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WIREs Comput Mol Sci
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In silico engineering of graphene‐based van der Waals heterostructured nanohybrids for electronics and energy applications

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The successful isolation of single‐layer graphene sheet has led to tremendous progress in the discovery of new 2D materials including boron nitride, silicene, mxene, phosphorene, and transition metal dichalcogenides. However, the practical applications based on one simple 2D material are still at very early stage. Interfacing electrically and optically active graphene with other 2D materials or crystalline substrate will form a van der Waals heterostructured nanohybrid, which is attracting growing research interest across the disciplines of physics, chemistry, and material science. Such delicate heterostructures can combine the electronic functionality from each individual 2D material, holding great promise for applications in nanoscale electronics and sustainable energy. Computational exploration of electronic functionality in 2D graphene‐based van der Waals heterostructures can offer great theoretical insights and design principle that may prove profitable for experimental synthesis and device fabrications. In this review, we highlight recent progress on modeling graphene‐based van der Waals nanohybrids using density functional theory‐based approach. Particular emphasis will be given on the design of van der Waals heterostructured nanohybrids to modulate stability, stacking geometry, band gap, quantum spin Hall effect, electrical conductivity, optical/friction properties, chemical reactivity, Schottky barrier, carbon dioxide capture, etc. We also comment on the challenges that need to be overcome and outline some interesting research opportunities for future computational exploration of electronic functionality in 2D van der Waals heterostructures. WIREs Comput Mol Sci 2016, 6:551–570. doi: 10.1002/wcms.1266

(a) The LDA and GW band structures and plot of density of state for graphene/h‐BN heterostructure in Bernal stacking and misaligned stacking arrangements; (b) band dispersion for a graphene/h‐BN van der Waals heterostructure at different interlayer separation; (c) band gap tuning by external electric field in a van der Waals h‐BN/bilayer‐graphene/h‐BN heterostructure; (d) band structure of graphene supported on magnetic insulator—EuO. Green (blue) and black (red) represent spin up and spin down bands of EuO (graphene), respectively. (Reprinted with permission from Refs and Copyright 2011 American Chemical Society; Ref Copyright 2011 American Institute of Physics; Ref Copyright 2013 American Physical Society)
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Plots of charge density difference for van der Waals nanohybrids: (a) graphene/Co3O4 and N‐doped‐graphene/Co3O4; (b) graphene/Mn3O4(001); (c) graphene/MAPbI3; (d) graphene/MoS2. (Reprinted with permission from Ref Copyright 2015 American Chemical Society; Refs and Copyright 2012 and 2015. Royal Society of Chemistry; Ref Copyright 2015 Nature Publishing Group)
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(a) The side and top views of graphene/Ru (0001) van der Waals nanohybrid showing a ripple configuration at ground state; (b) The moiré pattern arising from 2D graphene/h‐BN van der Waals heterostructure, for two different misalignment angles = 0° and θ = 1°, respectively. (Reprinted with permission from Ref Copyright 2007 American Institute of Physics; Ref Copyright 2015 WILEY‐VCH Verlag GmbH & Co)
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A schematic diagram of van der Waals heterostructured nanohybrid formed by interfacing electrically and optically active graphene with various 2D materials or crystalline substrate.
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CO2 capture on monolayer and bilayer h‐BN supported on monolayer graphene. (a) and (c) are in neutral state; (b) and (d) are in the presence of charge. E ads represents the calculated adsorption energy of CO2. (Reprinted with permission from Ref Copyright 2015 WILEY‐VCH Verlag GmbH & Co)
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(a) Geometrical structure and a low energy pathway for lithium diffusion in 2D phosphorene/graphene van der Waals heterostructure; (b) energy profiles for lithium diffusion on graphene with and without the support of TiO2. (Reprinted with permission from Ref Copyright 2015 American Chemical Society)
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(a) Side and (b) top views of van der Waals graphene/BN heterostructure; (c) schematic representation of graphene flake on top of an h‐BN layer with a misfit angle of 45°; (d) maximal variations of the registry index along the sliding paths as a function of interlayer misfit angle. (Reprinted with permission from Ref Copyright 2012 American Chemical Society)
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(a) Van der Waals force dominate the reactivity of graphene; (b) enhanced HER in 2D MoS2/graphene van der Waals heterostructure; (c) metal‐free g‐C3N4/N‐doped‐graphene catalyst for the HER; (d) CO oxidation confined in a 2D van der Waals graphene/Pt(111) heterostructure. (Reprinted with permission from Refs and Copyright 2014 American Chemical Society; Ref Copyright 2014 Nature Publishing Group; Ref Copyright 2014 National Academy of Sciences)
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Evolution of the band edges of (a) single‐layer phosphorene and (b) bilayer phosphorene with respect to the graphene's Dirac point as a function of the electric field; (c) Schottky barriers in hybrid graphene–phosphorene nanocomposite as a function of interfacial distance; (d) Schottky barrier for 2D van der Waals graphene/MoS2 heterostructure. (Reprinted with permission from Ref Copyright 2015 American Physical Society; Ref Copyright 2015 Royal Society of Chemistry; Ref Copyright 2015 American Chemical Society)
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(a) Proposed MoS2/graphene solar cell and band alignment; (b) the calculated optical absorbance of a MoS2/graphene interface using the Bethe–Salpeter equation (BSE) method; (c) schematic of the photo‐induced electron injection process in graphene/TiO2 heterostructures; (d) top panel: the evolution of the energies of the photoexcited states and TiO2 conduction band; bottom panel: evolution of the photoexcited state localizations on the graphene sheet. (Reprinted with permission from Refs and Copyright 2013 and 2012 American Chemical Society)
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The calculated optical absorption spectrum for van der Waals heterostructures between graphene and (a) lead iodide (PbI2); (b) bismuth iodide (BiI3); (c) Organic–inorganic perovskite (MAPbI3). (Reprinted with permission from Refs and Copyright 2015 Royal Society of Chemistry; Ref Copyright 2015 Nature Publishing Group)
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(a) Graphene/TiO2 van der Waals nanohybrid and optical absorption spectrum from DFT‐based modeling and experimental measurement; The calculated optical absorption spectrum for (b) pure g‐C3N4 and van der Waals graphene/g‐C3N4 heterostructure, (c) van der Waals graphene/ZnO heterostructure with p‐ and n‐type doping, and (d) van der Waals graphene/ZrS2 heterostructure, respectively. (Reprinted with permission from Refs and Copyright 2011 and 2012 American Chemical Society; Ref Copyright 2013 American Institute of Physics; Ref Copyright 2016 Royal Society of Chemistry)
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(a) and (b) Spin‐resolved band structures for graphene supported on the BiFeO3 substrate; (c) and (d) the calculated band structure in the presence of spin‐orbit‐coupling (SOC); geometry and SOC band structures for (e) graphene/WS2 and (f) WS2/graphene/WS2, respectively. (Reprinted with permission from Refs and Copyright 2014 American Physical Society and American Institute of Physics, respectively)
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(a) The Bi2Se3/graphene/Bi2Se3 heterostructure and the calculated band structures in the absence and presence of spin‐orbit‐coupling (SOC) and pressure. The red dots represent graphene's Dirac states; (b) the optimized 2D van der Waals BiTeI/graphene heterostructure and its band structure in the absence and presence of SOC. (Reprinted with permission from Refs and Copyright 2013 and 2014 American Chemical Society)
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Corrugated (a) heptazine‐based and (b) triazine‐based g‐C3N4 open graphene's band gap up to 75 and 100 meV, respectively; (c) Graphene's gap opening in a van der Waals graphene/ZnO heterostructure; (d) Charge density and band dispersion for van der Waals graphene/silicon nanohybrid (e) Tuning bilayer graphene's gap with top and bottom h‐BN substrate. (Reprinted with permission from Refs and Copyright 2012 and 2015 American Chemical Society; Refs and Copyright 2014 and 2015 Royal Society of Chemistry; Ref Copyright 2013 American Institute of Physics)
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