Multipolar topological field theories: Bridging higher order topological insulators and fractons

Abstract

The concepts of multipolar insulators and multipole symmetries have hinted at tantalizing connections between the disparate fields of higher-order topological insulators and fracton phases. Here, the authors show that these connections are not superficial, but instead arise from a unified field theory description of the topological response of these systems to external fields, similar to the quantized Hall conductance of Chern insulators, and the quantized axion magnetoelectric polarizability in 3D topological insulators. These response theories are built from the recently introduced higher-rank tensor gauge potentials, and can be interpreted, in some scenarios, as the topological response to ordinary electric and magnetic field gradients.