Floquet higher order topological insulators through time-varying topolectric circuits

Higher order topological insulators (HOTIs) are n-dimensional materials that exhibit gapless protected states having dimensionality n-2 or lower. While practical realizations are limited to three spatial dimensions, Floquet systems having periodic driving can be used to introduce synthetic dimensions that enable the exploration of higher dimensional physics. In this work we describe a general approach to producing Floquet HOTIs using time-varying topolectric circuits. Our approach enables dynamically reconfigurable time protocols and on-demand TI phases within the same material. As an explicit example, we discuss the realization of a Floquet quadrupole HOTI with anomalous dynamical polarization. This 2D material exhibits 0D corner modes analogous to a non-driven quadrupole HOTI, and additionally exhibits a new set of topologically protected states originating from interactions in the synthetic dimension.