Existence of double-pinning force maxima for a single pinning mechanism

Critical current measurements on a cold rolled Pb₆₀In₄₀ foil show two pinning maxima, one close to H_c2 in the neighborhood of h = 0.95, and the other at low fields around h = 0.15. The high field pinning force maximum shifts to lower fields, and the low field maximum shifts to higher fields with increasing pinning strength. The data is explained in terms of Kramer's pinning force model incorporating Brandt's expression for C>₆₆.     

Size effects on the charge-density-wave pinning in the quasi-one-dimensional conductor K0.30MoO3

We report size effects on the charge-density-wave pinning in the quasi-one-dimensional conductor K_0.30MoO₃ in the temperature range 77 K-160 K. The threshold field is approximately one order of magnitude larger in needle-like samples than in bulk crystals, temperature independent and strongly dependent on the width of the sample. In addition, the nonlinear conductivity shows a maximum near 130 K. The results are discussed in relation with various pinning models and CDW dislocations.     

Electromodulated infrared transmission spectra of blue bronze

The infrared transmission of the quasi-one dimensional charge-density-wave (CDW) conductor blue bronze (K_0.3MoO₃) is affected by polarization of the CDW, and therefore by application of a voltage near or above the threshold for CDW depinning. In this paper, we compare the spectra associated with the relative change in transmission taken for different temperatures and oscillating voltages. We find that the phonon spectrum is affected by CDW polarization; the linewidths or frequencies of most phonons change by cm^-1. However, no new intragap states that can be associated with current injection are observed; i.e. the spectra associated with polarization of the CDW in the crystal bulk is identical to that associated with CDW current injection near the contacts. Our results indicate that, for light polarized perpendicular to the conducting chains, the density (n), cross-section , and bandwidth of intragap states are related by: n (?cm^-1)^-1. For expected values of the cross-section and bandwidth, this implies that the intragap states can be optically excited for a time less than s. Received 21 February 2000     

Photo-induced enhancement of charge density wave current in the quasi-one-dimensional conductor TaS3

In the near vicinity of Peierls transition temperature T_P, we have measured the V-I characteristics of the quasi-one-dimensional conductor TaS₃ under dark and photo-irradiation conditions. It is found that a significant enhancement of CDW current occurs only around the threshold voltage V_t under photo-irradiation. This effect can be interpreted as a result of screening of pinning potential for CDW condensate by photo-excited quasi-particles (QP's). Further the distribution of pinning potential intensity is reflected in the behavior of V-I characteristics near V_t. Our finding suggests that the strength of pinning potential can be controlled by the photo-excited QP's in quasi-1D conductors.     

Dielectric constant and threshold electric field of charge-density-waves with strong impurity pinning

The dielectric constant ε and the threshold electric field E_T for the onset of charge-density-wave conduction are investigated within the phenomenological model proposed by Tua and Zawadowski for the strong pinning regime. The static dielectric constant ε (E) in a bias electric field E is found to be almost independent of E provided that E is not too close to E_T. For relatively small values of the pinning strength, the product ε E_T becomes independent of the parameters of the theory. Good agreement is found with the available experimental data on NbSe₃ for the case of strong pinning obtained by radiation damage.     

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     

Critical current density and flux pinning in an unconventional superconductor

The functional dependence of the critical current density on magnetic field, Jc(H), observed at fixed temperatures in the unconventional type-II superconductor, LaAg1−cMnc (c=0.1,0.2,0.3) alloys, but not the relative magnitude of Jc in different alloy compositions at any given temperature and field, is adequately described by the exponential-decay critical state model. In accordance with the predictions of the Kramer's flux-pinning model, the peak value of the pinning force density with the exponent 1.7?m?2.8 and scales with h=H/Hc₂, where Hc₂ is the upper critical field. Irrespective of sample composition and temperature in the superconducting state, the pinning of the flux line lattice (FLL) dominates over the plastic FLL shear.     

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.     

Line vortex pinning and spacing in a three-dimensional ordered Josephson medium

A method of calculating the configuration of two line vortices interacting in a three-dimensional ordered Josephson medium and a minimal distance between them at a given pinning parameter is proposed. The axes of the vortices lie in the middle row of an infinite slab 9 or 13 cells thick with different conditions at the boundaries of the slab. Away from the centers of the vortices, the system of finite-difference equations becomes linear. Fluxoid quantization conditions in cells near the centers of the vortices serve as boundary conditions. An exact solution is approached by iterations in those phase discontinuities which cannot be considered small. This technique provides a much higher calculation accuracy and offers a wider domain of applicability than the earlier methods. Critical values I _d of the pinning parameter at which two initial vortices keep given spacing d between them are calculated. For various vortex configurations, maximal pinning forces are calculated as functions of the pinning parameter and the distance to the nearest vortices. It is shown that the pinning force decreases near parallel vortices and increases near antiparallel ones.     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Interaction and pinning of plane vortices in a three-dimensional Josephson medium and possible distances between two isolated vortices

Within a continuous vortex model, exact expressions are obtained for the Josephson and magnetic energies of plane (laminar) vortices, as well as for the energy and force of pinning by cells in a three-dimensional Josephson medium. If the porosity of the medium is taken into account, the Josephson and magnetic energies of the vortex differ from those for the continuum case. The contributions to the pinning energy from the Josephson and magnetic energies have opposite signs. An algorithm for numerically solving a system of difference equations is proposed in order to find the shape and the energy of the vortex in its stable and unstable states. The continuous vortex model is shown to fail in predicting correct values of the Josephson and magnetic energy of the vortex, as well as of the pinning energy components. Expressions for the least possible distances between two isolated vortices are obtained for a small pinning parameter. Analytical results are in close agreement with computer simulation. An algorithm for numerically solving a system of difference equations is proposed in order to find the least possible distances between two isolated vortices when the pinning parameter I is not small. The minimal value of I at which the center-to-center distance N of the vortices equals three cells is 1.428; for N=2, I _min=1.947. At I>2.907, the vortices can be centered in adjacent cells.     

Pinning and depinning process of an incommensurate CDW as revealed by coherent X-ray diffraction

Experiments on the coherent X-ray diffraction, and their modeling, have been performed on the Charge Density Wave (CDW) system NbSe₃. The 2k_F$2k_F$ satellite reflection associated with the CDW has been measured with respect to external dc currents. Below the threshold current, reflection displays several fringes in the transverse direction which disappear when the threshold current is exceeded. In the sliding state, the transverse satellite profile has a form of two nonsymmetric peaks, one of them being centered at the same position as below the threshold and another one being shifted. The shift of the longitudinal peak position below the threshold current and the nonsymmetric peak in the transverse direction above the threshold one is interpreted as the influence of strong linear defect like a crystal step present on the sample surface, combined with induced arrays of dislocations. Coherent X-rays provide a new access to processes in a CDW driven by an external force in a random pinning potential.     

Impurities potential effect on the charge density wave dynamics in one-dimensional systems

In this work, we present in the weak pinning case the numerical simulation results of the one-dimensional deformable charge density wave (CDW) properties considering the potential amplitude fluctuations effect generated by different impurity types randomly distributed in the lattice. When the electric field approaches threshold value ET, the static equilibrium characteristic time τ and the polarization PCDW become large and seem to diverge at critical field Ecr from below ET following a power law [1−(E/Ecr)]^−α where α is an impurity dependant critical exponent. This divergence indicates that the CDW depinning can be described in terms of a dynamical critical phenomena, where the critical field Ecr plays the role of a transition temperature as in ordinary phase transitions. In agreement with several experimental results, we show that the electric current density JCDW and electric conductivity σCDW follow respectively a power law β[(E/ET)−1] and (ET/E)ν[(E/ET)−1] where β and ν are critical exponents. This results are analogous to these obtained in the case of one impurity type.     

Numerical study of one-dimensional incommensurate charge-density-wave in the weak pinning regime

By the joint use of the Monte Carlo and molecular dynamics techniques, we show, that a classical treatment of the Fukuyama-Lee model on ID incommensurate CDW in the weak pinning regime can well reproduce many peculiar transport properties attributed to a motion of CDW, such as the nonlinear electric conduction associated with narrow band noises. The results of the inspection of phase profiles in motion are also discussed and the importance of the CDW internal degrees of freedom is demonstrated.     

Effect of grain-boundary flux pinning in MgB2 with columnar structure

We studied the flux pinning properties by grain boundaries in MgB₂ films prepared by using a hybrid physical chemical vapor deposition method on the c-axis oriented sapphire substrates. All the films we report here had the columnar grains with the growth direction perpendicular to the substrates and the grain sizes in the range of a few hundred nanometers. At very low magnetic fields, no discernable grain-boundary (GB) pinning effect was observed in all measuring temperatures, but above those fields, the effect of GB flux pinning was observed as enhanced critical current densities (J_cs) and reduced resistances when an external magnetic field (B) was aligned parallel to the c-axis. We interpret the B dependence of J_c in the terms of flux line lattice shear inside the columnar grains activated by dislocations of Frank–Read source while the flux lines pinned by GB act as anchors for dislocations. Magnetic field dependence of flux pinning force density for B parallel to the c-axis was reasonably explained by the above model.     

Anisotropic pinning in macroscopic electrodynamics of superconductors

Anisotropy of critical currents and electric fields in superconductors with strong pinning has been ascribed in the macroscopic model to features of the material equation system relating the electric field to the current density in a superconductor. The anisotropy of the pinning proper is described by an operator relating the pinning force density to the vectors of magnetic induction and Lorentz force. In the approximation of an extended critical state model, a feasible expression of this operator is given in the form of an algorithm based on the concept of a collective anisotropic potential well containing fluxoids. The current-carrying capacity of a strongly anisotropic niobium-titanium foil as a function of the orientation of the current density and applied field with respect to the principal axes of the material has been investigated in detail. Given measurements of the transverse electric fields in the foil under magnetic fields normal to the foil plane, we can plot cross sections of surfaces describing the pinning force density in the space of magnetic induction and Lorentz force. Zh. éksp. Teor. Fiz. 112, 1055–1081 (September 1997)     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Statistical theory of pinning on point defects

The statistical treatment of pinning on point defects is given including the correlations of the number of defects in neighbouring volumes (the interaction of these volumes with the fluxoid is taken as the elementary interaction causing the pinning). For higher defect densities, the agreement with the experiments on niobium is better than with the previous theory. This method of correlations seemed suitable for study the effect of cutting-off the small elementary interactions and for the replacement of the Gauss distribution function by the Poisson distribution function for the number of defects in the elementary volumes. Both these efforts give negative results with respect to the experiments; so far we are therefore not able to explain quantitatively the large increase of the pinning force at small defect densities and small magnetic fields, as well as its decrease to zero always for fields smaller thanH _c2 . The attractive interaction between the flux lines in type II superconductors with small Ginzburg-Landau parameter could give a qualitative explanation of the enhancement of the pinning at small defect densities.Part of this work was performed during the author's stay at the Institut für Festkörperforschung, KFA Jülich. The kind hospitality of this institute and many valuable discussions, especially with Dr. H.Ullmaier, are acknowledged.     

Transient electrical response of K0.30MoO3: Effects of isoelectronic dopants

In this paper, we examine the variation of threshold fields and the transient response of tungsten- and rubidium- substituted K_0.30MoO₃. We find that the dc threshold electric field for the onset of nonlinear behavior scales linearly with tungsten concentration, but varies as the square of the rubidium concentration, indicating strong and weak pinning effects, respectively. In tungsten- substituted samples, the threshold field becomes a strong function of frequency in the range 0.01– 1000 Hz. Above a critical frequency which depends on the doping level, the threshold field is proportional to -log (frequency). We interpret these results as a further example of the spin glass- like response of the CDW. Nonlinear conductivity is observed only after the voltage has exceeded the threshold for a finite time interval.     

Static and dynamic behaviours of multivortex states in a superconducting sample with mesoscopic pinning sites

This preliminary work has focused on the static transitions between the multivortex states interacting with square arrays of the mesoscopic pinning sites in superconducting samples. Our results were obtained from an extensive series of numerical simulations as functions of the magnetic field, pinning radius, and sample size. We have presented a wide range of multivortex configurations from commensurate dimer states to more concentric vortex shells at the matching fields. The stability of these states was also studied by means of the current-voltage V(I) curves which illustrate dynamic phase transitions as a function of applied driving force. These transitions manifested themselves as either a sudden jump in velocity or a nonlinear increase with velocity fluctuations in V(I) curves. We have investigated whether that the phase transitions between the pinned regime and the elastic flow regime are indicative of the stability of the initial vortex states. The variety of intermediate flow phases is attributed to large pinning size (reentrant behavior), strong commensurability and caging effects. In particular, three-shell vortex structures were obtained in the presence of larger pinning sites at adequate matching magnetic fields.