The discovery of graphene and other two-dimensional (2D) materials together with recent advances in exfoliation techniques have set the foundations for the manufacturing of single layered sheets from any layered 3D material. The family of 2D materials encompasses a wide selection of compositions including almost all the elements of the periodic table. This derives into a rich variety of electronic properties including metals, semimetals, insulators and semiconductors with direct and indirect band gaps ranging from ultraviolet to infrared throughout the visible range. Thus, they have the potential to play a fundamental role in the future of nanoelectronics, optoelectronics and the assembly of novel ultrathin and flexible devices. We categorize the 2D materials according to their structure, composition and electronic properties. In this review we distinguish atomically thin materials (graphene, silicene, germanene, and their saturated forms; hexagonal boron nitride; silicon carbide), rare earth, semimetals, transition metal chalcogenides and halides, and finally synthetic organic 2D materials, exemplified by 2D covalent organic frameworks. Our exhaustive data collection presented in this Atlas demonstrates the large diversity of electronic properties, including band gaps and electron mobilities. The key points of modern computational approaches applied to 2D materials are presented with special emphasis to cover their range of application, peculiarities and pitfalls.

The electronic structure of the recently synthesized (3 × 3) reconstructed silicene on (4 × 4) Ag(111) is investigated by first-principles calculations. New states emerge due to the strong hybridization between silicene and Ag. Analyzing the nature and composition of these hybridized states, we show that (i) it is possible to clearly distinguish them from states coming from the Dirac cone of free-standing silicene or from the sp bands of bulk Ag and (ii) assign their contribution to the description of the linearly dispersing band observed in photoemission. Furthermore, we show that silicene atoms contribute to the Fermi level, which leads to similar scanning tunneling microscopy patterns as observed below or above the Fermi level. Our findings are crucial for the proper interpretation of experimental observations.