Continuum field theory of string-like objects. Dislocations and superconducting vortices

Abstract

Dense distributions of string-like objects in material media are considered in terms of continuum field theory. The strings are assumed to carry a quantized abelian topological charge, such as the Burgers vector of dislocations in solids or magnetic flux of supercurrent vortices in type-II supercondoctors. Within this common framework the facts known from dislocation theory can be extended, in appropriately modified forms, to other physical contexts. In particular, the concept of incompatible distortions is transplanted into the theory of type-II superconductivity. The compatibility law for type-II superconductors is derived in terms of differential forms. As a result, one obtains an appropriate generalization of the classic Londons' equation.