Session J10: Superconductivity: Vortex I

Progression of the vortex-solid to vortex-liquid phase boundary with oxygen doping in Y$_{0.8}$Ca$_{0.2}$Ba$_{2}$Cu$_{3}$O$_{x}$ Films

By extending magneto-transport measurements to magnetic fields of 35 tesla we have been able to examine the vortex-solid to vortex-liquid transition of thin film Y$_{0.8}$Ca$_{0.2}$Ba$_{2}$Cu$_{3}$O$_{x}$ samples (6.45~$\le $~x~$\le $ 7.0) over a field-temperature range larger than heretofore reported. It is found in this work that the shape of the phase boundary, H$_{g}$(T), evolves from a very shallow low-field temperature dependence to an extremely rapid high field temperature dependence in the highly underdoped regime (x~$\approx $ 6.45). However, in the lightly overdoped regime (x $\approx $ 6.9 - 7.0), H$_{g}$(T) displays an increasingly steep low-field temperature dependence followed by a lessening of the steepness of the high-field region as oxygen content increases. This trend suggests that the boundary of the dissipation-less superconducting region of this unconventional high-T$_{c}$ cuprate based compound is evolving in the overdoped state towards a form that is consistent with what is observed in conventional superconductors. This research was supported by U.S. DOE Grant No. DE-FG02-04ER46105. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement No. DMR-0084173, by the State of Florida, and by the DOE.   

Measurements of the anisotropic irreversibility field in the electron-doped high-T$_{c}$ superconductor Pr$_{2-x}$Ce$_{x}$CuO$_{4-y}$

We report measurements of the irreversibility field $(H_{\rm {irf}})$ in single crystals of the electron-doped high-T$_{c}$ superconductor (HTSC) Pr$_{2-x}$Ce$_{x}$CuO$_{4-y}$ ($x$ = 0.15 and 0.17) with an applied magnetic field ($B_{0}$) up to 28 T, using the method of the shift in a nuclear magnetic resonance (NMR) probe circuit resonance frequency (f) caused by the susceptibility of the sample. It is observed that $H_{\rm{irf}}$ is highly anisotropic, and that as the temperature $T$ $\rightarrow$ 0 the upper critical field [$H_{c2, \parallel c}$($T$ $\rightarrow$ 0)] at $B_{0}$ $\parallel$ $c$ is far less than the Pauli limit and very different from that at $B_{0}$ $\perp$ $c$. A phase diagram that involves the vortex solid and/or vortex liquid states depending on the alignment of $B_{0}$ relative to the lattice $c$-axis is proposed, and the obtained anisotropic $H_{c2}$ character along with the evaluated zero $T$ coherence length [$\xi_{ab(c)}$($T$ $\rightarrow$ 0)] and penetration depth [$\lambda_{ab(c)}$( $T$ $\rightarrow$ 0)] at $B_{0}$ $\parallel$ $ab(c)$ is compared with that of hole-doped HTSCs. This work is supported at UCLA by NSF Grants DMR-0334869 (WGC) and 0520552 (SEB), at U. Maryland by 0352735 (RLG), and NHMFL by 0084173 and the State of Florida.   

Evolution of Vortex Phase diagram in heavy ion irradiated YBCO

We present a systematic study of the effect of columnar defects induced by heavy ion irradiation on the vortex phase diagram of single-crystal YB2Cu3O7 using ac-specific heat measurements obtained with a micro-calorimeter. The first order vortex melting line where the vortex lattice transforms into a vortex liquid at intermediate magnetic fields is tracked by the peak in the specific heat. In our pristine untwinned YBCO crystal, the vortex melting line extends from a lower critical point Hlcp=0.2T to an upper critical point Hucp $>$ 6T. The crystal was cleaved into several pieces and then irradiated along the c-axis with 1.4GeV Pb ions with different dose matching fields, B$_{\Phi}$ ranging from 100G to 3000G. We explored the behavior of Hucp and Hlcp in the presence of increasing columnar defects to determine whether the transformation of the first order melting line to higher order occurs abruptly at a defect threshold value or continuously with increasing amount of defects.   

Evidence for Hexatic Bose Glass in the Mixed Phase of Type-II Superconductors with Material Line Defects

Dislocation lines and nano-rod inclusions in thin films of YBa$_2$Cu$_3$O$_y$ aligned parallel to the c-axis are known to significantly enhance the critical current in external magnetic field that is also aligned in parallel. In contrast to correlated pinning centers created by irradiation, the former material line defects notably arrange themselves in a ``liquid'' fashion that shows no clusters or voids. Theoretical calculations predict the existence of a hexatic Bose glass at low temperature in such case[1]. We test that prediction by performing Monte-Carlo simulations of the corresponding two-dimensional Coulomb gas ensemble with close to 3000 vortices. In the regime of weak (``liquid'') pinning centers, we find a 2D hexatic vortex liquid at non-zero temperature characterized by isolated edge dislocations. It freezes into a phase-coherent hexatic vortex glass in the zero-temperature limit in accordance with theory [1]. \newline [1] J.P. Rodriguez, Phys. Rev. B {\bf 72}, 214503 (2005); Phys. Rev. B {\bf 70}, 224507 (2004).   

Competition of Point and Correlated Vortex Pinning in Irradiated YBCO

We present a systematic study of vortex pinning on an optimal-doped untwinned YB$_{2}$Cu$_{3}$O$_{7-\delta }$ single-crystal irradiated with 1.4 GeV Pb ions and subsequently irradiated with protons. Irradiation to a dose matching field of B$_{\Phi }$=2T completely transforms the first order vortex melting transition to a higher order Bose glass transition. The transformation is also marked by a pronounced increase in vortex pinning at all temperatures, determined from SQUID measurements. We compare the irreversibility line and the remanent moment of the irradiated sample after subsequent irradiation with protons to determine the contribution to vortex pinning from point and correlated defects on the same sample.   

Dynamics of driven vortices in type-II superconductors in the presence of strong point or columnar pinning centers

We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. We characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex gyration radius, number of double-kink and half-loop excitations, and velocity / voltage noise features. We use different annealing methods to minimize numerical artifacts originating from long-lived metastable states. We compare the results for the above quantities for randomly distributed point and columnar defects.   

Vortex dynamics and critical current in superconductors with unidirectional twin boundaries

The pinning of superconducting vortices is important in device applications of superconductors, because immobilization of vortices at pinning sites is essential for lossless transport. Twin boundary (TB) is one of possible candidates for effective pinning centers, in particular in YBa$_{2}$Cu$_{3}$O$_{7-x}$. Thus, their pinning properties have been actively studied both experimentally and theoretically. However, the pinning characteristics of high-density TBs, which have recently been fabricated successfully, are still unclear. We have studied the dynamics of vortices interacting with unidirectional twin boundaries in a superconductor using molecular dynamics simulation. Current-voltage curves and critical currents have been calculated as a function of vortex density. We found that the critical current as a function of vortex density reveals a staircase pattern and this pattern depends on the pinning strength. This behavior corresponds to discontinuous change of vortex configurations, which reflects vortex pinning characteristics of superconductors with TBs. We also discuss the matching effect of vortex lattice with TBs, and reveal its behavior is different from the one in superconductors with columnar pinning.   

Non Arrhenius creep motion of interacting vortices in high-$T_c$ cuprate superconductors

Dynamics of driven vortices attracted much attention in many different fields of physics. In addition to the understanding of the dynamic phase diagram, the understanding of the elementary process of the vortex motion is crucially important. For a rather large driving force, the existence of the so-called washboard motion has been well established (Y. Togawa et al. : PRL 85 (2000) 3716.). On the other hand, very close to the critical driving force (critical current density), the Anderson-Kim creep picture has been believed for a long time, which is characterized as the Arrhenius process with the linear decrease of the potential barrier as a function of the external driving force. Quite recently, Luo and Hu proposed the possibility of the non-Arrhenius creep process for the vortex motion in Bragg glass phase, based on a numerical simulation (M. B. Luo and X. Hu, PRL98(2007) 267002.). Stimulated by this theoretical work, we performed a detailed $I- V$ study in a high-$T_c$ cuprate, LSCO, and found (1) The creep process is non-Arrhenius like in the Bragg glass phase, (2) With increasing magnetic field, the creep process changes into the Arrhenius type one suddenly. (3) The field where the process changes roughly agrees with the Bragg-glass-Vortex glass transition, (4) Aging effect of the critical driving force also changes close to the Bragg glass - Vortex liquid boundary. These features agree well with predictions by Lou and Hu.   

Anisotropy of the Vortex Magnetic Field Distribution in LuNi$_2$B$_2$

It is well known that the vortex lattice (VL) symmetry and orientation in type-II superconductors is very sensitive to any anisotropy within the screening current plane. A classic example is the sequence of transitions from hexagonal to rhombic to square symmetry, which was first observed in the borocarbide superconductors and explained by a Fermi surface anisotropy coupled with the non-local electrodynamics responsible for vortex-vortex interactions. Recently, however, this is mounting experimental evidence for a strong gap anisotropy and possible point nodes in the basal plane of these materials. Here we report on small-angle neutron scattering studies of the VL in a carefully annealed, high quality LuNi$_2$B$_2$C single crystal, which permitted us to measure the VL form factor for a large number of reflections. These measurements allow a reconstruction of the real space profile of the magnetic field around the vortices, reflecting the basal plane anisotropy of the screening currents in LuNi$_2$B$_2$C. The results will be compared to predictions for both Fermi surface and gap anisotropies, and will serve as a valuable reference for more complicated compounds as e.g. Sr$_2$RuO$_4$, heavy fermions and high-$T_c$'s.   

An infrared study of the pancake vortex state in La$_{2-x}$Sr$_{x}$CuO$_{4}$ across the phase diagram

We report on a doping dependent study of the far-infrared interlayer response in the high-temperature superconductor La$_{2-x}$Sr$_{x}$CuO$_{4}$ (La214). A magnetic field up to 8 Tesla applied perpendicular to the CuO$_{2}$ planes is found to increasingly suppress the Josephson plasma resonance (JPR) with decreased doping. By 6 Tesla at a temperature of 8 Kelvin, the c-axis reflectivity is identical to that of the normal state in the most underdoped samples, suggesting the sample is in a two dimensional superconducting state. This behavior is in contrast to fields parallel to the CuO$_{2}$ planes, where only a small suppression of the JPR is seen up to 17 Tesla. Vortex wandering and static spin density waves are considered as possible mechanisms for plane decoupling.   

Torque magnetometry on the electron-doped high-temperature superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta }$

We have used cantilever and extraction magnetometry to measure magnetization in optimally doped $n$-type high-temperature superconductors Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta }$ ($T_{c}$ = 24K) for magnetic field aligned close to the $c$-axis, over the temperature range (4K to 300K). We observed a distinct irreversibility line below which the torque magnetization is irreversible. Also, we observed a complex torque behavior where the sign of normal state torque response with field (d$\tau $/dH) is the same as that of the superconducting counterpart. From dc magnetization experiments, we conclude that superconducting torque signal arises primarily from out-of-plane diamagnetism, whereas in-plane paramagnetism dominates for the normal state.   

Vortex pinning and local density of states in an inhomogeneous d-wave superconductor

We study a model for vortex pinning in a two-dimensional, inhomogeneous, type-II superconductor at low temperatures. The model is based on the Ginzburg-Landau free energy functional with position dependent coefficients, which we chose in such a way that regions with large gap also have large penetration depth. This choice of parameters (suggested by scanning tunneling spectroscopy experiments) results in vortices being pinned by superconducting regions where the gap is large, in contrast to the usual pinning picture. We also compute the density of states of a model BCS Hamiltonian with $d$-wave symmetry, in which the pairing field is given by the superconducting order parameter appearing in the free energy functional described above. We find that the type of inhomogeneity that we introduce is an indispensable ingredient for our model to reproduce some of the most salient experimental features of the local density of states spectra of cuprates.   

Superconducting Froth

Studying the structure and dynamics of froths helps to understand the behaviour of complex systems where topological intricacy prohibits exact evaluation of the ground state. Though exact solutions are difficult, general laws that take into account both, the topological constrains and physics and chemistry of the froth matter have been developed. We used low temperature magneto-optical imaging in superconducting lead to add a new member to the froths family, - superconducting quantum froth, in which the boundaries are the superconducting and the interior is the normal phase. Despite very different microscopic origin, the topological analysis of the structure has shown that von Neumann's and Lewis' laws apply. Furthermore, for the first time in the froths analysis there is an external global parameter of known behaviour - the total magnetic moment. We show that the statistical laws are in a good agreement with the predicted macroscopic response. We assert that superconducting froth is the new playground for the analysis of complex physics of froths with magnetic field and temperature as tuneable control parameters.   

Vortex relaxation of the noncentrosymmetric CePt$_{3}$Si

The discovery of superconductivity (SC) in CePt$_{3}$Si by Bauer et al. (PRL. 92, 027003 (2004)), has attracted much interest since the compound lacks an inversion center and it has an unusually high upper critical field $H_{c2}$. Theoretical studies have pointed out that spin-orbit coupling could lead to a pairing state of mixed parity. For CePt$_{3}$Si it has been proposed that the combination of spin triplet $p$-wave and spin-singlet $s$-wave symmetries could explain most of the experimental facts consistently. Here we report on flux dynamics on a single crystal of CePt$_{3}$Si. The SC probed by means of magnetic susceptibility and specific heat shows a sharp transition at $T_{c}$= 0.45 K with a width of 0.1 K. Decays of the remnant magnetization display a clean logarithmic time dependence with rates that follow the temperature dependence expected from the Kim -- Anderson theory. However, the creep rates are extremely low, lower than observed in any other superconductor. The low rates are not caused by high critical currents. On the contrary, the critical current in CePt$_{3}$Si is considerably lower than in other superconductors with higher vortex relaxation rates.   

Model for nodal quasiparticle scattering in a disordered vortex lattice

Recent experiments by T. Hanaguri et al. on underdoped Ca2-xNaxCuO2Cl2 [1] have observed quasiparticle interference effects [2], which are sensitive to the sign of the d-wave order parameter. In a magnetic field, they observe a sizable transfer of scattering spectral weight from scattering events between anti-nodes of opposite sign to scattering events between anti-nodes of the same sign. We interpret high momentum phase-coherent scattering in terms of the quasiparticle scattering off the vortex walls. The reduction of scattering at even-odd scattering points indicates that the vortices ``screen'' some of the underlying impurity scattering, as the impurities get trapped inside the vortex cores. [1] T. Hanaguri, Y. Kohsaka, J. C. Davis, C. Lupien, I. Yamada, M. Azuma, M. Takano, K. Ohishi, M. Ono, H. Takagi, cond-mat/07083728. [2] Y. Kohsaka, C. Taylor, K. Fujita, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, J. C. Davis, Science 315, 1380-1385 (2007).