Chiral Topological Insulators, Superconductors and other competing orders in three dimensions

Understand

We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion.

• Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological superconductor.
• While the former requires a special "chiral" symmetry, the latter is stable as long as time reversal and SU(2) spin rotation symmetry are present.
• These phases are characterized by stable surface Dirac fermion modes, and by an integer topological invariant in the bulk.