Abstract: In many-body quantum systems, it has long been known that the interplay of nontrivial topology and strong interactions can lead to the emergence of intriguing phenomena that transcend standard doctrines. One such phenomenon is fractionalization, where excitations in a many-body system become "smaller" than the smallest building block of the system, carrying fractional charge or exhibiting fractional statistics. Although these theoretical concepts and principles were developed decades ago, the realization of fractional topological states remains sparse. In this talk, we will discuss recent developments in the study of two-dimensional (2D) materials and their moiré superlattice structures, which have opened new pathways toward realizing these novel quantum states of matter, such as the fractional quantum anomalous Hall effect. We will also examine the similarities and differences between these newly discovered states and the well-studied fractional quantum Hall effects.
