Topological and strong correlation physics in orbital-active honeycomb lattice materials -- applications to twisted bilayer graphene, bismuthene, transition-metal oxide film, etc

We apply the symmetry principle to analyze the physical properties of orbital-active honeycomb systems which include a large class of mateirals (e.g. the twisted-bilayer graphene, transition-metal-oxide layer, bismuthene, stanene, metal-organic framework, and quantum dot array). Their orbital degree of freedom transforms as a two-dimensional irreducible representation of the lattice symmetry group, which results in band structures consisting of both the dispersionless flat bands and orbital-active Dirac bands. The flat bands amplify strong correlation effect to yield Wigner crystal and flat-band ferromagnetism. The active-orbital degree of freedom boosts the topological gap of the Dirac bands to the order of atomic scale spin-orbit coupling, i.e. at the scale of 1eV, as observed experimentally in bismuthene. In the Mott-insulating states, the orbital exchange becomes heavily frustrated as described by a novel 120 degree model whose classic ground states are mapped to all possible loop configurations covering the lattice, and quantum fluctuations select the closest packed loop configuration. The orbital degree of freedom also facilitate an f-wave superconductivity in which the gap nodal lines are determined by the orbital symmetry independent of the concrete pairing interactions.