Quantum geometric effects in interacting systems

NONTECHNICAL SUMMARY This award supports research and education towards understanding the role of light and interactions in the behavior of electrons in a new type of materials called topological insulators. In these materials, even though their interior behaves like a typical insulator, their surfaces allow the flow of electrons in an electrical current. The PI will investigate the effects of shining light on topological insulators, which results in the creation of new composite particles. The project will also examine the fundamental nature of interacting electrons in topological substances in two different regimes: The diffusive regime, where electrons propagate as overlapping waves; and the hydrodynamic regime, where electrons collide against each other so frequently that they flow as a viscous stream of water. Theoretical advances from this award may help the development of new electronic devices that operate through the coupling of light with topological matter. The PI will perform outreach to undergraduate students within the NSF sponsored REU program at OU and will offer public lectures at the Osher Longlife Learning Institute, which organizes a successful program of public lectures. The PI will also offer public lectures to high schools in the Oklahoma City area. TECHNICAL SUMMARY This award will advance our fundamental understanding of the interplay of quantum geometry, band topology, and interactions in electron systems. This project is organized in two main thrusts: 1) Quantum geometry in out-of-equilibrium systems, and 2) Many-body effects in Chern bands. The first thrust will address the physics of many-body quantum states driven by light, with emphasis on topological excitons, bound states of electrons and holes whose profile wavefunction has a finite vorticity in momentum that is dictated by the topology of the electronic bands. In the second thrust the PI will investigate the existence of collective modes and emergent many-body states with finite momentum vorticity in 3D topological metals, and will examine the interplay of interactions and quantum geometric effects in topological flat bands. The research will theoretically investigate out-of-equilibrium effects in Chern bands pumped with light, will address the nature of the quasiparticles in interacting topological flat bands in equilibrium and in the hydrodynamic regime, and will examine novel collective modes and many-body ground states set by quantum geometry. The advances of this award may result in the development of a novel class of optoelectronic devices based on topology. The PI will perform outreach to undergraduate students within the NSF sponsored REU program at OU and will offer public lectures at the Osher Longlife Learning Institute, which organizes a successful program of public lectures. The PI will also offer public lectures to high schools in the Oklahoma City area. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.