Session II: Phase Diagram

II-1: Bulk and surface melting in layered superconductors

Gianni Blatter
ETH Zürich, Switzerland

Vortex matter melts like ice and ice is slippery; these features have attracted interest of physicists over centuries. We combine classical Density Functional Theory, the anisotropic interaction within a pancake vortex matter system, and the general Landau theory of surface melting, to give an `ab initio' description of bulk and surface melting in layered superconductors. We obtain a consistent melting scenarium satisfying the Clausius Clapeyron relation and explain the anisotropic hysteresis observed in experiments on vortex melting in BiSCCO.

II-2: Effect of planar defects on the stability of the Bragg glass phase of type-II superconductors

Thomas Nattermann
Institute for theoretical physics, University of Cologne (Köln), Germany

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current-voltage relation is changed to lnV(J)~-J^-1. The theory exhibits striking similarities to the physics of Luttinger liquids with impurities.

II-3: Vortex Liquid State in YBCO and Novel Vortex Behavior in 3D Meso-Crystals

Wai-K. Kwok
Materials Science Division, Argonne National Laboratory, USA

High-energy heavy ion irradiation provides a unique way to inject‘countable’ discrete line or columnar defects into vortex matter. The anisotropic pinning of induced columnar defects, the control of vortex density by applied magnetic field and the tuning of thermal energy in the laboratory environment provide us with a unique opportunity to study phase diagrams in general since all the statistical mechanics and thermodynamic parameters can be fine tuned. In the first part of the presentation I will demonstrate how such exceptional control of these parameters led to the observation of a vortex line tension transition in the liquid state of YBCO. In addition, I will report on our progress in using the vortex matter platform to investigate the transformation of a first order vortex melting transition to higher order by a monotonic increase of defect density.

In the second part of the presentation, I will present our recent study of the nature of magnetic flux lines confined in 3D mesoscopic type I superconductors in which the period of the domain structure in the intermediate state is larger than the crystal dimensions. The magnetic flux confinement leads to the observation of a giant vortex state.

This work was supported by the U.S. Department of Energy, BES, Materials Science under Contract No. DE-AC02-06CH11357 at Argonne National Laboratory.

II-4: Ground state of interlayer Josephson vortex systems:
Configurations, energy landscape and shear modulus

Yoshihiko Nonomura and Xiao Hu
Computational Materials Science Center, National Institute for Materials Science,
Tsukuba, Ibaraki 305-0047, Japan

In the present talk, we evaluate ground state of Josephson vortex systems on the basis of the Lawrence-Doniach (LD) model, which consists of the Ginzburg-Landau model in the superconducting layer and the Josephson coupling along the anisotropy axis.

For low fields, the ground state is characterized by structural phase transitions between various configurations of vortex lattices, which are approximately represented by rotated triangular lattices adjusted to the layered structure and characterized by specific shearing angles. The shear modulus c₆₆ is well described by the elastic theory, where c₆₆ is proportional to the external field.

For intermediate fields, the shearing angle of vortex lattices decreases continuously as the field increases. In this field region, c₆₆ decreases continuously together with the shearing angle, and vanishes at the field on which the vortex lattice aligns along the superconducting layer. The onset field of the aligned Josephson vortex lattice, namely the field for c₆₆=0, is much enhanced by the screening effect. Even for material parameters of cuprate high-T_c superconductors, in which the screening effect is usually considered negligible, the onset field is increased twice or more in comparison with the unscreened case.

For high fields, the dense aligned lattice including Josephson vortices in every layer remains stable. As the field increases from the onset one, c₆₆ increases first, takes a maximum value, and decreases exponentially in the conventional London model. This behavior has been interpreted that the Josephson vortex lattice becomes fragile for high fields. On the other hand, c₆₆ in the present model increases monotonically as the field increases, and converges to a constant value. Even though inhomogeneity of the superconducting amplitude is taken into account, such behavior of c₆₆ holds when the coherence length along the c axis is smaller enough than the interlayer distance, which is generally satisfied in cuprate high-T_c superconductors.

II-5: Dynamics of Josephson vortices in Cuprate

Qing-Hu Chen^1,2 and Xiao Hu^2
1Department of Physics, Zhejiang University, Hangzhou 310027, China
²CMSC, National Institute for Materials Science, Tsukuba 305-0047, Japan

We will report our numerical study on Josephson vortices (JV) driven by in-plane current in high-T_c superconductors. For high anisotropy and magnetic field, we find power-law I-V characteristics with exponent jumping from 3 to 1 when temperature decreases, indicating to a Kosterlitz-Thouless (KT) transition. In the KT phase, simulations reveal a resistivity independent of the angle between the current and the magnetic field, i.e. orientation-independent dissipation, due to the intralayer quasi long-range order and interlayer short-range order of JV. For low anisotropy and magnetic field, an orientation-dependent non-Ohmic dissipation is observed where the three-dimensional long-range order exists. The present approach provides a unified explanation to previous experimental observations in non-Ohmic regime. When the current is applied along c-axis, the JV is driven mainly along the block layers. Our preliminary results for JV dynamics in this case will also be presented.

Reference:
Q.-H. Chen and X. Hu, Phys. Rev. B 75, 064504 (2007)

II-6: Density Functional Theory for the Melting Phenomena of Interlayer Josephson Vortex Lattice

Mengbo Luo^1,2) and Xiao Hu¹⁾
1) National Institute for Materials Science, Tsukuba, Japan
2) Department of Physics, Zhejiang University, China

The freezing transitions of interlayer Josephson vortex lattice in high temperature cuprate superconductors with magnetic field B parallel to ab plane are explored by the density functional theory [1]. The stable state at given temperature and magnetic field, and thus phase transition, is obtained by numerical minimization of the free energy in terms of vortex density and liquid direct-pair correlation functions. Using DFT, we estimate quantitatively the effect of the layer pinning to the vortex configuration, which stabilizes the lattice order to higher temperatures near commensurate magnetic fields. Moreover, we find a smectic phase near the field at which vortices exist in every other layer in the ground state. The smectic phase freezes into lattice via a first-order transition and transforms into liquid via a second-order transition upon temperature sweeping. The B-T phase diagram with a meandering phase boundary is derived for the first time [2]. The results, especially the smectic phase, are in agreement with recent experimental results for YBa₂Cu₃O_7-δ by Nishizaki et al [3].

[1] X. Hu, M.-B. Luo, and Y.-Q. Ma, Phys. Rev. B 72, 174503 (2005).
[2] M.-B. Luo and X. Hu: in preparation.
[3] T. Nishizaki, Y. Takahashi, and N. Kobayashi: Int. J. Mod. Phys. in press; private communications.

II-7: Vortex Phase of Underdoped YBa₂Cu₃O_y in Parallel Magnetic Fields

Terukazu Nishizaki, Yuki Takahashi and Norio Kobayashi
Institute for Materials Research, Tohoku University, Japan

We report on transport measurements of untwinned single crystals of underdoped YBa₂Cu₃O_y in the magnetic field H parallel to the ab plane. The vortex phase diagram determined by the c-axis resistivity ρ_c(T,H) depends strongly on the oxygen content y, because the anisotropy parameter γ increases with decreasing y. In YBa₂Cu₃O_y (T_c~30K), the vortex liquid freezes into the Josephson vortex solid through two-stage processes with decreasing temperature T in the field region between 4.5 T and 9.5 T. The two phase transition lines consist of the first-order melting transition at T_m(H) and the broad transition at T_s(H). The resistivity ρ_c(T,H) in the intermediate phase [T_m(H) < T < T_s(H)] is lower than that in the vortex liquid phase above T_s(H). The origin of the anomalous feature of the phase transition lines is discussed in terms of the vortex smectic phase. The characteristic feature of the vortex phase diagram and the field region of the anomaly in this study are consistent with the recent theory of the phase diagram by Hu and Luo. We also present that the oscillatory field dependence of T_m(H) and ρ_c(H) corresponds to the commensurability between the vortex spacing and the period of the CuO₂ planes. The novel vortex phase diagram due to the layered structure in underdoped YBa₂Cu₃O_y will be discussed as a function of y.