Boundary modes of a charge density wave state in a topological material

Charge density waves appear in numerous condensed matter platforms ranging from high-temperature superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study of boundary states that can uniquely stem from the charge order. Here we directly visualize the bulk and boundary phenomenology of the charge density wave in a topological material, Ta₂Se₈I, using scanning tunnelling microscopy. At a monolayer step edge, we demonstrate the presence of an in-gap boundary mode persisting up to the charge ordering temperature with modulations along the edge that match the charge density wave wavevector along the edge. Furthermore, these results manifesting the presence of an edge state challenge the existing axion insulator interpretation of the charge-ordered phase in this compound.