On minimizers of the 2D Ginzburg-Landau energy with tangential anchoring

TL;DR

This paper investigates the behavior of minimizers of the 2D Ginzburg-Landau energy under different boundary conditions, revealing the formation of boundary defects or vortices depending on the anchoring strength.

Contribution

It provides a rigorous analysis of boundary and interior defect formation in the singular limit of the 2D Ginzburg-Landau model with tangential boundary conditions, inspired by liquid crystal experiments.

Findings

Boundary defects appear under weak anchoring.

Both boundary and interior vortices occur under strong anchoring.

Vortex formation depends on the boundary condition strength.

Abstract

We analyze Ginzburg--Landau minimization problems in two dimensions with either a strong or weak" tangential boundary condition. These problems are motivated by experiments in liquid crystal with boundary defects. In the singular limit when the correlation length tends to zero, we show that boundary defects will be observed for weak anchoring, while both boundary and interior vortices are possible for strong anchoring in the first order limit.