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First-principles calculations show that the geometric and electronic properties of silicene-related systems have diversified phenomena. Critical factors of group-IV monoelements, like buckled/planar structures, stacking configurations, layer numbers, and van der Waals interactions of bilayer composites, are considered simultaneously. The theoretical framework developed provides a concise physical and chemical picture. Delicate evaluations and analyses have been made on the optimal lattices, energy bands, and orbital-projected van Hove singularities. They provide decisive mechanisms, such as buckled/planar honeycomb lattices, multi-/single-orbital hybridizations, and significant/negligible spin–orbital couplings. We investigate the stacking-configuration-induced dramatic transformations of essential properties by relative shift in bilayer graphenes and silicenes. The lattice constant, interlayer distance, buckling height, and total energy essentially depend on the magnitude and direction of the relative shift: AA → AB → AA′ → AA. Apparently, sliding bilayer systems are quite different between silicene and graphene in terms of geometric structures, electronic properties, orbital hybridizations, interlayer hopping integrals, and spin interactions.

In this work, the various electronic properties of silicon nanotubes (SiNTs) were investigated by the density functional theory. The cooperative and competitive relationships between the chiral angle, periodic boundary conditions, and multi-orbital hybridizations create unusual narrow gaps and quasi-flat bands in the ultra-small armchair and zigzag tubes, respectively. The features varied dramatically with tube radii. Armchair SiNTs (aSiNTs) have an indirect-to-direct band gap transition as their radius is increased to a particular value, while zigzag SiNTs (zSiNTs) present a metal-semiconductor transition. The projected density of states was used to elucidate the critical transitions, and the evolution of p and s orbital mixing states during the process are discussed in detail. The information presented here provides a better understanding of the essential properties of SiNTs.

How to form carbon nanoscrolls with non-uniform curvatures is worthy of a detailed investigation. The first-principles method is suitable for studying the combined effects due to the finite-size confinement, the edge-dependent interactions, the interlayer atomic interactions, the mechanical strains, and the magnetic configurations. The complex mechanisms can induce unusual essential properties, e.g., the optimal structures, magnetism, band gaps and energy dispersions. To reach a stable spiral profile, the requirements on the critical nanoribbon width and overlapping length will be thoroughly explored by evaluating the width-dependent scrolling energies. A comparison of formation energy between armchair and zigzag nanoscrolls is useful in understanding the experimental characterizations. The spin-up and spin-down distributions near the zigzag edges are examined for their magnetic environments. This accounts for the conservation or destruction of spin degeneracy. The various curved surfaces on a relaxed nanoscroll will create complicated multi-orbital hybridizations so that the low-lying energy dispersions and energy gaps are expected to be very sensitive to ribbon width, especially for those of armchair systems. Finally, the planar, curved, folded, and scrolled graphene nanoribbons are compared with one another to illustrate the geometry-induced diversity.