Abstract: Moiré patterns formed by stacking atomically thin van der Waals crystals can give rise to
dramatic new physical properties, in select cases generating flat bands that host a variety of intertwined correlated and topological states of matter. I will discuss two distinct moiré
platforms that each exhibit their own unique topological properties. The first is twisted
bilayer-trilayer graphene, in which we observe the formation of generalized anomalous Hall
crystals that either triple or quadruple the area of the moiré unit cell. These states exhibit a
fully-developed integer quantum anomalous Hall effect, with a Chern number that can be
flipped between +1 and -1 by out-of-plane or in-plane magnetic fields or by an electric
displacement field. The second system we study is twisted molybdenum ditelluride (tMoTe 2 ), which was recently found to host the fractional quantum anomalous Hall effect. By probing tMoTe2 on the atomic scale using scanning tunneling microscopy and spectroscopy, we are able to detect fingerprints of the layer pseudospin skyrmion lattice responsible for generating the topology of the moiré bands. Our findings showcase the diverse range of novel topological properties that can arise in moiré materials.