Topological Defect

In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the boundary conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are classified by their homotopy class. Topological defects are not only stable against small perturbations, but cannot decay or be undone or be de-tangled, precisely because there is no continuous transformation that will map them (homotopically) to a uniform or "trivial" solution.

Examples include the soliton or solitary wave which occurs in many exactly solvable models, the screw dislocations in crystalline materials, the skyrmion and the Wess–Zumino–Witten model in quantum field theory.

Topological defects are believed to drive phase transitions in condensed matter physics. Notable examples of topological defects are observed in Lambda transition universality class systems including: screw/edge-dislocations in liquid crystals, magnetic flux tubes in superconductors, vortices in superfluids.