Recent experiments have produced evidence for fractional quantum anomalous Hall
(FQAH) states at zero magnetic field in the semiconductor moiré superlattice system t MoTe …

The Moiré superlattice realized in two-dimensional heterostructures offers an exciting
platform to access strongly correlated electronic states. In this work, we study transition metal …

Fractal Hofstadter bands have become widely accessible with the advent of moiré
superlattices, opening the door to studies of the effect of interactions in these systems. In this …

We study mean-field states resulting from the pairing of electrons in time-reversal broken
fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps …

Pair-density waves (PDWs) are superconducting states that spontaneously break translation
symmetry in systems with time-reversal symmetry (TRS). Evidence for PDWs has been seen …

Recently, two-dimensional Dirac materials patterned with a superlattice structure have
emerged as a rich platform for exploring correlated and topological quantum matter. In this …

Topological field theories emerge at low energy in strongly correlated condensed matter
systems and appear in the context of planar gravity. In particular, the study of Chern-Simons …

An interplay between pairing and topological orders has been predicted to give rise to
superconducting states supporting exotic emergent particles, such as Majorana particles …

This dissertation investigates novel quantum phenomena in fractal electronic energy bands
also known as Hofstadter bands. In two-dimensional lattices subject to an external …

Topological superconductors have been proposed as a platform for realizing Majorana
modes—non-Abelian anyons, and a possible first step towards topological quantum …