Topological properties of matter
Title: Topological properties of matter
SNIC Project: SNIC 2013/1-250
Project Type: SNAC Medium
Principal Investigator: Edwin Langmann <>
Affiliation: Kungliga Tekniska högskolan
Duration: 2013-10-01 – 2014-10-01
Classification: 10304


Topological properties of matter are familiar in many contexts from the instantons of particle physics to the vortices of superconductors and defects in liquid crystals. Lately, there has been an important addition to this zoo of phenomena, namely skyrmions in condensed matter systems. Although initially thought of in a particle physics context, skyrmions have found a home in experimental condensed matter systems. However, most of these systems have only ever been investigated in two dimensions. The aim of the proposed research is to determine what kinds of three dimensional topological solitons exist in condensed matter systems. The systems exhibiting skyrmions in two dimensions, like MnSi [Science 323, 915 (2009)] and chiral p-wave superconductors [Phys. Rev. B 86, 060514(R) (2012)] will be of particular interest, as both are prime candidates for knot solitons; another likely candidates are Bose-Einstein condensates [Phys. Rev. Lett. 100, 180403 (2008)] and ferromagnets [Phys. Rev. B 76, 184439 (2007)]. All these systems are not just readily accessible in a laboratory, but also mathematically very interesting as they reveal a deep connection between the Skyrme family of models and other models, such as the Ginzburg-Landau model.