Since its fabrication in 2004, graphene has attracted huge attention due to its exceptional electronic properties, and is now considered as one of the most promising candidates to replace the current semiconductor technology as silicon approaches its miniaturization limit. However, the absence of an electronic band gap in pristine graphene makes it ill-suited for many electronic applications. Semiconducting character can be imparted by a variety of methods, including chemical or structural modifications. For instance, a band gap can be opened by confining the electronic wave function in one dimension by cutting graphene to form graphene nanoribbons (GNRs). To possess a band gap comparable to conventional semiconductors like silicon, GNRs are required to have a width less than 3 nm and must also display sharp edges, which remains a great experimental challenge. Recently, a breakthrough advance has been achieved with the controlled synthesis of atomically precise nanoribbons using a bottom-up approach where small aromatic molecules chemically assemble into high-quality subnanometer ribbons. This method not only allows for the synthesis of high-quality straight GNRs, but also for more complex structures like wiggle-like GNRs, called graphene nanowiggles (GNWs).;In Part I of this thesis, first-principles density functional theory (DFT) calculations are carried out on a variety of GNWs to reveal their unusual electronic and magnetic properties that are absent in their individual GNRs components, such as tunable band gaps and versatile magnetic states. The relationship between the band gap and the geometry is dictated by the armchair or zigzag characters of the corresponding parallel and oblique sectors, enabling GNWs to offer a broader set of geometrical parameters to tune the electronic structures compared to GNRs. In addition, first-principles many-body Green's function calculations within the GW approximation are performed to yield a quantitative prediction of GNWs' electronic properties. The enhanced electron-electron interaction in the quasi-one-dimensional GNWs results in significant self-energy corrections to their DFT band gaps. Consequently, the quasiparticle band gaps are typically more than twice of the DFT band gaps and are within the most interesting range 0.0-3.7 eV.;In Part II of this thesis, we venture beyond graphene-based systems and investigate graphene-like materials: transition metal dichalcogenides MX 2(M = Mo, W; X = S). Similar to graphite, they are also layered structures stacked by weak van der Waals (vdW) forces. Single-layer MoS2 and WS2 have been synthesized and found to show enhanced carrier charge mobilities and strong photoluminescence with direct band gaps, and thus they have been considered as replacements or complements to graphene for applications. Raman spectroscopy is often considered as one of the most popular tools to characterize them. Despite extensive experimental Raman studies on MoS 2 and WS2, it remains unclear how Raman intensities and especially intensity ratio of Raman modes E2g1 and A1g depend on the materials' thickness, due to the large spectrum of seemingly contradictory findings.;In the final part of the thesis (Part III), we highlight the experimental collaboration project with Prof. Plummer's group from Louisiana State University: spin-dependent surface reconstruction of layered Fe-based superconductors CaFe2As2. Low energy electron diffraction, scanning tunneling microscopy and spectroscopy, and first-principles spin-polarized DFT are utilized to investigate the geometric, electronic, and magnetic structures of the stripe-ordered (1x2) surface of Ca(Fe1-xCox) 2As2 (x=0, 0.075). The surface is terminated with a 50% Ca layer. Compared to the bulk, the surface Ca layer has a large inward relaxation (∼ 0.5 A), and the underneath As-Fe2-As layer displays a significant buckling. First-principles calculations show that the (1x2) phase is stabilized by the bulk anti-ferromagnetic spin ordering through the spin-charge-lattice coupling. Strikingly, a superconducting gap (∼7 meV at 7.4 K) is observed on such surface (x=0.075 compound), suggesting the coexistence of both superconductivity and AFM ordering at the surface. (Abstract shortened by UMI.).
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