# Vorticies in Anisotropic Multi-component Ginzburg-Landau theory and the Dichotomy of Superconductor Type

**Date**: Friday 17 November 2017, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Applied Mathematics seminars, Integrable systems seminars, Seminar series**Cost**: Free

#### Tom Winyard, University of Leeds. Part of the integrable systems seminars series.

Vorticies are topological solitons that appear in Ginzburg-Landau theory, an effective static theory for superconductors that takes the form of complex scalar fields coupled to a U(1) gauge field. Introducing crystal anisotropy has been demonstrated to be rather trivial in the case with a single complex field, leading to rescalings of the parameters, however, I will show that when considered with multiple interacting fields, the anisotropy leads to a coupling between the phase difference and the gauge field of the model.

The additional modes this leads to will cause the generated magnetic field to invert and thus the inter-vortex interactions to become non trivial, leading to markedly different solutions and bound states than have been seen before. Moving away from the standard boxes of superconductor types, that multiband models are usually inelegantly forced into in physics, will allow us to point towards solutions for some long standing questions in the subject, such as striping and the divergence of correlation lengths in the small Josephson limit.

Tea and coffee will be available at 3.40pm on level 9 of the School of Mathematics.

**Tom ****Winyard**, *University of Leeds*