Unscreened universality class for superconductors with columnar disorder

Abstract

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 new universality class, with new 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 ζ = ν /ν ⊥ . The exponents we find, ζ = 1.25 ± 0.1, ν ⊥ = 1.0 ± 0.1, z = 1.95 ± 0.1, are similar to certain experimental results for YBCO. Columnar defects have proven very effective at pinning vortex lines in high temperature superconductors (SC), resulting in significant increases in the critical magnetic fields and currents [1]. The columnar defects are often produced as damage tracks by irradiating the sample with high-energy heavy ions. Such correlated disorder strongly affects the phase transition from the SC to normal state and there is an ongoing theoretical and experimental effort to investigate the phase diagram and properties of the transition [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Below a critical temperature the vortices freeze into a glassy SC state, known as a Bose glass, which replaces the Abrikosov vortex lattice of the clean system. Upon heating the system undergoes a continuous phase transition to a resistive vortex liquid state. The transition is characterized by critical exponents, that have been measured in a number of experiments. The critical exponents are universal, i.e., they are common for all systems in the same universality class, and depend only on general features like the range of the interaction and distribution of the disorder. In spite of the fact that the screening length λ in high temperature SC is quite large, most theoretical work on columnar defects has concentrated on strongly screened systems with short range interactions [3,4,18]. In general, long range interactions often change the universality class of a transition, compared to short range interactions. It is therefore natural to study the universality class with long range interactions. In this paper we present a systematic study of the SC transition in systems with columnar disorder, an applied magnetic field, and weak screening, and compare the results with experiments.The superconducting phase transition with columnar disorder is also interesting from the perspective of quantum phase transitions in systems with disorder [2,3,18,19,20]. In fact, statistical mechanics of vortex lines in three-dimensions is closely analogous to world-lines of quantum bosons in (2+1) dimensions, where the vortex phase transition corresponds to the zero-temperature boson localization by substrate disorder. The quantum bosons have static disorder in imaginary time, co...

Vortex dynamics in heavy-ion-irradiated single crystals ofBi2Sr2CaCu2O8+δandAmmor1, Hong2, Pignon3 et al. 2004Phys. Rev. B

“…25 Those exponents are also consistent with those reported for heavy-ion-irradiated Tl 2 Ba 2 CaCu 2 O 8 thin films. 31 In the BSCCO system, Miu et al 32 reported an average of the combined critical exponents n = Ќ ͑z −2͒ of 9 for BSCCO thin films irradiated at B = 1 T, while Seow et al 7 obtained n as of 8.5 from the c-axis resistivity measurements on BSCCO single crystals irradiated at B = 2 T. These two values are about 3 times larger than our results.…”

“…This volume is anisotropic in the presence of CD's and the correlation lengths ʈ parallel to and Ќ perpendicular to the columns obeying the relation ʈ ϰ Ќ ␣ with ␣ = 2 in the case of screened vortex interactions (␣ = 1 for isotropic pinning such as point disorder as well as for an incompressible Bose-glass with long-range interactions). 25 The current density J which is perpendicular to the CD's and the magnetic field H aligned with the correlated defects can be derived from the following scaling ansatz:…”

Effect of columnar disorder on the superconducting transition of a type-II superconductor in zero applied magnetic field

“…Columnar defects 2, 3,4 have received considerable attention, as they are particularly effective in pinning vortex lines and reducing flux flow resistance. In contrast, in this paper we will focus on the effect of columnar defects on the superconducting phase transition in zero applied magnetic field.…”

“…The first is the limit of an "unscreened" superconductor 4,13 in which magnetic field fluctuations are frozen out, corresponding to the approximation of an infinite bare magnetic penetration length, λ 0 → ∞. Here, vortex line segments have long ranged Coulombic-like interactions.…”

Generalized Anisotropic Scaling Theory and the Transverse Meissner Transition

“…We use the superconductor language and call the line degrees of freedom a vorticity. This model is relevant for disordered high temperature superconductors far from the upper critical field H c2 [18,19]. The partition function and the Hamiltonian of the short range interaction, lattice version of the model described in Refs.…”