Topologic connection between 2-D layered structures and 3-D diamond structures for conventional semiconductors

When coming to identify new 2D materials, our intuition would suggest us to look from layered instead of 3D materials. However, since graphite can be hypothetically derived from diamond by stretching it along its [111] axis, many 3D materials can also potentially be explored as new candidates for 2D materials. Using a density functional theory, we perform a systematic study over the common Group IV, III-V, and II-VI semiconductors along different deformation paths to reveal new structures that are topologically connected to but distinctly different from the 3D parent structure. Specifically, we explore two major phase transition paths, originating respectively from wurtzite and NiAs structure, by applying compressive and tensile strain along the symmetry axis, and calculating the total energy changes to search for potential metastable states, as well as phonon spectra to examine the structural stability. Each path is found to further split into two branches under tensile strain-low buckled and high buckled structures, which respectively lead to a low and high buckled monolayer structure. Most promising new layered or planar structures identified include BeO, GaN, and ZnO on the tensile strain side, Ge, Si, and GaP on the compressive strain side.