Conformal phase transition in topological superconductors

A conformal phase transition (CPT) is a phase transition defining a critical point with a non-power law diverging correlation length, but which nevertheless exhibits a universal jump in some generalized stiffness of the system. A well-known example is the Berezinskii-Kosterlitz-Thouless (BKT) phase transition taking place in two-dimensional superfluids and superconductors when they transition from the low-tenperature phase to the normal state, and in the melting transition of two-dimensional crystals. In this talk we will introduce a more subtle type of CPT, one that is driven by a topological term in the effective action in 2+1dimensions. The main motivation comes from the modification of Maxwell electrodynamics in topological insulators and superconductors. Quite generally, the surface of a topological insulator features an electromagnetic response characterized by a Chern-Simons term in the Lagrangian. We will show in this context that a topological Abelian Higgs model exhibits quantum criticality with BKT scaling when the Hall conductivity lies in a well defined interval where conformality is lost. We explore the physical consequances of this novel quantum critical phenomenon in topological materials.