Tutorial 4: Layered Materials

Following the isolation of graphene fifteen years ago, the field of atomically thin, layered materials has flourished to incorporate an essentially comprehensive range of condensed matter properties. At the same time, graphene has proven to be an extraordinarily protean material with new surprises arriving continually, such as topological currents, fractal bands, and intrinsic superconductivity to name only a few. The aim of this tutorial is to be both broad, providing an overview of what has been achieved and what may await discovery, and deep, providing specific and detailed examples of the kinds of new questions that increasingly draw researchers to this field. Spurred by the availability of high-quality single crystals of diverse layered materials, a general theme of the past and future of this field is the ability to create van der Waals heterostructures. These combinations of similar or dissimilar layers enable the preservation of delicate materials, new probes of constituent layers, and the radical alteration of band structures, for example through the formation of Moiré bands. Potential applications will be mentioned but are too numerous to be described in any detail; instead the focus will be on the fundamental physics of atomically thin layered materials.