Orbital frustration and topological flat bands

We expand the concept of frustration in Mott insulators and quantum spin liquids to metals with flat bands. We show that when interorbital hopping t2 dominates over intraorbital hopping t1, in a multiband system with strong spin-orbit coupling lambda, electronic states with a narrow bandwidth A - (t2)2/lambda are formed compared to a bandwidth of order t1 for intraorbital hopping dominated models. We demonstrate the evolution of the electronic structure, Berry phase distributions for time-reversal and inversion breaking cases, and their imprint on the optical absorption in a tight-binding model of d-orbital hopping on a honeycomb lattice. Going beyond quantum Hall effects and twisted bilayer graphene, we provide an alternative mechanism and a richer materials' platform for achieving flat bands poised at the brink of instabilities toward novel correlated and fractionalized metallic phases.