As the devices used in daily life become smaller and more concentrated,traditional three-dimensional (3D) bulk materials have reached theirlimit in size. Low-dimensional nanomaterials have been attracting moreattention in research and getting widely applied in many industrialfields because of their atomic-level size, unique advanced properties,and varied nanostructures. In this thesis, I have studied the stability andmechanical and electronic properties of zero-dimensional (0D)structures including carbon fullerenes, nanotori, metallofullerenes andphosphorus fullerenes, one-dimensional (1D) structures including carbonnanotubes and phosphorus nanotubes, as well as two-dimensional (2D)structures including layered transition metal dichalcogenides (TMDs),phosphorene and phosphorus carbide (PC).I first briefly introduce the scientific background and the motivationof all the work in this thesis. Then the computationaltechniques, mainly density functional theory (DFT), are reviewed inChapter 2.In Chapter 3, I investigate the stability and electronic structure ofendohedral rare-earth metallofullerene La@C$_{60}$ and thetrifluoromethylized La@C$_{60}$(CF$_3$)$_n$ with $n{\leq}5$. Odd $n$ ispreferred due to the closed-shell electronicconfiguration or large HOMO-LUMO gap, which is also meaningful for theseparation of C$_{60}$-based metallofullerenes.Mechanical and electronic properties of layered materials includingTMDs and black phosphorus are studied in Chapter 4 and 5. In Chapter 4,a metallic NbSe$_2$/semiconducting WSe$_2$ bilayer is investigated andbesides a rigid band shift associated with charge transfer, thepresence of NbSe$_2$ does not modify the electronic structure ofWSe$_2$. Structural similarity and small lattice mismatch results in theheterojunction being capable of efficiently transferring charge across theinterface. In Chapter 5, I investigate the dependence of stability andelectronic band structure on the in-layer strain in bulk blackphosphorus.In Chapters 6, 7 and 8, novel 2D structures are predictedtheoretically. In Chaper 6, I propose two new stable structural phasesof layered phosphorus besides the layered $\alpha$-P (black) and$\beta$-P (blue) phosphorus allotropes. A metal-insulator transitioncaused by in-layer strain or changing the number of layers is foundin the new $\gamma$-P phase. An unforeseen benefit is the possibilityto connect different structural phases at no energy cost, which furtherleads to a paradigm of constructing very stable, faceted phosphorusnanotube and fullerene structures by laterally joining nanoribbons orpatches of different planar phosphorene phases, which is discussed in Chapter 7.In Chapter 8, I propose previously unknown allotropes of PC in thestable shape of an atomically thin layer. Different stable geometries,which result from the competition between $sp^2$ bonding found ingraphitic C and $sp^3$ bonding found in black P, display differentelectronic properties including metallic, semi-metallic with ananisotropic Dirac cone, and direct-gap semiconductors with their gaptunable by in-layer strain.In Chapter 9, I propose a fast method to determine the localcurvature in 2D systems with arbitrary shape. The curvatureinformation, combined with elastic constants obtained for a planarsystem, provides an accurate estimate of the local stability inthe framework of continuum elasticity theory. This approach can beapplied to all 2D structures.Finally, I present general Conclusions from the PhD Thesis work inChapter 10.
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