Quantum geometry of the multi-orbital triangular lattice

The triangular lattice is a simple yet powerful motif for studying emergent phases of matter and is ubiquitous in nature. The addition of multiple p or d orbitals on each site can allow for an onsite orbital angular momentum, which can provide a simple chemical design principle for enabling topological phases to persist to elevated temperatures. Here we discuss the interplay between the lattice and quantum geometries that stabilize large gap topologically nontrivial phases, and discuss our recent progress in their experimental realization.