Physics and theory of defects in 2D materials: the role of reduced dimensionality

Similar to their bulk counterparts, most crystalline two-dimensional materials (2DMs) have defects and impurities. Even when the formation energy of defects in a 2D system is high, so that the equilibrium defect concentration is negligible (as, e.g., in graphene in a wide range of temperatures), the defects can appear due to the interaction with the environment, as 2DMs have a very high surface-to-volume ratio. Moreover, any species on the surface of 2DMs can have strong effect on the material properties, while most species found on the surfaces of bulk systems are normally completely ignored in the context of point and line defects. Defects can have both detrimental and beneficial effects on the properties of 2DMs, as in the case of the bulk systems. Specifically, defects can deteriorate the electronic, optical and mechanical characteristics of 2DMs, and at the same time, add new functionalities, e.g., magnetism, or improve their catalytic performance. The reduced dimensionality of 2DMs, however, modifies the influence of defects on the materials properties. The geometry of 2DMs also makes it possible to deliberately introduce defects with nearly atomic spatial resolution using focused ion and electron beams and also helps in imaging the defects using scanning probe and transmission electron microscopy. At the same time, the reduced dimensionality of 2DMs also requires to modify the theoretical approaches aimed at assessing the formation energy of defects to account for the environment and much weaker screening of electrical point charges when defects are not neutral. In this chapter, we give a brief overview of the types of defects in 2DMs and bulk systems with the main focus on the differences originating from the reduced dimensionality of the former. We also discuss the changes which should be made in the theoretical description of point and line defects and give examples of the calculations for 2DMs with defects.