According to Prof Egor Babaev and others, it seems possible to have knotted solitons in certain superconductors. He has had numerous articles published in Physical Review and Nature. The most understandable one I've found is Hidden symmetry and knot solitons in a charged two-condensate Bose system . If a superconductor has two charge carriers, then electromagnetic interactions between the carriers stabilize the knots. A twisted vortex loop of a preferred size is metastable, as either an increase or decrease in size costs energy. The researchers hope that such solitons can be observed in Type 1.5 superconductors such as magnesium diboride, or in metallic hydrogen in which both the electrons and protons become superconductive. In Type 1.5 superconductors "only one band is superconducting while superfluid density is induced in another band via an interband proximity effect." In Type 1.5 superconductors the vortices attract at long range and repel at short range, hence they tend to form groups. It would seem that such grouped vortices could form braided knots, but I haven't seen any papers about this. An even more exotic type of soliton might be found in three band superconductors called a phase soliton which is not a vortex. http://iopscience.iop.org/1367-2630/14/6/063021/article Finally there is the possibility of a knot soliton made of light. http://physicsworld.com/cws/article/news/2013/oct/16/physicists-tie-light-into-knots A few years ago I saw the abstract of a paper in which it was claimed one of these had been created via a hologram, but I can't be bothered to dig it up.