Topological Flat Bands in Spin-orbit Assisted Orbital Frustrated Systems

We expand the concept of frustration in Mott insulators and quantum spin liquids to semimetals with flat bands.  In this approach topological flat bands are engineered through models with large onsite potentials, V, that split the spin and orbital degrees of freedom on the lattice into multi-degenerate band multiplets.  Kinetic processes, t, that forbid intra-multiplet hopping, but allow inter-multiplet hopping frustrate the degrees of freedom on the lattice giving rise to flat bands with small bandwidths of order t²/V compared to general models for which bandwidths are of order t.  We demonstrate this spin-orbit assisted orbital frustration on lattices in one and two dimensions with a variety of onsite potential spin-orbit structure.  Spin-orbit assisted orbital frustration provides a new route that goes beyond the flat bands of quantum Hall effects and those generated from moire potentials as in twisted bilayer graphene.  We provide an alternative mechanism that can guide the search for a richer materials' platform, including cold atoms systems, that can achieve topological flat bands poised at the brink of instabilities toward novel correlated and fractionalized metallic phases.