Coupling Lattice Curvature and Electromagnetism in Topological Insulators

Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. Here, we consider a class of topological insulators in 3D with n-fold lattice rotation symmetry. These insulators realize quantized mixed geometry-charge responses, where line-like disclination defects of the lattice carry fractionally quantized electric polarization. When the surface of these insulators is gapped, disclinations of the surface carry a fractional charge that is half the minimal amount that can occur in purely 2D systems. These effects and other related phenomena, are captured by a 3D topological response term that couples the lattice curvature to the electromagnetic field strength. In this talk, we will discuss the origin and physical observables of this topological response term, and how it can be realized in real lattice systems.