When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state 1-3 .Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface 1 . Of particular interest might be the properties of topological defects between the two commensurate phases: solitons 2,4 , domain walls 1 , and dislocation walls 5-7 . Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN) 8,9 . Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest 1 , and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered 10 .

Silicene, a two-dimensional (2D) honeycomb structure similar to graphene, has been successfully fabricated on an Ir(111) substrate. It is characterized as a (√7×√7) superstructure with respect to the substrate lattice, as revealed by low energy electron diffraction and scanning tunneling microscopy. Such a superstructure coincides with the (√3×√3) superlattice of silicene. First-principles calculations confirm that this is a (√3×√3)silicene/(√7×√7)Ir(111) configuration and that it has a buckled conformation. Importantly, the calculated electron localization function shows that the silicon adlayer on the Ir(111) substrate has 2D continuity. This work provides a method to fabricate high-quality silicene and an explanation for the formation of the buckled silicene sheet.

Single-layer transition-metal dichalcogenides (TMDs) receive significant attention due to their intriguing physical properties for both fundamental research and potential applications in electronics, optoelectronics, spintronics, catalysis, and so on. Here, we demonstrate the epitaxial growth of high-quality single-crystal, monolayer platinum diselenide (PtSe2), a new member of the layered TMDs family, by a single step of direct selenization of a Pt(111) substrate. A combination of atomic-resolution experimental characterizations and first-principle theoretic calculations reveals the atomic structure of the monolayer PtSe2/Pt(111). Angle-resolved photoemission spectroscopy measurements confirm for the first time the semiconducting electronic structure of monolayer PtSe2 (in contrast to its semimetallic bulk counterpart). The photocatalytic activity of monolayer PtSe2 film is evaluated by a methylene-blue photodegradation experiment, demonstrating its practical application as a promising photocatalyst. Moreover, circular polarization calculations predict that monolayer PtSe2 has also potential applications in valleytronics.