Journal of Superconductivity and Novel Magnetism, Vol. 19, Nos. 3−5, July 2006 ( C  2006) DOI: 10.1007/s10948-006-0177-4 Hierarchical Nature of the Vortex Matter in Type II Superconductors due to Competition Between Interactions, Thermal Fluctuations and Disorder D. Li, 1 B. Rosenstein, 2,3 and V. Vinokur 4 Published online: 9 December 2006 We describe quantitatively the combined effects of both the thermal fluctuations and of the quenched disorder via the replica trick applied to the Ginzburg–Landau (GL) theory. We show that the vortex state can appear in either of the three disordered phases: (i) unpinned vortex liquid, (ii) amorphous vortex glass (pinned), and (iii) the crystalline (pinned but not containing topological defects) Bragg glass. The formation of the vortex glass is associated with the continuous replica symmetry breaking (RSB) reflecting the hierarchial structure of the potential barriers in a vortex glass state. An earlier analysis in the framework of London approximation have established that activation barriers controlling vortex dynamics obey the extreme value statistics within roughly the same domain of the phase diagram. We show that the disordered GL model in which only the coefficient at the quadratic term |ψ| 2 is random, first considered by Dorsey et al., exhibits, in the gaussian approximation, an additional non- hierarchical state possessing certain glassy properties like nonzero Edwards–Anderson order parameter. We associate this state with the “marginal glass phase” predicted in the earlier work of one of the authors; the marginal glass state being characterized by the marginally glassy dynamics. We show further that when the random component of the coefficient of the quartic term |ψ| 4 in GL free energy is taken into account, RSB effects appear. Application of the obtained results to description of various disorder-generated phenomena in vortex matter are briefly considered. The location of the glass transition line is determined and compared to experiments. This line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. The phase diagram is separated by these two lines into the four phases described above. 1. INTRODUCTION Any superconductor contains inhomogeneities of either natural or artificial origin which affect both its thermodynamic and dynamic properties. The effect of inhomogeneities in the type II supercon- ductors is described most often in terms of pinning 1 School of Physics, Peking University, Beijing 100871, China. 2 Electrophysics Department, National Chiao Tung University, Hsinchu 30050, Taiwan, ROC. 3 Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel. 4 Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA. of the vortex lines. These effects become especially interesting in high-temperature superconductors where the interplay between disorder and thermal fluctuations gives rise to a wealth of thermodynamic and dynamic phases. While in perfectly clean su- perconductors, vortex system can be found in either crystalline or vortex liquid state [1], disorder can drive vortex system into a glass. Although naively one can distinguish three generic vortex phases asso- ciated with the dominance of one of the three basic energies (elastic energy, pinning energy, and the energy of thermal fluctuations), the actual vortex phase diagram reveals much more of complex diversity (see [2,3] for a review, and also [4,5]). In 369 1557-1939/06/0700-0369/0 C  2006 Springer Science+Business Media, Inc.