Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Interaction of both charge density waves in NbSe3 from interlayer tunneling experiments

An interlayer tunneling technique has been used for spectroscopy of charge density wave (CDW) energy gaps (Δ_1,2) in NbSe₃ subsequently opened at the Fermi surface on decreasing temperature at T _p1 = 145 K (CDW1) and at T _p2 = 60 K (CDW2). We found that the CDW2 formation is accompanied by an increase of the CDW1 gap below T _p2. The maximum enhancement of Δ₁, δΔ₁ is about 10%. The effect observed has been predicted theoretically as resulting from the joint phase locking of both CDWs with the underlying crystalline lattice below T _p2. The text was submitted by the authors in English.     

Shapiro steps in the torsion of a quasi-one-dimensional conductor TaS<Subscript>3</Subscript>

Features have been observed in the current dependences of the torsion angle, φ(I), for samples of a quasi-one-dimensional conductor TaS₃ irradiated by a high-frequency (HF) field. The features appear at the same current values as the Shapiro steps on the current-voltage characteristics, i.e., correspond to the synchronization of the motion of a charge-density wave (CDW) by the HF field. The shape of the features in the φ(I) dependences indicates a decrease in the inhomogeneous deformation of the CDW under the synchronization conditions. The investigation of torsion appears to be a highly sensitive method for determining the spatial coherence of the CDW.     

Dielectric losses in statistical mixtures

The specific features of the dielectric spectra of statistical mixtures in the form of heterogeneous systems with spherical particles chaotically arranged in the space have been investigated. The distribution function of relaxation times f(τ) has been restored. It has been established that the relaxation times are continuously distributed within a wide interval [τ₁, τ₂]. Different methods for broadening the relaxation time distribution interval and approximating the relaxation time distribution function f(τ) have been analyzed. It has been demonstrated that f(τ) is a nonmonotonic function with two maxima at the boundaries and a minimum in the vicinity of the midpoint of the interval [τ₁, τ₂]. These features of the relaxation time distribution function are responsible for the large difference between the average relaxation frequencies of the permittivity and the dielectric loss (electrical conductivity).     

2kF and 4kF charge-density waves in TTF0.4TSeF0.6-TCNQ — An X-ray study

In the quasi one-dimensional conductor TTF_0.4TSeF_0.6-TCNQ, it is found that the 2k_F CDW has three-dimensional correlations of relatively long range below the metal-insulator transition temperature ～40K, although the 4k_F CDWs are only one-dimensional in character at all temperatures. This result supports the speculation that the 2k_F CDWs and the 4k_F CDWs are present predominantly on the TCNQ and the fulvalene stacks, respectively. The 2k_F-value of the present material is similar to that of TTF-TCNQ but far from that of TSeF-TCNQ. The change of the value with the concentration of TSeF (or TTF) is nonlinear. The transverse period of the ordered 2k_F CDW along the a-axis is $\text{a}$ just below the transition temperature and becomes 4$\text{a}$ below 34.5K. A discussion is given based on the two-chain model.     

Temperature-dependent Time-resolved Fluorescence Study of Cinchonine Alkaloid Dication

Photo induced excited state dynamical processes of cinchonine alkaloid dication (C⁺⁺) have been studied over a wide range of temperature using steady state and nanosecond time-resolved fluorescence spectroscopic techniques. The temperature-dependent fluorescence studies of C⁺⁺ clearly indicate the existence of two distinct emitting species having their own characteristic decay rates. The shorter-lived species shows a usual temperature dependence with increasing non-radiative deactivation at higher temperatures, while the longer-lived species show features resembling to the excited state solvent relaxation process with a large solvent relaxation time (τ _r ∼ 6 ns). The species emitting in the lower energy side, having longer decay time is found to be more sensitive towards chloride ion quenching and has a charge transfer character. Further, concentration quenching with decrease in τ _r of long lived species shows the possibility of energy migration along with solvent relaxation in C⁺⁺.     

Thermal expansion measurements of the quasi-one-dimensional conductor K0.30MoO3

The charge density wave (CDW) dynamics of the quasi-one-dimensional conductor K_0.30MoO₃ shows two different regimes depending on the temperature: a strongly damped CDW motion above ∼50 K and CDW motion with almost no damping below ∼50 K. In a search for a characterization of this CDW behaviour, we performed thermal expansion measurements on K_0.30MoO₃ single crystals in the temperature range 4-250 K. In addition to the anomaly observed at the Peierls transition at 180 K along the [102] direction, an anomaly is observed at ∼50 K along the [−201] and [102] directions. The results are discussed in relation with the change in the CDW rigidity at ∼50 K.     

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.     

Direct measurements of energy relaxation times on an AlGaAs/GaAs heterointerface in the range 4.2–50 K

The temperature dependence of the energy relaxation time τ_e (T) of a two-dimensional electron gas at an AlGaAs/GaAs heterointerface is measured under quasiequilibrium conditions in the region of the transition from scattering by acoustic phonons to scattering with the participation of optical phonons. The temperature interval of constant τ_e, where scattering by the deformation potential predominates, is determined. In the preceding, low-temperature region, where piezoacoustic and deformation-potential-induced scattering processes coexist, τ _e decreases slowly with increasing temperature. Optical phonons start to participate in the scattering processes at T∼25 K (the characteristic phonon lifetime was equal to τ_LOτ4.5 ps). The energy losses calculated from the τ_e data in a model with an effective nonequilibrium electron temperature agree with the published data obtained under strong heating conditions. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 371–375 (10 September 1996)     

Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Energy spectrum of excitations in quasi-one-dimensional conductors with a charge-density wave

A well-formed energy gap Δ is observed in the energy spectrum of the quasi-one-dimensional orthorhombic conductor TaS₃ at temperatures much lower than the Peierls transition temperature T _P . As the temperature increases, in the region T>T _P /2 there is a growth of the density of states in the gap and a relative decrease of the density at energies greater than Δ. In addition, absorption lines which probably correspond to soliton states in a charge-density wave are observed in the gap. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 246–250 (25 February 1996)     

Effects of radiation damage on the charge density wave transitions in NbSe3

We have measured the electrical resistivity of NbSe₃ samples which have been radiation damaged with 2.5 MeV protons up to a defect concentration of 0.5%. We find that, unlike substitutional impurities, the defects do not destroy the charge density wave (CDW) transitions and the samples do not go superconducting. The defects become more effective scatterers below the CDW transitions so that the defect resistivity is temperature dependent. The defects pin the CDWs randomly so that carriers in the unnested regions can be scattered by the CDW. This leads to an enhancement of the defect resistivity. The resistivity of the highly damaged samples is still increasing with decreasing temperatures to below 1 K.     

Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.     

Different path of pressure-induced oxygen ordering and disordering processes in YBa2Cu3O6+x near a metal-insulator transition

The relaxation of the superconducting transition temperature T _c in YBa₂Cu₃O_6.38 is investigated with increasing oxygen order in the CuO_x plane under 1 GPa pressure and with decreasing oxygen order after the pressure is relieved. It is established that the oxygen disordering process is more rapid than the pressure-induced ordering process: The ratio of the relaxation times of T _c in these processes τ _ord/τ _disord≈5. This behavior could be caused by different mechanisms of the pressure-induced increase in the Cu-O chain length and decrease of this length after pressure relief. Fiz. Tverd. Tela (St. Petersburg) 40, 1968–1973 (November 1998)     

Basic physics of semiconductor hydrogen sensors

The most probable physical models of hydrogen sensors based on thin stannic oxide films, MOS-structures, and tunnel MOS-diodes are discussed. The emphasis is on the mechanisms of formation of sensor response to hydrogen. The analytical equations describing the dependence of the response on the hydrogen concentration nH₂ are derived for all types of sensors. The relations describing the dependences of the SnO ₂-sensor conductivity and response on the absolute humidity of a gas mixture are given. It is shown that the relaxation time τ_rel of the response of SnO ₂-and MOS-structure sensors is determined by the relaxation time τ_a of hydrogen atom adsorption on the SnO ₂ and SiO ₂ surfaces, respectively. For the MOS-diodes, τ_rel = τ_a at nH₂ and τ_rel = τ_d at nH₂≥7.5·10³, where τ_d is the relaxation time of hydrogen atom diffusion through an SiO ₂ layer. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–98, April, 2008.     

Effects of charge-density-wave depinning on the low frequency shear compliance of NbSe3

We report on measurements of the voltage dependence of the complex shear compliance of two crystals of the charge-density-wave (CDW) conductor NbSe₃, for torsional frequencies between 1 Hz and 71 Hz. For both samples, there is a frequency independent, ∼1% increase of the magnitude of the compliance when the voltage exceeds the threshold for CDW depinning, but the internal friction has a striking sample dependence which we do not understand. For one sample, there is a frequency independent decrease in internal friction with CDW depinning, suggesting that the elastic changes are not relaxational and might reflect changes in the screening of the crystal strain by the CDW. For the second sample, the sign and magnitude of the change in internal friction is strongly frequency dependent, which we associate with a change in screening due to the finite electron diffusion time. The second sample also exhibits a frequency dependent peak in internal friction near threshold that may reflect relaxation of the CDW phase. Received 14 August 2001 and Received in final form 3 October 2001     

Nonlinear low-temperature magnetization of the quasi-one-dimensional charge-density-wave conductor K0.3 MoO3

A study is made of the temperature and field dependences of the anisotropic magnetization of a quasi-one-dimensional charge-density-wave conductor — the blue bronze K_0.3 MoO₃. Nonlinearity of the magnetization curves is observed at temperatures below 100 K. The temperature and field dependences of the magnetic moment show the effect to be of a collective nature. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 281–286 (25 August 1998)     

Rheology of semi-dilute solutions of calf-thymus DNA

We study the rheology of semi-dilute solutions of the sodium salt of calf-thymus DNA in the linear and nonlinear regimes. The frequency response data can be fitted very well to the hybrid model with two dominant relaxation times τ₀ and τ₁. The ratio (τ₀/τ₁) ∼5 is seen to be fairly constant on changing the temperature from 20 to 30°C. The shear rate dependence of viscosity can be fitted to the Carreau model.     

Charge density wave transport in NbSe<Subscript>3</Subscript> at low temperatures under high magnetic field

Charge density wave (CDW) depinning and sliding regimes have been studied in NbSe₃ at low temperatures down to 1.5 K under magnetic field of 19 T oriented along the c-axis. We found that the threshold field for CDW depinning becomes temperature independent below T ₀ ≈ 15 K. Also CDW current to frequency ratio characterizing CDW sliding regime increases by factor 1.7 below this temperature. The results are discussed as a crossover from thermal fluctuation to tunneling CDW depinning at T < T ₀. Besides, we found that CDW sliding strongly suppresses the amplitude of Shubnikov-de Haas oscillations of magnetoresistance.