velocity low enough that backflow currents of thermally excited quasiparticles can screen the local electric fields produced by the moving CDW. The results are compared with recent experiments on the blue bronze K_0.3MoO₃.     

On the origin of quasi-periodic current noise in charge-density wave conductors: Experiments on orthorhombic tantalum trisulphide

The quasi-periodic components, which appear in the voltage V developed across a charge-density wave (CDW) conductor when the steady current I exceeds the threshold current I_T at which motion of the CDW begins, have been observed in orthorhombic TaS₃ at 77 K at frequencies v down to less than 1 Hz. Although its relation to the nonlinear part of the current when I?I_T indicates that v is, or is a low multiple of, the ‘washboard’ frequency v/λ, where v is the velocity and λ the wavelength of the CDW, the amplitude of the periodic variation of V when v<1 kHz is much too great to represent a modulation of the Frohlich current. The alternative is that the variation of V arises from a periodic modulation of the single-electron conductivity, resulting from distortion of the CDW as it moves through the crystal. Such a modulation of conductivity has been demonstrated experimentally, by interrupting a current I>I_T at different stages of the cyclic variation of V, and then using a current I<I_T to observe the resistance of the specimen when the CDW is at rest. Mechanisms whereby a periodic dependence of resistance on the position of the CDW may arise are briefly discussed.     

Deformation of a charge density wave in the vicinity of a point contact with a normal metal

The current-voltage characteristics of Cu-K_0.3MoO₃ point contacts between a metal and a semiconductor with a charge density wave (CDW) are studied for various diameters of the contacts in a wide range of temperatures T and voltages V. In the interval 80 K ? T ? 150 K, the current-voltage characteristics are correctly described in the framework of a semiconductor model: screening of an external electric field causes CDW deformation, shifts the chemical potential of quasiparticles, and changes the point contact resistance. It is shown that the chemical potential is above the middle of the Peierls gap in equilibrium and approaches the middle upon an increase in temperature. The current-voltage characteristics of point contacts with a diameter d ? 100 Å exhibit a sharp decrease in resistance for |V| > V _t , which is associated with the beginning of local CDW sliding within the contact region. The V _t (d, T) dependence can be explained by the size effect in the CDW phase slip.     

Electron diffraction study of the charge-density wave superlattice in 2H-NbSe2

In addition to the well-known 3a₀ CDW superlattice, we have observed in 2H-NbSe₂ a 2a₀ superlattice and a well-defined elliptical contour of diffuse intensity between the 3a₀ CDW spots. The 2a₀ superlattice is indicative of a CDW formation through the saddle-point nesting on the Fermi-surface.     

Hysteresis in the electrical properties of orthorhombic tantalum trisulphide: Evidence for an incommensurate-commensurate charge-density wave transition?

A study of electrical conduction in orthorhombic TaS₃ has revealed the existence of thermal hysteresis throughout the temperature range 55 K < T < 205 K. This is attributed to variability in the wavevector q of the charge-density wave (CDW) which develops below T_p = 215 K, and confirms the recent finding, from electron diffraction, that at temperatures not too far below T_p the CDW is incommensurate with the underlying lattice. Evidence that q becomes commensurate, at least along the chain direction at 55 K is provided by the vanishing of hysteresis at that temperature, and also by a rise in the threshold field for continuous motion of the CDW.From its dependence on temperature it is concluded that between T_p and 55 K the conduction in the linear regime is better described as that of a Peierls semi-metal, rather than that of a Peierls intrinsic semiconductor. At most temperatures within that range electrical hysteresis also is observed, and a detailed study of this leads to the tentative conclusion that translation of the CDW conveys negative charge, carried presumably by negatively-charged discommensurations. The mechanisms of conduction below 55 K remain uncertain.     

Current induced deformation of charge density waves in orthorhombic TaS3

The low electric field ohmic resistance R of orthorhombic TaS₃ measured at 90 and 120 K well below the Peierls transition temperature depends on the product of a temperature difference ΔT applied along the sample and the sign of a previously applied current pulse if this pulse is larger than threshold for non-ohmic conductivity. This resistance change is about ΔR/RΔT ∽ 1×10^-3 K^-1 for a pure sample and ΔR/RΔT ∽ 6×10^-3 K^-1 for a slightly electron irradiated one at 90 K. The relative resistance change is insensitive to the sample length. We deduce that the CDW current changes inhomogeneously the Peierls gap E_g. ΔE_g < O at the contact where the CDW current enters and ΔE_g > O at the exit. The effect is attributed to a CDW current induced inhomogeneous deformation of the CDW itself.     

Non-local conduction by charge-density waves in niobium triselenide

The threshold field E_T for the onset of nonlinear conduction in NbSe₃ has been measured using both the normal 4-terminal arrangement, and a transposed version with current flow between the inner pair and voltage measured between the outer. When the distance between the inner terminals is small, and the temperature between 60 and 110 K, E_T is significantly greater for the transposed than for the normal arrangement. The phenomenon is thought to demonstrate that the nonlinear conduction, which arises from motion of the charge-density wave (CDW) forming at 144 K, is non-local over distances of the order of 100μm.Further experiments indicate that E_T is greater with the transposed arrangement because the CDW then has to be broken near the inner terminals, in order that its central section might move independently. Evidence is presented that the breaking process at an inner terminal depends on whether current flows from or towards it, and that above 110 K breaking occurs even when the normal configuration is used, apparently because the CDW is then too weak to overcome the pinning introduced by the contact material.No corresponding effects have been observed in nonlinear conduction by the CDW which forms at 59 K.     

Effect of charge density waves on the tunnel spectra of the Bi2Sr2CaCu2O8+δ superconductor

The differential tunnel conductance G _S of the junction between a normal metal and a superconductor with a charge density wave (CDW) is calculated as a function of the voltage V across the junction. The results are averaged over the spread of superconducting and CDW energy gaps in the nanoscale-inhomogeneous superconductor. It is shown that, if both order parameters are nonzero, a dip-hump structure is formed beyond the superconducting gap of G _S (V). If the phase of the CDW order parameter is not equal to π/2, a dip-hump structure will appear solely or mainly for one sign of the bias polarity. The results agree with the experimental data for Bi₂Sr₂CaCu₂O_8+δ and other high-temperature oxides     

Raman study of charge-density-wave phase transition in quasi-one-dimensional conductor (TaSe4)2I

Polarized Raman spectra were obtained in the quasi-one-dimensional conductor (TaSe₄)₂I above and below the charge-density-wave (CDW) transition temperature (T_c=263 K). The Raman intensities of many peaks become intenser and two of the phonon peaks shift to higher frequency with decreasing temperature. Moreover a new broad peak at about 90 cm^?1 and a new peak around 166 cm^?1 appear in the low-temperature phase. The polarization characteristic shows that the former is assigned to totally symmetric mode. The damping constant of the phonon at 90 cm^?1 increases markedly with increasing temperature. The frequency shifts to higher frequency as the temperature increases and the coupling coefficient is approximately proportional to (T_c?T)^{$\text{1}\text{2}$}. This peak becomes Raman active owing to the CDW phase transition. The temperature dependence of the damping constant and the frequency shift may have a relation to the dynamical properties of the CDW phase transition.     

Ultraviolet photoemission spectroscopy of (TaSe4)2I

The vacuum ultraviolet photoemission spectra of quasi-one-dimensional charge density wave ( CDW ) system, (TaSe₄)₂I, were measured for photon energies between 32 and 100 eV at room temperature ( in the normal phase ) and at about 100 K ( in the CDW phase ). The spectrum of Ta 4f core-levels has shown no additional splitting due to the two different Ta sites. The spectra of the valence and conduction bands have revealed the resonant enhancement for the excitation of the Ta 5p core states, which demonstrates the remarkable hybridization of Ta 5d orbitals with Se 4p orbitals with binding energies smaller than 4 eV. In the CDW phase, the partial cross section decreases for both Ta 5d bands and Se 4p bands with Ta 5d components.     

Electronic transport and specific heat of 1T-V Se2

The low-temperature thermoelectric power and the specific heat of 1T-V Se₂ (vanadium diselenide) have been reported along with the electrical resistivity and Hall coefficient of the compound. The charge density wave (CDW) transition is observed near 110 K in all these properties. The thermoelectric power has been measured from 15 K to 300 K, spanning the incommensurate and commensurate CDW regions. We observed a weak anomaly at the CDW transition for the first time in the specific heat of V Se₂. The linear temperature dependence of the resistivity and thermoelectric power at higher temperatures suggests a normal metallic behavior and electron–phonon scattering above the CDW transition. The positive thermoelectric power and negative Hall coefficient along with strongly temperature-dependent behavior in the CDW phase suggest a mixed conduction related to the strongly hybridized s–p–d bands in this compound.     

Growth,crystal structure and transport properties of quasi one-dimensional conductors NbS3

We report synthesis of quasi-one-dimensional conductor NbS₃, TEM studies and transport properties of the prepared samples. The grown NbS₃ whiskers are Peierls conductors known as phase II with the transitions at T_P1=365 K and T_P2=150 K. CDW1 is stable and not so sensitive to growth conditions. It can slide and be synchronized by the external microwave irradiation up to 16 GHz. CDW2 strongly depends on growth conditions. Nevertheless, it also shows sliding and synchronization.     

Breathing charge density waves in intrinsic Josephson junctions

We demonstrate the creation of a charge density wave (CDW) along a stack of coupled Josephson junctions (JJs) in layered superconductors. Electric charge in each superconducting layer oscillates around some average value, forming a breathing CDW. We show the transformation of a longitudinal plasma wave to CDW in the state corresponding to the outermost branch. Transition between different types of CDW’s related to the inner branches of IV characteristic is demonstrated. The effect of the external electromagnetic radiation on the states corresponding to the inner branches differs crucially from the case of the single JJ. The Shapiro steps in the IV characteristics of the junctions in the stack do not correspond directly to the frequency of radiation ω. The system of JJs behaves like a single whole system: the Shapiro steps or their harmonics in the total IV characteristics appear at voltage $\sum {V_l } = N_R \frac{m} {n}\omega$ , where V _l is the voltage in the lth junction, N _R is the number of JJs in the rotating state, and m and n are integers.     

Thermoelectric power of TTF[Ni(dmit)2]2

The 1D organic salt TTF[Ni(dmit)₂]₂ becomes superconductor with T_c=1.6 K under an applied hydrostatic pressure of 7 kbar. Structural determinations in this system lead us to suspect that superconductivity (SC) coexists with a charge density wave (CDW) instability at low pressure. In order to better understand how SC emerge from a CDW and to revisit the pressure–temperature phase diagram of the TTF[Ni(dmit)₂]₂ we performed transport and thermoelectric power measurements under pressure.     

Puzzle of low temperature phase of α-(ET)2 salts

α-(ET)₂ salts split into two groups: one superconducting and another with mysterious low temperature phase (LTP). The LTP does not exhibit X-ray signiture of conventional CDW or magnetic one for SDW. But the magnetic phase diagram suggests strongly a kind of CDW. We have analysed the threshold electric field of unconventional CDW (UCDW) both for H=0 and H≠0. The threshold electric field for UCDW with H=0 and for 3D weak-pinning limit describes reasonably well the one determined in α-(ET)₂KHg(SCH)₄. The result for H≠0 is also presented. We propose that the LTP in α-(ET)₂ salts is most likely UCDW.     

Joint density of states and charge density wave in 2H-structured transition metal dichalcogenides

The joint density of states of two different 2H-structured transition metal dichalcogenides (TMDs) with and without charge density wave (CDW), Na_0.05TaS₂ and Cu_0.09NbS₂, respectively, are compared. While there is a clear maximum at the 3×3 charge density wavevector for Na_0.05TaS₂, the joint density of states for Cu_0.09NbS₂ does not show such behavior, consistent with the absence of CDW in the system. Our results illustrate that the joint density of states well represents the charge instability in 2D systems.     

Phase analysis of non-coherent processes in a moving CDW

Earlier it has been found that the signal produced by a moving CDW contains along with fundamental of narrow band frequency (ω₁) and its harmonics (ω_n) a non-coherent part—a lot of non-coherent oscillations. Due to a rather broad frequency range the power associated with non-coherent oscillations is comparable to or even greater than that for fundamental frequency, and hence, can play an essential role in CDW dynamics.