Topological Defects in Anisotropic Multicomponent Superconductors

Aims and objectives

To perform a careful mathematical analysis of the effects of spatial anisotropy on topological defects in multicomponent Ginzburg-Landau models, focussing on domain walls. In particular:

1) In specific anisotropic two band GL models with broken time reversal symmetry, exhibiting more than one gauge equivalence class of vacua, to numerically construct domain wall solutions (energy minimizers interpolating between inequivalent vacua) at arbitrary spatial orientation.

2) Extract the energy per unit length of such domain walls as a function of their orientation.

3) Numerically construct those closed domain walls enclosing a fixed area whose total energy in minimal.

4) In bounded domains of simple shape (e.g. rectangles), construct domain walls starting and ending on the boundary with minimal total energy.

The overall aim is to understand as thoroughly as possible the geometry and energetics of domain walls in this class of models.

This will involve a mixture of analytic approximation and numerical simulation. Several standard techniques in the theory of topological solitons (gradient flow, linearization, point source analysis) will be generalized (if possible) to deal with the addition of spatial anisotropy. The variational problem in part (3) will be interpreted as an isoperimetric problem in Finsler geometry, and techniques and concepts from differential geometry will be applied in its solution.


Potential applications and benefits

This is fundamental research with no immediate application.