A new vortex lattice solution for unconventional superconductors

The aim of this project is the development of a new vortex lattice solution of the quasi-classical equations for superconductors with anisotropic gap parameter. This anisotropy may be of an unconventional type, i.e. at least one of the symmetries of the crystal lattice may be broken, in addition to the broken gauge symmetry. The numerical procedure may then be used to study the following properties of strongly anisotropic superconductors, in particular high-Tc superconductors: (1) Stability of the vortex lattice, (2) Spatial variation of order parameter and local magnetic field, (3) Local density of states, (4) Thermodynamic properties (magnetization curvers). The best self-consistent vortex lattice solution used today to study superconductors with anisotropic gap has been developed by the author of this proposal in collaboration with scientists from Bayreuth more than ten years ago. Despite its success the Linz-Bayreuth method is still unable to study points (1), (2) above for strongly anisotropic materials. This is even true, if supercomputing equipment is used. On top of that, the present development in the field of high-Tc super-conductivity points into a direction of increasing complexity. Most likely, the final set of basic equations for inhomogeneous superconducting states will be even more complex than the present framework of a "weak coupling", anisotropic, space-dependent version of BCS theory, which is being used by the majority of workers in this field. Therefore, the aim of this project is the development of a new and more efficient method of solving the quasi- classical equations for a vortex lattice.