Simulating Higher-Order Topological Insulators in Density Wave Insulators

TL;DR

This paper develops a method to simulate higher-order topological insulators using density wave modulations, revealing new topological phases and edge states in higher dimensions.

Contribution

It introduces a general procedure to compute gauge fields in higher dimensions from low-dimensional density wave systems, enabling the simulation of higher-order topological phases.

Findings

Constructed 2D models with modulations promoting to 3D higher-order topological phases.

Demonstrated corner modes can be pumped to hinge modes via phase sliding.

Connected 3D Weyl semimetals gapped by CDWs to 4D topological systems with nonzero second Chern number.

Abstract

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 work, we develop a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic (charge- and spin-) density wave modulations. We construct two-dimensional (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 inversion-symmetry protected phases of the 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.