Absence of localization in a class of topological systems

Topological matter is a trending topic in condensed matter: From a fundamental point of view it has introduced new phenomena and tools, and for technological applications, it holds the promise of basic stable quantum computing. Similarly, the physics of localization by disorder, an old paradigm of obvious technological importance in the field, continues revealing surprises when new properties of matter appear. This work deals with the localization behavior of electronic systems based on partite lattices with special attention to the role of topology. We find an unexpected result from the point of view of localization properties: A robust topological metallic state characterized by a non--quantized Hall conductivity arises from strong disorder in class A (time reversal symmetry broken) insulators. The key issue is the nature of the disorder realization: selective disorder in only one sublattice in systems based on bipartite lattices. The generality of the result is based on the partite nature of most recent 2D materials as graphene or transition metal dichalcogenides, and the possibility of the physical realization of the particular disorder demonstrated in ref. 1. An anomalous Hall metal arises also when the original clean insulator is topologically trivial.