Splitting electrons without a magnetic field: The story of fractional Chern insulators

Abstract: In the realm of condensed matter physics, the fractional quantum Hall effect stands as a unique experimental manifestation of topological order, characterized by the emergence of anyons—quasiparticles that can be viewed as fractions of electrons—with no counterpart among elementary particles. Discovered more than four decades ago, this phenomenon arises at cryogenic temperatures and relies crucially on the application of a strong external magnetic field.

Fifteen years ago, theoretical work predicted that similar anyons could emerge in materials with specific crystalline structures, even in the absence of an external magnetic field. These systems are known as fractional Chern insulators. Recent advances in stacking two-dimensional materials, such as graphene and transition metal dichalcogenides, have made it possible to engineer new structures based on moiré patterns. In 2023, within the span of just a few months, several pioneering experiments exploiting the high controllability of moiré systems turned this long-standing theoretical proposal into reality. Even more excitingly, these experimental realizations have proven to be richer than initially anticipated.

In this seminar, we will provide an overview of this rapidly evolving field, highlighting how it is driven by the interplay between experimental advances, elegant analytical models, and powerful quantum many-body simulations. We will also discuss the future challenges and the surprises that still lie ahead.