Pathways towards non-Abelian physics in moiré materials

One of the most fascinating prospects of two-dimensional quantum systems is the realization of anyons, a unique category of quasiparticles that defy classification as either fermions or bosons, hence transcending the standard model of particle physics. Exploring and manipulating these anyons carries profound fundamental implications and the potential for paradigmatic-shifting technologies. Notably, a subset known as non-Abelian anyons should enable universal and topologically fault-tolerant quantum computations. Traditionally, the search for these anyons has focused on quantum Hall systems, where the strong magnetic fields required to stabilize them have significantly hindered advances in their characterization and manipulation. In the last year, groundbreaking experiments on twisted moiré bilayers successfully realized fractional Chern insulators, serving as zero-field analogs of quantum Hall states where anyons can naturally occur. I present the Twist2Braid project to capitalize on the advancements from these pioneering experiments and unlock the promises offered by non-Abelian anyons. My proposal is structured around three key pillars: (1) identifying ideal moiré heterostructures through a high-throughput search over two-dimensional materials and their stacking and twisting configurations; (2) modeling topological moiré materials and predicting experimental signatures indicative of anyonic physics; and (3) designing new systems acting as traps for non-Abelian anyons using both interfaces between topologically ordered phases and proximity with superconductors. To achieve the latter two objectives, I will develop innovative variational numerical methods that overcome the limitations of state-of-the-art computational techniques and allow simultaneous access to the bulk and edge properties of systems under consideration.