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WIREs Comput Mol Sci
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# Electronic properties and charge carrier mobilities of graphynes and graphdiynes from first principles

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The sp1 + sp2 hybridized carbon allotropes, graphynes (GYs) and graphdiynes (GDYs), have attracted increased attention, and researches from both theoretical and experimental communities are emerging. Theoretical calculations show that the electronic properties of GYs and GDYs can be tuned by straining, cutting into nanoribbons with different widths and edge morphology, and applying external electric fields. Due to their unique electronic properties, GYs and GDYs exhibit charge carrier mobility as high as ∼104–105 cm2 V−1 second−1 at room temperature based on the first‐principle calculations and the Boltzmann transport equation. Interestingly, the charge carrier mobility in 6,6,12‐GY with double Dirac cone structure is found to be even larger than that in graphene at room temperature. Through an in‐depth description of electron–phonon couplings by density functional perturbation theory, it is suggested that the intrinsic charge carrier transport in these carbon allotropes is dominated by the longitudinal acoustic phonon scatterings over a wide range of temperatures, although scatterings with optical phonon modes cannot be neglected at high temperatures. The unique electronic properties of GYs and GDYs make them highly promising for applications in next generation nanoelectronics. WIREs Comput Mol Sci 2015, 5:215–227. doi: 10.1002/wcms.1213

• Structure and Mechanism > Computational Materials Science
Geometric structures of (a) α‐graphyne (GY), (b) β‐GY, (c) γ‐GY, (d) graphdiynes (GDY), and (e) 6,6,12‐GY.
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(a), (b) and (c) are the scattering times of an electron at the conduction band (CB) minimum by different phonon modes as a function of temperature for graphene, α‐graphyne (GY), and γ‐GY. (d) Electron mobility limited by longitudinal acoustic (LA) phonon scattering as a function of temperature for these systems. (Reprinted with permission from Ref . Copyright 2014 AIP Publishing LLC)
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Contour plots showing the square of e‐ph coupling matrix elements $gjiλk,q2$ (in eV2) calculated by density functional perturbation theory (DFPT) and Wannier‐interpolation for (a) graphene, (b) α‐graphyne (GY) and (c) γ‐GY, as a function of longitudinal acoustic (LA) phonon wave vector q (near the center of the Brillouin zone). k is at the conduction band (CB) minimum (K‐point for graphene and α‐GY, M‐point for γ‐GY) and the initial i and final j electronic states are both limited to the CB. (d) The matrix element of LA phonon scattering as a function of phonon wave vector q in the long‐wavelength limit. The slope is the LA deformation potential (DP) constant. (Reprinted with permission from Ref . Copyright 2014 AIP Publishing LLC)
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Calculated mobilities of (a) electron and (b) hole for graphdiynes nanoribbons (GDY NRs) with different widths at room temperature (300 K) from Ref (black symbols) and Ref (red symbols), respectively. (Reprinted with permission from Ref . Copyright 2011 The Royal Society of Chemistry; Ref . Copyright 2011 American Chemical Society)
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Structures of armchair nanoribbon (ANR) and zigzag nanoribbon (ZNR) for graphdiynes (GDY) with different widths (number of C6 hexagons).
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(a) The most stable configuration of bilayer graphdiynes (GDY) AB (β1) and the band structure without electric field; (b) ABA configuration of trilayer GDY and the band structure without electric field. (Reproduced with permission from Ref . Copyright 2012 The Royal Society of Chemistry)
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Two most stable stacking configurations for bilayer α‐graphyne (GY): (a) AB stacking and (b) its gapless parabolic band structure, (c) Ab stacking and its Dirac cone in the absence (d) and presence (e) of an electric field (0.1 VÅ−1). (Reprinted with permission from Ref . Copyright 2013 AIP Publishing LLC)
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Band structures of (a) γ‐graphyne (GY) and (b) graphdiynes (GDY) at the Perdew, Burke, and Ernzerhof (PBE) level. (Reprinted with permission from Ref . Copyright 2012 American Chemical Society); Band structure and density of states (DOS) of (c) α‐, (d) β‐, and (e) 6,6,12‐GYs at the PBE level. (Reprinted with permission from Ref . Copyright 2013 American Chemical Society)
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