Tue, Nov 10, 2015, 1:00 pm to 2:00 pm
A fundamental property of any material is the electron filling, i.e., the number of electrons per unit cell. Within band theory, materials at odd filling must be metals, while those at even filling can be insulators. In the presence of interactions, flux-threading arguments can generalize this constraint, ruling out un-fractionalized insulators at certain fillings, with important implications for the interpretation of experiment. However, these arguments break down in the presence of spin-orbit coupling, which is playing an increasing role in quantum materials. In this talk I will show that “filling constraints” can be made both more general - and far more constraining - than has long been thought. These constraints have interesting applications to the hunt for topological semi-metals and spin-orbit coupled spin-liquids. I will conclude by applying these constraints in some detail to experimental and numerical studies of kagome anti-ferromagnets, for which there is growing evidence for the first gapped spin-liquid.