Session V9: Superconductivity: Vortex States

Does a Bose-Glass State Exist in Commercial High-T$_c$ Wires?

The hypothesis that the vortex lattice induced by perpendicular magnetic field in films of PLD-YBCO is in a thermodynamic Bose glass state accounts for the inverse-square-root power law shown by the critical current density versus perpendicuar magnetic field.$^0$ We study here how robust such a state is to the addition of point pinning centers. This is done by first calculating the tilt modulus of the ``pristine'' Bose-glass state. It is found to diverge at long-wavelength along the magnetic-field/correlated-defect direction. A Larkin-Ovchinnikov analysis then yields a 2D/3D phase transition in collective pinning that is first-order. In particular, a {\it broken} Bose glass state characterized by finite Larkin domains, within which correlated pinning centers remain effective, exists at strong enough point pinning, at small enough coherence lengths. A signature of the broken glass state is found in the dependence shown by the critical current with film thickness along the c axis, which is predicted to crossover from [1] 2D to 3D collective-pinning behavior at a film thickness equal to the longitudinal Larkin scale $L_c$. \newline [1] J. Rodriguez \& M. Maley, Phys. Rev. B {\bf 73}, 094502 (2006).   

The low-temperature vortex liquid in $\rm La_{2-x}Sr_xCuO_4$ and $\rm Bi_2Sr_{2-y}La_yCuO_6$

Diamagnetism in lightly-doped crystals of $\rm La_{2-x}Sr_xCuO_4 $ (LSCO)with doping $x$ = 0.03 to 0.09 has been investigated by torque magnetometry, which resolves weak 2D supercurrents against a nearly isotropic paramagnetic spin response.By carefully subtracting the large paramagnetic susceptibilities of the van Vleck and spin terms, we observe the diamagnetic signal of vortices in fields up to 45 T, even for $x$ as low as 0.03. The torque results allow the $x$ dependence of both the melting field $H_{irr}$ and upper critical field $H_{c2}$ to be measured. We find that $H_{c2}$ extends smoothly across the critical doping value $x_c\simeq 0.055$. Below $x_c$, the pair condensate survives as a vortex liquid in intense fields, but long-range phase coherence is absent down to our lowest temperature $T$ = 0.35 K. We discuss the interesting differences between the vortex liquid and solid phases, and the collapse at low $T$ of phase coherence at the boundary. The close correlation of $T_{onset}$ to $H_{c2}$ in LSCO and Bi 2201 will also be reported. Resarch supported by NSF grant DMR 0213706.   

High-frequency response of Josephson vortex lattice in layered superconductors

Magnetic field applied along the layer direction of layered superconductors generates the Josephson vortex lattice. We studied response of this state to the high-frequency c-axis electric field. Numerically solving equations for the oscillating phases, we computed the frequency dependences of the loss function, $\mathrm{Im}[1/\epsilon(\omega)]$, at different magnetic fields, including regions of both dilute and dense Josephson vortex lattices. The main feature of the response is the Josephson-plasma-resonance peak. In the dilute-lattice regime this peak is displaced to slightly lower frequency. An interesting feature of the dilute regime is the appearance of satellites at the higher-frequency part, which are caused by excitation the plasma modes with the wave vectors set by the lattice structure. In the dense-lattice limit the plasma peak moves to higher frequency and its intensity rapidly decreases, in agreement with analytical theory. An additional broad peak exists at low frequencies, and can be described by phenomenological theory of vortex oscillations.   

Universality in the Self Organized Critical behavior of a cellular model of superconducting vortex dynamics

We study the universality and robustness of variants of the simple model of superconducting vortex dynamics first introduced by Bassler and Paczuski in Phys.\ Rev.\ Lett.\ {\bf 81}, 3761 (1998). The model is a coarse-grained model that captures the essential features of the plastic vortex motion. It accounts for the repulsive interaction between vortices, the pining of vortices at quenched disordered locations in the material, and the over-damped dynamics of the vortices that leads to tearing of the flux line lattice. We report the results of extensive simulations of the critical ``Bean state" dynamics of the model. We find a phase diagram containing four distinct phases of dynamical behavior, including two phases with distinct Self Organized Critical (SOC) behavior. Exponents describing the avalanche scaling behavior in the two SOC phases are determined using finite-size scaling. The exponents are found to be robust within each phase and for different variants of the model. The difference of the scaling behavior in the two phases is also observed in the morphology of the avalanches.   

Molecular Dynamics simulations of the vortex matter two-stage melting transition in Bi$_2$Sr$_2$CaCu$_2$O$_8$ in the presence of straight and of tilted columnar defects

In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi$_2$Sr$_2$CaCu$_2$O$_8$ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalyne vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for a $45^0$ tilt of the CDs show that the location of the melting transition is not affected by the tilt when the ratio of flux lines to CDs remains constant.   

Disparities in the vortex state electrodynamics of high Tc cuprates

We report new far infrared measurements of underdoped YBCO in magnetic field and situate these new data within earlier work on related compounds. We show that the cuprate superconductors, including YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO), and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ (BSCCO), have revealed strikingly different vortex state electrodynamic responses between the various families. For example, in the Josephson vortex regime a strongly field dependent transverse resonance is observed in the interplane conductivity of YBCO, whereas no such feature is found in LSCO. Microwave magnetoabsorption spectra of BSCCO exhibit two resonances which are separated by a temperature gap, again at variance with the other systems. We compare and contrast these findings with several models of the electrodynamics in the vortex state and offer possible explanations for the observed discrepancies.   

Magnetic measurement of RF-induced flux lattice annealing (RIFLA) in the electron-doped superconductor Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-y}$.

A strained flux lattice (FL) in a superconductor (SC) can be annealed to a lower free energy by the RF-field used to generate an NMR spin-echo signal [W.G. Clark et al., J. Phys. IV Proceedings \textbf{9}, Pr10-49-52 (1999)]. Here, we report the change in the rf magnetic susceptibility ($\chi )$ in the SC phase of a single crystal of Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-y}$ with a strained FL by successive RIFLA pulses. The distorted FL is prepared by rotating the sample through a small angle in a magnetic field well below the SC transition temperature, leaving the FL pinned in a non-equilibrium configuration. RIFLA pulses then reduce $\chi $, which is measured by the change in the inductance of a coil surrounding the sample using an NMR probe and spectrometer. The interpretation is that shaking the FL by the RF pulses progressively anneals it to a lower free energy configuration, which has a smaller $\chi $. These measurements provide a very sensitive measure of the RIFLA effect. Work at UCLA was supported by NSF Grants DMR-0334869 (WGC) and DMR-0520552 (SEB).   

Puzzling magnetic behavior of non-centrosymmetric superconductor Re$_{3}$W

We have studied magnetic properties of non-centrosymmetric superconductor Re$_{3}$W. Unlike ordinary BCS superconductors, annealed samples of Re$_{3}$W exhibit linear Abrikosov-like dependence of the equilibrium (M$_{eq})$ and non-equilibrium (M) magnetization on magnetic field H in an anomalously large range H$\approx $(0.1-1)H$_{c2}$. This behavior is drastically different for the quenched (``as prepared'') samples of Re$_{3}$W. Equilibrium magnetization was obtained by ``shaking'' the flux line lattice with an alternating transverse field. M$_{eq}$(H) curves show change in slope in about the same region of magnetic fields where the slopes of corresponding critical currents J$_{c}$(H) also change. In our talk, we discuss probable causes of these effects. ORNL is managed by UT-Battelle, LLC for USDOE under contract DE-AC05-00OR22725.   

Ground state of interlayer Josephson vortex systems and the shear modulus

Ground state of interlayer Josephson vortex systems is investigated on the basis of the full Lawrence-Doniach model. We find: (1) For low fields, field dependence of $c_{66}$ approximately coincides with the elastic theory, and jumps in $c_{66}$ correspond to the structural phase transitions between various rotated-lattice configurations. (2) For intermediate fields, the ground state is characterized by continuously-varying shearing angle of vortex lattices. In this region $c_{66}$ becomes smaller than those in the elastic theory, and vanishes at the shear instability field. This critical field is increased by inhomogeneity of the magnetic field. (3) For high fields, $c_{66}$ converges to a constant value, which is quite different from the exponentially-decaying $c_{66}$ in the London theory. This saturation of $c_{66}$ can be interpreted as the effect of ``effective core size" within the elastic theory, and is not affected by inhomogeneity of the superconducting amplitude for material parameters of cuprate high-$T_{\rm c}$ superconductors.   

Thermal study of vortex states in mesoscopic superconducting disks

We present low temperature highly sensitive heat capacity $C$ measurements [1,2] of aluminum disks with diameters close to $\xi(T)$, the superconducting coherence length. $C(T)$ scans under fixed perpendicular magnetic fields $H$ reveal a quasiperiodic modulation of the height $\Delta C$ of the $C$ jump at the superconducting to normal phase transition. This behavior is due to transitions between several arrangements of vortices in the disks. Indeed giant vortex states or multivortex states can be observed, with a vorticity (an integer equal to the number of vortices threading a single disk) depending on $H$, $T$, and on the size of the disks. Heat capacity measurements enable to study phase transitions between such states, without contacting or biasing them. Thus phase boudaries in the $H-T$ plane can be drawn in all the superconducting region. \newline \newline [1] O. Bourgeois, F. Ong, S.E. Skipetrov, and J. Chaussy, \textit{Phys. Rev. Lett.} {\bf{94}}, 057007 (2005) \newline [2] F.R. Ong, O. Bourgeois, S.E. Skipetrov, and J. Chaussy, \textit{Phys. Rev. B} {\bf{74}}, 140503(R) (2006)   

Vortex Lattice Structural Transitions: A generalized (thermal fluctuations and quench disorder) Ginzburg-Landau Approach

Base on Guzburg-Landau model, we study the rhombic-to-square transition for tetragonal material in the magnetic fields along c axis with the account of thermal fluctuation and disorder influence. The nonperturbative method are used to approach the melthing line of vortex lattice.The result will compare with the recent neutron scattering data and second peak effect on high $T_{c} $ SC and Low $T_{c}$ SC.   

Deconfinement of Vortices with Continuously Variable Fractions of the Unit Flux Quanta in Two-Gap Superconductors

We propose a new stage of confiment-decofinment transition, which can be observed in laboratory. In two-gap superconductors, two kinds of vortex exist by the presence of two different $U(1)$ phases. Each of them carries a continuously variable fraction of the unit flux quanta $\Phi_0=h c / 2 e$. The confined state of these two is a usual vortex and stable in the low temperature region of the system under a certain magnetic field above $H_{c1}$. We see an analogy to quarks in a charged pion. An entropy gain causes two fractional vortices to be deconfined above a certain temperature. We estimate the condition of the deconfinement by using parameters for a typical two-gap superconductor MgB$_2$.