We will describe a new superconductivity mechanism, proposed by the authors
in [1], which is based on a topologically ordered ground state rather than on
the usual Landau mechanism of spontaneous symmetry breaking. Contrary to anyon
superconductivity it works in any dimension and it preserves P-and
T-invariance. In particular we will discuss the low-energy effective field
theory, what would be the Landau-Ginzburg formulation for conventional
superconductors.Comment: invited review, to appear in "Superconductivity Research Advances",
Nova Publishers, 32 page
