An overview is given of recent advances in experimental and theoretical understanding of optical properties of ultra-thin crystal structures (graphene, phosphorene, silicene, MoS2, MoSe2 , WS2 , WSe2 , h-AlN, h-BN, fluorographene, graphane). Ultra-thin crystals are atomically-thick layered crystals that have unique properties which differ from their 3D counterpart. Because of the difficulties in the synthesis of few-atom-thick crystal structures, which are thought to be the main building blocks of future nanotechnology, reliable theoretical predictions of their electronic, vibrational and optical properties are of great importance. Recent studies revealed the reliable predictive power of existing theoretical approaches based on density functional theory (DFT).
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