Higher-Order Topology and Defect States in the Charge-Density-Wave Phase of (TaSe₄)₂I

Recent theoretical and experimental investigations have identified the quasi-1D compound (TaSe₄)₂I as a Weyl semimetal phase that becomes gapped by an incommensurate charge-density wave (CDW) just below room temperature. Although dynamical excitations of the CDW phase angle φ have been shown to exhibit incipient experimental signatures of (valley-) axion electrodynamics, the bulk topology of the insulating CDW phase at static φ remains uncertain. We present a physically motivated, lattice-commensurate coupled-wire model based on Topological Quantum Chemistry and crystalline symmetry that approximates the CDW phase of (TaSe₄)₂I. Our model hosts several higher-order and weak topological phases, which depend on the values of several symmetry-allowed Dirac mass terms corresponding to distinct CDWs. We also present evidence for helical modes bound to line defects, including disclinations, boundary hinges, and Dirac mass(phase angle) vortices, in the CDW state.