Patrick Ledwith – Harvard University

Title: Vortexability Chern bands in Twisted and Strained Graphene

Abstract: Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable for realizing fractional Chern insulators (FCI). Previous approaches to stabilizing FCIs focused on mimicking the LLL through momentum space criteria. Here instead we take a real-space perspective by introducing the notion of vortexability. Vortexable Chern bands admit a fixed operator that introduces vortices into any band wavefunction while keeping the state entirely within the same band. Vortexable bands admit trial wavefunctions for FCI states, akin to Laughlin states. In the absence of dispersion and for sufficiently short ranged interactions, these FCI states are the ground state — independent of the distribution of Berry curvature. Vortexable Chern bands were found to emerge naturally in chiral twisted graphene, and fractional Chern insulators were subsequently observed experimentally. They were also recently proposed in periodically strained graphene.

Bio: Patrick Ledwith grew up near Philadelphia, Pennsylvania. He got his undergraduate degree in Physics and Mathematics at MIT. There he worked with Leonid Levitov on electron hydrodynamics, discovering and elucidating long-lived collective excitations in two-dimensional electron gases. He is now a graduate student working in Ashvin Vishwanath’s group. Here he has worked on several aspects of moiré materials including fractional Chern insulators, superconductivity, correlated insulators, and topological charge density waves. He has been especially interested in developing analytic approaches to fractional Chern insulators. He has applied these methods to twisted bilayer graphene where they work especially well. He subsequently partnered with Amir Yacoby’s group in realizing and understanding experimentally observed fractional Chern insulating states at small magnetic fields. In his free time, he likes to cook and play video games with his dog.