Two-dimensional topological nanomaterials and related Hall effects

As a geometric concept, "topology" is now used to describe the electronic properties of an insulator. Various topological materials have been predicted and observed, including topological insulators, Chern insulators, topological crystalline insulators, and Weyl semimetals. The first three of these materials can all be realized as two-dimensional nanomaterials. Due to their unique properties compared with normal insulators, these materials can exhibit quantum spin Hall effect and/or quantum anomalous Hall effect, protected by different symmetries. In this perspective, we review the current progress made in these topological nanomaterials, including their fundamental physical mechanisms and material realizations. We also discuss the possible material challenges and the issues that still need to be resolved in the future.