Bi14Rh3I9: weak topology, crystal chemistry, and emerging functionalities.

The discovery of topological insulators has revolutionized condensed matter physics by introducing materials with insulating bulk states yet symmetry-protected metallic boundary states. Among these, the ternary compoundstands out as the first realized weak three-dimensional topological insulator constructed from stacked two-dimensional quantum spin Hall layers. This review comprehensively examines the advances inand its derivatives, tracing the journey from theoretical prediction to experimental validation. We discuss the material's unique crystal structure comprising graphene-analogue intermetalliclayers alternating with insulatingspacer layers and its electronic structure characterized by a robust210 meV topological gap opened via strong spin-orbit coupling. Critical aspects of crystal growth, intrinsic defects, and real-structure effects are analyzed, alongside experimental confirmations through angle-resolved photoemission spectroscopy and scanning tunneling microscopy, revealing one-dimensional helical edge channels. Furthermore, we explore strategies for Fermi-level tuning via chemical gating and isoelectronic substitution, as well as the correlation between chemical bonding and topological character in related topological materials. This review highlightsas a model system for understanding weak topology, while critically identifying the key open challenges, including the absence of direct transport evidence for edge-channel conduction, Fermi-level misalignment at the cleaved surfaces, real-structure defects, and limited chemical design rules for the weak topological insulator class that must be addressed to fully realize the proposed functionalities of this material family.