• Volume 66, Issue 1

      January 2006,   pages  1-312

    • Preface

      S K Malik A K Grover S N Bhatia

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    • Vortices in Bose-Einstein condensates: A review of the experimental results

      R Srinivasan

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      Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity. Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature, (d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures, nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature; (d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations (Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed.

    • Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

      M Cozzini

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      The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.

    • Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

      S S Banerjee S Goldberg Y Myasoedov M Rappaport E Zeldov A Soibel F de la Cruz J van der Beek M Konczykowski T Tamegai V Vinokur

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      Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.

    • Weak point disorder in strongly fluctuating flux-line liquids

      Panayotis Benetatos M Cristina Marchetti

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      We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid ofrelativistic charged bosons in 2 + 1 dimensions [P Benetatos and M C Marchetti,Phys. Rev.B64, 054518 (2001)]. In this model, flux lines are allowed to be arbitrarily curved and can even form closed loops. Point defects can be scalar or polar. In the latter case, the direction of their dipole moments can be random or correlated. Within the Gaussian approximation of our hydrodynamic model, we calculate disorder-induced corrections to the correlation functions of the flux-line fields and the elastic moduli of the flux-line liquid. We find that scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease the tilt modulus.

    • Vortices in superconducting bulk, films and SQUIDs

      Ernst Helmut Brandt

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      The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).

    • Why pinning by surface irregularities can explain the peak effect in transport properties and neutron diffraction results in NbSe2 and Bi- 2212 crystals?

      Charles Simon Alain Pautrat Christophe Goupil Joseph Scola Patrice Mathieu Annie Brulet Antoine Ruyter M J Higgins Shobo Bhattacharya D Plessis

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      The existence of a peak effect in transport properties (a maximum of the critical current as function of magnetic field) is a well-known but still intriguing feature of Type II superconductors such as NbSe2 and Bi-2212. Using a model of pinning by surface irregularities in anisotropic superconductors, we have developed a calculation of the critical current which allows estimating quantitatively the critical current in both the high critical current phase and the low critical current phase. The only adjustable parameter of this model is the angle of the vortices at the surface. The agreement between the measurements and the model is really very impressive. In this framework, the anomalous dynamical properties close to the peak effect is due to coexistence of two different vortex states with different critical currents. Recent neutron diffraction data in NbSe2 crystals in the presence of transport current support this point of view.

    • Quantitative theory of thermal fluctuations and disorder in the vortex matter

      Dingping Li Baruch Rosenstein P Lin

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      A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.

    • Vortex phase diagram studies in the weakly pinned single crystals of YNi2B2C and LuNi2B2C

      D Jaiswal-nagar D Pal M R Eskildsen P C Canfield H Takeya S Ramakrishnan A K Grover

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      We present a study of magnetization measurements performed on the single crystals of YNi2B2C and LuNi2B2C. For both the compounds, we find flux jumps in magnetisation values in the respective field regions, where the structural transitions in the flux line lattice symmetry have been reported in these systems via the small angle neutron scattering experiments. The magnetisation hysteresis loops and the AC susceptibility measurements show pronounced peak effect as well as second magnetisation peak anomaly for both YNi2B2C and LuNi2B2C. Based on these results, a vortex phase diagram has been constructed for YNi2B2C forH∥c depicting different glassy phases of the vortex matter.

    • Magnetic phase diagram of Josephson vortices in Bi2Sr2CaCu2O2+y

      K Hirata

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      We show experimental results on magnetic phases of Josephson vortices (JVs) in Bi2Sr2CaCu2O2+y, obtained from the JV flow-resistance measurements. Periodic oscillations in the flow-resistance enable us to assign the phase of the long-range 3D ordered state, which was confirmed by the beating effect. We have made preliminary experiments on the doping effect to the JV magnetic phase. The doping effect is reflected not only in the lower boundary of 3D ordered phase, but also in the upper boundary. Above the upper boundary, the flow-resistance shows different behaviours, which may be related to the strength of the interlayer coupling of the JVs along the c-axis, and to the creation/annihilation of pancake vortex/anti-vortex pairs, thermally and magnetically.

    • Effects of sample size on the second magnetization peak in Bi2Sr2CaCuO8+δ at low temperatures

      B Kalisky A Shaulov Y Yeshurun

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      Effects of sample size on the second magnetization peak (SMP) in Bi2Sr2CaCuO8+δ crystals are observed at low temperatures, above the temperature where the SMP totally disappears. In particular, the onset of the SMP shifts to lower fields as the sample size decreases —a result that could be interpreted as a size effect in the orderdisorder vortex matter phase transition. However, local magnetic measurements trace this effect to metastable disordered vortex states, revealing the same order-disorder transition induction in samples of different size.

    • Vortex lattice mobility and effective pinning potentials in the peak effect region in YBCO crystals

      G Pasquini V Bekeris

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      The peak effect (PE) in the critical current density in both low and high temperature superconductors has been the subject of a large amount of experimental and theoretical work in the last few/several years. In the case of YBCO, crucial discussions describing a dynamic or a static picture are not settled. In that region of field and temperature the mobility of the vortex lattice (VL) is found to be dependent on the dynamical history. Recently we reported evidence that the VL reorganizes and accesses to robust VL configurations (VLCs) with different effective pinning potential wells arising in response to different system histories. One of the keys to understand the nature of the PE is to investigate the VL behavior in the vicinity of the various VLCs in the region of the PE. The stability of these VLCs was investigated and it was found that they have distinct characteristic relaxation times, which may be related to elastic or plastic creep processes. In this paper we review some of these results and propose a scenario to describe the PE in YBCO crystals.

    • Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

      A D Thakur S S Banerjee M J Higgins S Ramakrishnan A K Grover

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      We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe2 and CeRu2 with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe2, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe2 which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.

    • Pulverization of the flux line lattice, the phase coexistence and the spinodal temperature of the order—disorder transition in a weakly pinned crystal of Yb3Rh4Sn13

      S Sarkar C V Tomy A D Thakur G Balakrishnan D McK Paul S Ramakrishnan A K Grover

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      We have studied metastability effects pertaining to the peak effect (PE) in critical current density (Jc) via isofield scans in AC susceptibility measurements in a weakly pinned single crystal of Yb3Rh4Sn13 (Tc(0) ≈ 7.6 K). The order-disorder transition in this specimen proceeds in a multi-step manner. The phase coexistence regime between the onset temperature of the PE and the spinodal temperature (where metastability effects cease) seems to comprise two parts, where ordered and disordered regions dominate the bulk behavior, respectively. The PE line in the vortex phase diagram is argued to terminate at the low field end at a critical point in the elastic (Bragg) glass phase.

    • Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

      S Sarkar A D Thakur C V Tomy G Balakrishnan D McK Paul S Ramakrishnan A K Grover

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      New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJc(H)) in isothermalMH scans in a weakly pinned single crystal of Ca3Rh4Sn13, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJc(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca3Rh4Sn13 has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.

    • Antivortices due to competing orbital and paramagnetic pair-breaking effects

      U Klein

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      Thermodynamically stable vortex—antivortex structures in a quasi-twodimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle θ. The spectrum of possible states contains the ordinary vortex state (for large θ) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state (for θ = 0) as limits. The quasi-classical equations are solved nearHc2 for arbitrary θ and it is shown that stable states with co-existing vortices and antivortices exist in a small interval close to θ= 0. The results are compared with recent predictions of antivortices in mesoscopic samples.

    • Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

      Lia Krusin-Elbaum Takasada Shibauchi Gianni Blatter

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      In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature Tc, the regionTc⪯ T ⪯ T* is a vast fluctuation regime.Tc andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field Hc2 bounding the superconducting response and the pseudogap closing field Hpg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi2Sr2CaCu2O8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field Hc2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.

    • Possible Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconducting state in CeCoIn5

      R Movshovich A Bianchi C Capan P G Pagliuso J L Sarrao

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      We present specific heat and thermal conductivity of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical fieldHc2, measured with magnetic field in the plane of this quasi-2D compound and at temperatures down to 50 mK. The superconducting phase diagram and the first order nature of the superconducting phase transition at high fields close to a critical fieldHc2 indicate the importance of the Pauli limiting effect in CeCoIn5. In the same range of magnetic field we observe a second specific heat anomaly within the superconducting state, and interpret it as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. In addition, the thermal conductivity data as a function of field display a kink at a fieldHk below the superconducting critical field, which closely coincides with the low temperature anomaly in specific heat tentatively identified with the appearance of the FFLO superconducting state. The enhancement of thermal conductivity within the FFLO state calls for further theoretical investigations of the real space structure of the order parameter (and in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.

    • Multiple superconducting phases in heavy fermion compounds PrOs4Sb12 and CeCoIn5

      Yuji Matsuda

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      In recently discovered heavy fermion compounds, quasi-two-dimensional CeCoIn5 and skutterudite PrOs4Sb12, multiple superconducting phases with different symmetries manifest themselves belowTc. The angle-resolved magnetothermal transport measurements revealed that in PrOs4Sb12 a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state. The ultrasound velocity measurements revealed that in CeCoIn5 the Fulde-Ferrel-Larkin-Ovchinikov (FFLO) phase, in which the order parameter is spatially modulated and has planar nodes aligned perpendicular to the vortices, appears at low temperature and high field. These results open up a new realm for the study of the superconductivity with multiple phases.

    • Spontaneous vortex phase (SVP) of ruthenocuprate highTc magneto-superconductors

      V P S Awana H Kishan

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      The Ru0.9Sr2YCu2.1O7.9 compound synthesized by HPHT (high pressure high temperature) solid-state reaction route exhibits bulk superconductivity below 30 K. Also the Ru-spins are ordered magnetically above 143 K, with a ferromagnetic component at 5 K. Low field (<1000 Oe)M vs.H plots show that both the superconducting and ferromagnetic components are present in the compound at 5 K. At low temperatures, the compound though remains in spontaneous vortex phase, itsM vs.H hysteresis loop is symmetric instead of the theoretically expected asymmetric one. Our results cast doubts on either theoretical model or the intrinsic nature of ferromagnetic superconductivity in studied ruthenate.

    • Anomalous density of states in hybrid normal metal-superconductor bilayers

      A K Gupta L Crétinon B Pannetier H Courtois

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      In contact with a superconductor, the Andreev reflection of the electrons locally modifies the N metal electronic properties, including the local density of states (LDOS). We investigated the LDOS in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM on the normal metal side. High resolution tunneling spectra measured on the Au surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk Nb gap. The dependence of this mini-gap width with the normal metal thickness is discussed in terms of the Thouless energy. Within the mini-gap, the density of states does not reach zero and shows clear sub-gap features. We compare the experimental spectra with the well-established quasi-classical theory.

    • Unusual vortex dynamics in the quantum-liquid phase of a-MoxSi1−x films

      S Okuma

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      We find the unusual vortex dynamics in the low-temperature liquid phase of amorphous MoxSi1−x films by measuring the fluctuating component of the flux-flow voltage δV(t) about the average voltage. For the thick film, in which the quantum vortex liquid (QVL) phase has been well-determined in the field-temperature plane, δV(t) originating from the vortex motion is clearly visible in the QVL phase, where the distribution of δV(t) is anomalously asymmetric, implying large velocity and/or number fluctuations of driven vortices. For the thin film, in which the QVL phase has not been determined from the static transport measurements, similar unusual vortex motion is observed in nearly the same reduced-temperature regime. We suggest that vortex dynamics in the low-temperature liquid phase of thick and thin films is dominated by common physical mechanisms related to quantum-fluctuation effects.

    • Bitter decoration and magneto-optical observations of vortex chains in high temperature superconductors

      T Tamegai H Aoki M Matsui M Tokunaga

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      In tilted magnetic fields, vortices in anisotropic superconductors form one-dimensional arrangements, called vortex chains. We have visualized vortex chains by Bitter decoration and magneto-optical technique. The fundamental energy scale for the attractive interaction between pancake and Josephson vortices is evaluated by observing vortex chains under various conditions. We also explore how the vortex chains evolve when the large in-plane field is applied or when the anisotropy parameter of the system is changed

    • Direct observation of rectified motion of vortices by Lorentz microscopy

      Yoshihiko Togawa Ken Harada Tetsuya Akashi Hiroto Kasai Tsuyoshi Matsuda Atsutaka Maeda Akira Tonomura

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      We have investigated the vortex dynamics for the ‘ratchet’ operation in a niobium superconductor via a direct imaging of Lorentz microscopy. We directly observe one-directional selective motion of field-gradient-driven vortices along fabricated channels. This results from the rectification of vortices in a spatially asymmetric potential under the oscillating magnetic field in a temporally symmetric manner. Based on the observation of the individual motion of vortices, we clarify the elementary process involved in this rectification.

    • Experimental adiabatic vortex ratchet effect in Nb films with asymmetric pinning trap

      J E Villegas N O Nunez M P Gonzalez E M Gonzalez J L Vicent

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      Nb films grown on top of an array of asymmetric pinning centers show a vortex ratchet effect. A net flow of vortices is induced when the vortex lattice is driven by fluctuating forces on an array of pinning centers without reflection symmetry. This effect occurs in the adiabatic regime and it could be mimiced only by reversible DC driven forces.

    • Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

      Mauro M Doria Antonio R de C Romaguera Welles A M Morgado

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      A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.

    • Interlayer magnetotransport study in electron-doped Sm2−xCexCuO4−δ

      Takasada Shibauchi Tsuyoshi Kawakami Yuhki Terao Minoru Suzuki Lia Krusin-Elbaum

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      Vortex and pseudogap states in electron-doped Sm2−xCexCuO4−δ (x ∼ 0.14) are investigated by the interlayer transport in magnetic fields up to 45 T. To extract intrinsic properties, we fabricated small 30 nm-high mesa structures, sufficiently thin to be free of the recently reported partial decomposition problems. On cooling, the c-axis resistivity ρc of the mesa structures reveals a semiconductive upturn above Tc, followed by a sharp superconducting transition at 20 K. When the magnetic fieldH is applied along the c-axis, ρc(T) shows a parallel shift without significant broadening, as also observed in the hole-doped underdoped cuprates. Above the transition we observe negative magnetoresistance (MR), which can be attributed to the field suppression of the pseudogap, whose magnitude is as small as 38 K. Our results in thex ∼ 0.14 samples closely correspond to the interlayer transport behavior in the ‘overdoped’ regime of hole-doped Bi2Sr2 CaCu2 O8+y.

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