Emergent Edge Modes in Shifted Quasi-One-Dimensional Charge Density Waves

We propose and study a two-dimensional (2D) phase of shifted charge density waves (CDW), which is constructed from an array of weakly coupled 1D CDW wires whose phases shift from one wire to the next. We show that the fully gapped bulk CDW has topological properties, characterized by a nonzero Chern number, that imply edge modes within the bulk gap. Remarkably, these edge modes exhibit spectral pseudo-flow as a function of \emph{position} along the edge, and are thus dual to the chiral edge modes of Chern insulators with their spectral flow in \emph{momentum} space. Furthermore, we show that the CDW edge modes are stable against inter-wire coupling. Our predictions can be tested experimentally in quasi-1D CDW compounds such as Ta${}_2$Se${}_8$I.