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arXiv:cond-mat/9812342 · Europhysics Letters (EPL)

Critical properties of Bose-glass superconductors

Jack Lidmar, Mats Wallin

Published Aug 15, 1999• 59 citations
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Abstract

We study vortex lines in high-temperature superconductors with columnar defects produced by heavy-ion irradiation. We reconsider scaling theory for the Bose-glass transition with tilted magnetic fields, and propose, e.g. , a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 ± 0.3.

DOI
10.1209/epl/i1999-00415-5

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We study vortex lines in high-temperature superconductors with columnar defects produced by heavy-ion irradiation. We reconsider scaling theory for the Bose-glass transition with tilted magnetic fields, and propose, e.g. , a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 ± 0.3.
The vortex glass transition in the presence of columnar defects is studied by Monte Carlo simulations of a vortex loop model, suggested by the analogy to the T=0 superconductor-insulator transition for dirty bosons in (2+1) dimensions. From finite-size scaling analysis of the I-V characteristic we find two dynamical exponents describing the nonequilibrium behavior. We obtain ${\mathit{z}}_{\mathrm{\ensuremath{\perp}}}$=6\ifmmode\pm\else\textpm\fi{}0.5 and ${\mathit{z}}_{\mathrm{\ensuremath{\parallel}}}$=4\ifmmode\pm\else\textpm\fi{}0.5 when the current is applied perpendicular and parallel to the columnar defects, respectively.
The phase transition in a model for vortex lines in high temperature superconductors with columnar defects, i.e., linearly correlated quenched random disorder, is studied with finite size scaling and Monte Carlo simulations. Previous studies of critical properties have mainly focused on the limit of strongly screened vortex line interactions. Here the opposite limit of weak screening is considered. The simulation results provide evidence for a distinct universality class, with values of the critical exponents that differ from the case of strong screening of the vortex interaction. In particular, scaling is anisotropic and characterized by a nontrivial value of the anisotropy exponent $\ensuremath{\zeta}={\ensuremath{\nu}}_{\ensuremath{\Vert}}/{\ensuremath{\nu}}_{\ensuremath{\perp}}.$ The exponents we find, $\ensuremath{\zeta}=1.25\ifmmode\pm\else\textpm\fi{}0.1,{\ensuremath{\nu}}_{\ensuremath{\perp}}=1.0\ifmmode\pm\else\textpm\fi{}0.1,z=1.95\ifmmode\pm\else\textpm\fi{}0.1,$ are similar to certain experimental results for YBa2Cu3O7.{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}.YBa2​Cu3​O7​.
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.
We investigate the critical behavior of the gauge-glass model for the vortex-glass transition in three-dimensional superconductors, including screening of the interaction between vortices. A Monte Carlo study of the linear resistivity and a scaling analysis of current-voltage characteristics indicates that screening destroys the finite-temperature transition found earlier when screening was neglected. The correlation-length exponent at the resulting zero-temperature transition is found to be $\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01$.
Phase transitions in a number of models related to hightemperature superconductors are investigated, using scalingmethods and Monte Carlo simulations. This thesis considers twomain topics. The first topic is phase transitions, phase diagrams, andvortex motion in high temperature superconductors at finitetemperature, subject to magnetic fields and disorder. We studya vortex glass model at finite temperature, with stronguncorrelated vortex pinning and a magnetic field. We find thatthe vortex glass exists at finite temperature and calculate thecritical exponents of the transition. We also investigate hightemperature superconductors with columnar disorder in zero andapplied magnetic fields. Some of these studies are alsorelevant for the superfluid to Mott insulator transition ofbosons in two dimensions. We find that the unscreened Boseglass transition belongs to a new universality class. Wecalculate the critical exponents of the superconductingtransition with columnar defects in zero applied magneticfield. The transverse Meissner transition is studied, and wefind an exotic universality class with a correlation volumethat is infinitely anisotropic in all directions. The second topic is confinement-deconfinement transitions incompact Abelian Higgs models. We develop a new order parameter,related to a large Wilson loop for fractionalized charges, anduse it to study the concept of topological order. Thesetransitions may be relevant for strongly correlated electronsin two dimensions.
We study the phase diagram of flux lines in superconductors with columnar pins. Based on numerical exact diagonalization simulations on small clusters, we get two phases of vortices: A low-temperature pinned glass with diverging tilt modulus and a high-temperature delocalized entangled vortex liquid. For random potential disorder we find a new phase transition temperature TBG{T}_{\mathrm{BG}}TBG​ from a pinned Bose glass to an entangled liquid that reduces with increasing vortex density. This occurs primarily because vortices screen the disorder potential and generate an effective weaker random potential with increasing vortex density. For a fixed fraction of randomly placed attractive columnar pins, we find a Mott-insulating phase when the vortex density exactly matches the density of pins at the matching field ${B=B}_{\ensuremath{\varphi}}.$ We also find a transition from a strongly pinned Bose glass for $B<{B}_{\ensuremath{\varphi}}$ to a weakly pinned Bose glass for $B>{B}_{\ensuremath{\varphi}}$ as the vortex density is varied.