From topological insulators to superconductors and confinement

Topological matter in three dimensions (3D) is characterized by the presence of a topological BF term in its long-distance effective action. We show that, in 3D, there is another marginal term that must be added to the action in order to fully determine the physical content of the model. The quantum phase structure is governed by three parameters that drive the condensation of topological defects: the BF coupling, the electric permittivity and the magnetic permeability of the material. For intermediate levels of electric permittivity and magnetic permeability, the material is a topological insulator. We predict, however, new states of matter when these parameters cross critical values: a topological superconductor when the electric permittivity is increased and the magnetic permeability is lowered and a charge confinement phase in the opposite case of low electric permittivity and high magnetic permeability. Synthetic topological matter may be fabricated as 3D arrays of Josephson junctions.