Collective Phenomena in Dirac and Chern Electronic Systems

Two-dimensional electron systems whose band structure supports Dirac cones are hosts of intriguing phases of matter, characterized by nontrivial topological indices analogous to the Chern number in conventional quantum Hall (QH) states. Prominent examples include low-filling QH states in graphene monolayers and biased bilayers, and topological insulators realizable in other honeycomb lattices (e.g. layered alkali iridates or silicene) or heavy semiconductor quantum wells due to spin-orbit coupling. When combined with interactions, the nontrivial topology leads to the formation of novel many-body states. Their measurable physical properties are dominated by collective excitations, which likely encode the topological structure. The proposed theoretical research is intended to develop an understanding of the excitations in a variety of topologically nontrivial collective states, and their manifestations in measurable physical properties. The research plan consists of three main directions: (a) Studying the quantum dynamics of multi-component collective modes emerging near domain walls in QH ferromagnetic states, e.g. in a double-gated undoped bilayer graphene. Particularly, we will examine the anticipated rich phase diagram and the consequent transport properties. (b) Investigating the properties and physical signatures of excitons in systems possessing bands with multiple Chern numbers; e.g., excitons involving quasiparticles in two bands with different Chern indices. (c) Developing a composite Fermion theory for fractional QH states in graphene and fractionally-filled Chern bands. In particular, we aim to construct a theoretical description which accounts for the interplay of interactions and strong, smooth disorder, to shed light on puzzling experimental data.