Hierarchical Nature of the Vortex Matter in Type II Superconductors due to Competition Between Interactions, Thermal Fluctuations and Disorder

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.