Berry Curvature Renormalization

A scaling scheme for the Berry curvature in topological insulators and superconductors is proposed, from which the topological phase transition can be identified from the flow of the energy scales (hopping, chemical potential, etc.) that control the topology under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the energy scales in the form of differential equations. A length scale defined from the Berry curvature is suggested to characterize the scale invariance at the critical point.