Title: Exploring Moiré 2D Materials and Topological Quasicrystals
Abstract: When distinct 2D materials with varying periodicities are overlaid, a moiré interference pattern emerging from lattice mismatches leads to exceptional electronic properties. This phenomenon is prominently observed in twisted bilayer graphene (TBG), where an moiré pattern gives rise to intriguing flat bands and associated correlated phenomena. In this tutorial talk, I will present a theoretical perspective on moiré materials and the emergent behaviors. I start with an introduction to the fundamental long-range continuum model, a essential tool to describe the electronic characteristics of representative moiré systems, including TBG, graphene/hBN superlattices, twisted topological insulators.
The latter segment of the talk focuses on recent theoretical works on moiré systems beyond TBG.
Particularly, emphasis is placed on trilayer systems,where interference among multiple moiré patterns results in quasiperiodic nature. A fascinating example is the twist-angle-dependent electronic spectrum, which exhibits fractal minigaps akin to the Hofstadter butterfly. These minigaps possess distinct topological numbers, which can be expressed as second Chern numbers through a formal connection with the quantum Hall effect in four-dimensional space.