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WIREs Comput Mol Sci
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# Computing optical properties of ultra‐thin crystals

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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, and 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. WIREs Comput Mol Sci 2016, 6:351–368. doi: 10.1002/wcms.1252

(a) The radiative transitions related to excitons at the K‐point in the BZ. Eg, Δ, ε A, ε B, and $ε A ‐$ correspond to band gap, valence band splitting, binding energy of A, B, exciton and A trion, respectively. (b) Contour plots of the Coulomb potential in the middle of the layer for four different dielectric configurations. (c) The PL peak energies of A exciton (red) and A trion (black) as a function of the effective dielectric constant. (d) The binding energies of A, B exciton (green) and A trion (blue) as function of the effective dielectric constant. (Reprinted with permission from Ref . Copyright 2014)
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PL spectrum of a CVD‐grown WS2/MoS2/ bilayer made by mechanical transfer, and CVD‐grown MoS2 and WS2 bilayers. (Reprinted with permission from Ref . Copyright 2014)
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(a) Current response of TiS3 field effect transistor under a 10 Hz mechanically modulated optical excitation. (b) Zoom on a single switching cycle at 10 Hz frequency. (c) Responsivity versus increasing modulation frequency for an excitation wavelength of 640 nm at 500 μW. (Reprinted with permission from Ref . Copyright 2014)
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(a) Photograph of a 50‐µm aperture partially covered by graphene and its bilayer. (b) Transmittance spectrum of single‐layer graphene (open circles) and theoretically predicted results for two‐dimensional Dirac fermions. Inset shows the transmittance of white light as a function of the number of graphene layers (squares). (Reprinted with permission from Ref . Copyright 2008)
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The band structure of (a) MoS2 and (b) WSe2 with SOC, Fermi level is set to 0 eV. (c) Calculated band aligment for MoS2 and WSe2 monolayers. Imaginary part of the dielectric function for (d) MoS2 and (e) WSe2 together with oscillator strength of the optical transitions.
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(a) Top and (b) side view of a graphene/h‐BN. (c) Band structure of graphene/h‐BN calculated with GLLBSC (solid lines) and LDA (dotted lines). The top of the valence bands is set to zero.(d) Optical absorption spectrum of graphene/h‐BN calculated using the LDA‐ALDA (dash‐dotted line), GLLBSC‐ALDA (dashed line), and GLLBSC‐BSE (solid line). (e) The GLLBSC‐BSE spectrum of the interface (repeated) together with the sum of the absorption spectrum of an isolated graphene and h‐BN layer, respectively (Reprinted with permission from Ref . Copyright 2012)
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(a) Absorption spectrum of MoS2 without (dashed red curve) and with (solid green curve) electron–hole interaction using a constant broadening of 20 meV. (b) Same data using an ab initio broadening based on the electron–phonon interaction. (c) Previous calculation using G0W0. (d) Experimental data. (Reprinted with permission from Ref . Copyright 2013)
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Imaginary part of the dielectric function, obtained by solving BSE, of MoS2 for several k‐point meshes (Left axis). Binding energy of the exciton (Eb as a function of the number of irreducible k‐points, right axis). (Reprinted with permission from Ref . Copyright 2013)
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Imaginary part of the dielectric constant for monolayer (a) MoS2, (b) MoSe2, (c) MoTe2, (d) WS2, and WSe2. The blue lines correspond to the relative oscillator strengths for the optical transitions. The dashed red lines indicate the G0W0 band gap. The binding energy of A exciton is indicated in the figure. (Reprinted with permission from Ref . Copyright 2012)
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Absorption spectrum of monolayer (a) CCl, (b) CF, and (c) CH for light polarization parallel to the surface plane. Insets show amplified regions of the absorption spectrum in the vicinity of the first exciton peak and G0W0 (PBE) gap (dashed line). (Reprinted with permission from Ref . Copyright 2013)
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Interband transition energies along high‐symmetry lines in the Brillouin zone (BZ) for graphene (a), silicene (b), and germanene (c). (d) Ab initio calculated optical absorbance of graphene (black solid line), silicene (red dashed line), and germanene (blue dotted line) versus photon energy. The infrared absorbance is shown in the inset. (Reprinted with permission from Ref . Copyright 2012)
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Fit of experiment to the Fano model using the optical conductivity obtained from GW calculations for σ cont. The dashed line is the optical conductivity spectrum obtained from the full GW‐BSE calculation. (Reprinted with permission from Ref . Copyright 2011)
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(a) Optical absorption spectrum, (b) density of excited states, and (c) absorbance of graphene, with and without excitonic effects included. (Reprinted with permission from Ref . Copyright 2009)
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