Vortices in High Temperature Superconductors: a Phenomenological Approach

摘要

It is well known that magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices. Many properties of the vortices are well described by phenomenological Ginzburg-Landau theory. High temperature superconductor also belongs to the class of type-II superconductors. These vortices (also known as flux-line lattice) form a triangular lattice in the low-temperature type-II superconductors. But experiments have shown that in the high-temperature superconductors, these vortices form an oblique lattice. This is attributed to various characteristics of high temperature superconductors, namely, pairing state symmetries, anisotropy, planar nature of the superconducting plane, symmetry of the unit cell modulated by the presence of CuO-chain, thermal fluctuations etc. The experimentally observed softening and subsequent melting of the vortex lattice is attributed to the small shear modulus of the vortex lattice. In this review we address these problems associated with the vortex lattice of high temperature superconductors. One of the central issues associated with the high-T_c superconductors is the pairing state symmetry of the order parameter components. Based on the experimental evidences a consensus could now be reached that these materials possesses mixed symmetry state scenario where the dominant order parameter is of d-wave symmetry along with which there is an admixture of a small s-wave order parameter component. We have studied the properties of the high-T_c superconductors involving mixed symmetry state of the order parameters in the framework of a two-order parameter Ginzburg-Landau (GL) model, over the entire range of applied magnetic field (H_(c1) < H < H_(c2)) and wide range of temperature and for arbitrary GL parameter κ and vortex lattice symmetry. Using the present model the limitations of the earlier the-oretical works involving the GL theory could be overcome, wherein the studies were restricted to the upper (H_(c2)) and lower (H_(c1)) critical magnetic field regions and the problem was reduced to an effective single order parameter model by using an ansatz. The present theoretical model has been further generalized to take into account the effect of in-plane anisotropy. We calculate various properties of the high temperature superconductors including vortex core radius, penetration depth, vortex lattice symmetry, upper critical magnetic field, shear modulus of the vortex lattice etc. Furthermore, the effect of the admixture of the sub-dominant s-wave order parameter on the various properties of the high-Tc cuprates have been explored. The variations of these properties with applied magnetic field and temperature are also calculated and shown to be in very good agreement with experiments on high-T_c cuprate YBa_2Cu_3O_(7-δ) supercon-ductors [1] - [5]. We have also used the same two-order parameter Ginzburg-Landau model appropriately modified to study the properties of the two-band inter-metallic high temperature superconductor MgB_2. The results of the analytical calculations are shown to agree very well with the experimental results of MgB_2 [6].