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We employed first-principles calculations to investigate the electronic and optical properties of germanene nanotubes (GeNTs). Significant multi-orbital hybridizations lead to metallic and semiconducting behaviors in small-sized armchair and zigzag GeNTs, respectively. The changes in band gaps and subband dispersions with increasing diameter have been thoroughly understood by analyzing spatial charge densities and projected density of states. The optical absorption spectra exhibit diameter-dependent anisotropy and suggest a dimensional transition beyond a critical diameter. This comprehensive study not only deepens our understanding of GeNTs but also reveals new possibilities for various nanotechnology applications.

The feature-rich electronic and magnetic properties of fluorine-doped graphene nanoribbons are investigated by the first-principles calculations. They arise from the cooperative or competitive relations among the significant chemical bonds, finite-size quantum confinement and edge structure. There exist C-C, C-F, and F-F bonds with multi-orbital hybridizations. Fluorine adatoms can create p-type metals or concentration- and distribution-dependent semiconductors, depending on whether the π bonding is seriously suppressed by the top-site chemical bonding. Furthermore, five kinds of spin-dependent electronic and magnetic properties cover the non-magnetic and ferromagnetic metals, non-magnetic semiconductors, and anti-ferromagnetic semiconductors with/without spin splitting. The diverse essential properties are clearly revealed in the spatial charge distribution, spin density, and orbital-projected density of states.

This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.