The electronic and optical properties of a number of single-layered silicon sheets are investigated using density functional calculations. The energy bands of silicon sheets are found to possess direct gaps and thus facilitate the material's potential applications in optoelectronics. Bridging one-dimensional silicon chains and three-dimensional bulk silicon, two-dimensional single-layered silicon sheets present unique dimension and orientation dependencies of band structures and imaginary dielectric functions, which offer tunable band gaps and peaks in the dielectric functions associated with symmetry breaking and quantum confinement. Our study is expected to facilitate the understanding of general low-dimensional materials and their applications.
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