Title: Fractional Chern insulators in doped irradiated graphene

Abstract:

I will give an overview over recent theoretical studies of a class of topologically ordered states in two-dimensional electronic systems, the so-called fractional Chern insulators. These states emerge in lattice models of repulsively interacting electrons, if the electronic band in absence of electron-electron interactions (i) supports a nontrivial topological property and (ii) is reasonably flat as compared to the interaction energy scale. For one, fractional Chern insulators resemble in many ways the universal properties of fractional quantum Hall states, but at the same time lattice effects allow for new phases that go beyond what is found in Landau levels. I will also discuss proposed routes towards an experimental realization of fractional Chern insulators with a particular focus on their possible emergence in doped graphene, when irradiated with high-intensity circularly polarized light.