Graphene, other 2D atomic crystals and their heterostructures

Probably the most important ``property'' of graphene is that it has opened a floodgate of experiments on many other 2D atomic crystals: BN, NbSe$_{2}$, TaS$_{2}$, MoS$_{2}$, \textit{etc}. One can use similar strategies to those applied to graphene and obtain new materials by mechanical or liquid phase exfoliation of layered materials or CVD growth. An alternative strategy to create new 2D crystals is to start with an existing one (like graphene) and use it as an atomic scaffolding to modify it by chemical means (graphane and fluorographene are good examples). The resulting pool of 2D crystals is huge, and they cover a massive range of properties: from the most insulating to the most conductive, from the strongest to the softest. If 2D materials provide a large range of different properties, sandwich structures made up of 2, 3, 4 \textellipsis different layers of such materials can offer even greater scope. Since these 2D-based heterostructures can be tailored with atomic precision and individual layers of very different character can be combined together, - the properties of these structures can be tuned to study novel physical phenomena (Coulomb drag, Hostadter butterfly, metal-insulator transition, etc) or to fit an enormous range of possible applications, with the functionality of heterostructure stacks is ``embedded'' in their design (tunnelling or hot-electron transistors, photovoltaic devices). Of particular interest are the tunnelling structures. Being able to control the thickness with atomic precision and having a variety of different material in disposal allows us to modify both the height and the width of the tunnelling barrier in the wide range. The use of graphene as electrodes and utilising insulating (BN) or semiconducting (MoS$_{2}$, WS$_{2})$ materials as the tunnelling barrier led to the creation of tunnelling transistors and tunnelling photovoltaic devices and the observation of the resonance tunnelling associated with momentum conservation. We will also consider tunnelling in magnetic field and phonon-assisted tunnelling.