Superconductors with Topological Order and their Realization in Josephson Junction Arrays

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

Gauge Topological Nature of the Superconductor-Insulator Transition

It has long been believed that, at absolute zero, electrons can form only one quantum coherent state, a superconductor. Yet, several two dimensional superconducting systems were found to harbor the superinsulating state with infinite resistance, a mirror image of superconductivity, and a metallic state often referred to as Bose metal, characterized by finite longitudinal and vanishing Hall resistances. The nature of these novel and mysterious quantum coherent states is the subject of intense study.Here, we propose a topological gauge description of the superconductor-insulator transition (SIT) that enables us to identify the underlying mechanism of superinsulation as Polyakov's linear confinement of Cooper pairs via instantons. We find a criterion defining conditions for either a direct SIT or for the SIT via the intermediate Bose metal and demonstrate that this Bose metal phase is a Mott topological insulator in which the Cooper pair-vortex liquid is frozen by Aharonov-Bohm interactions