Topological Defects in Anisotropic Multicomponent Superconductors
Lead Research Organisation:
University of Leeds
Department Name: Pure Mathematics
Abstract
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.
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.
Organisations
Publications
Benfenati A
(2020)
Magnetic signatures of domain walls in s + i s and s + i d superconductors: Observability and what that can tell us about the superconducting order parameter
in Physical Review B
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509681/1 | 30/09/2016 | 29/09/2021 | |||
1950947 | Studentship | EP/N509681/1 | 31/08/2017 | 30/05/2021 | Alex Wormald |