Simulating Higher-Order Topological Insulators in Density Wave Insulators

Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this talk, we present a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic density wave modulations. We construct 2D models with modulations that can be promoted to higher-order topological phases with U(1) and SU(2) gauge fields in 3D. Corner modes in our 2D models can be pumped by adiabatic sliding of the phase of the modulation, yielding hinge modes in the promoted models. We also examine a 3D Weyl semimetal (WSM) gapped by charge-density wave (CDW) order, possessing quantum anomalous Hall (QAH) surface states. We show that this 3D system is equivalent to a 4D nodal line system gapped by a U(1) gauge field with a nonzero second Chern number. We explain the recently identified interpolation between QAH and obstructed QAH phases of a 3D WSM gapped by CDWs using the corresponding 4D theory. Our results can extend the search for (higher-order) topological states in higher dimensions to density wave systems.