Step-Edge Anomaly in Topological Metals

Bulk-boundary correspondence guarantees the presence of robust, anomalous states on the boundary of topological matter. The edges of a two-dimensional Chern insulator harbor one-dimensional chiral states, which have a conductance $n\, e^2/h$, where $n$ is an integer that is solely determined by the bulk. In this work we show that step edges on the surface of three-dimensional topological metals have a robust conductance $K\, e^2/h$, where $K$ is also fixed by the bulk and assumes non-integer values. We explain this prediction on the basis of the topology of gapless systems, exemplify it on a lattice model, and connect to recent experimental observations of enhanced density of states at step-edges in topological metals.