Ab initio study of energy-band modulation in graphene-based two-dimensional layered superlattices† Yang Xu,‡ ab Yunlong Liu,‡ ab Huabin Chen, ab Xiao Lin, ab Shisheng Lin, * ab Bin Yu * c and Jikui Luo ab Received 20th August 2012, Accepted 25th September 2012 DOI: 10.1039/c2jm35652j Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities in designing nanoelectronic and photonic devices. Using density functional theory (DFT) calculations, we demonstrate that various types of superlattices can be obtained by stacking two-dimensional (2D) materials alternately, namely, graphene, hexagonal boron nitride (h-BN), hydrogenated graphene, and fluorinated graphene. The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction. Our results indicate that the quantized energy states in atomic-layered superlattices can be effectively tuned by modifying each individual barrier/well layer, enabling atomic-scale material engineering. Introduction The discovery of the two-dimensional (2D) graphene monolayer has enabled the exploration of low-dimensional physics at the nanoscale, as exemplified by massless Dirac fermions 1 and anomalous quantum Hall effects. 2 While the research on gra- phene is overwhelming, graphene-like 2D materials, such as hexagonal boron nitride (h-BN), 3 hydrogenated graphene (CH), 4 and fluorinated graphene, 5 have also attracted extensive research interest. High-quality h-BN can be produced via chemical vapor deposition (CVD), 6,7 and CH or fluorinated graphene can be obtained by direct hydrogenation or fluorination of graphene. 4,5,8 Through low-pressure hydrogen–argon plasma exposure at room temperature, graphene can be hydrogenated to saturation. 4 By exposing graphene to xenon difluoride (XeF 2 ) gas for more than 30 seconds at 30  C, 5 graphene can be fluorinated to form single-side fluorinated graphene (C 4 F) when exposed on one side, or double-side fluorinated graphene (CF) if exposed on both sides. Besides the fabrication process being compatible with planar technology and the small lattice mismatch with gra- phene, 3–8 it is worth noting that their insulating properties have enabled these graphene analogues to serve not only as atomically smooth dielectric substrates to preserve the high carrier mobility in graphene, 9,10 but also as transport barriers for graphene based tunneling devices. 11 Hence, superlattices of periodically patterned graphene nanoribbons 12 and alternately aligned gra- phene/graphene-derivative heterostructures 13–15 have recently been studied. One important issue is that despite the theoretical capability of modulating the energy gaps in these in-plane superlattices, 12–14 the synthesis of graphene nanoribbons or het- erostructures with fine control of the edge and interface config- urations are still an experimental challenge. To overcome the difficulty in the fabrication of in-plane superlattices, atomic-layered superlattices formed by periodically stacking graphene and graphene analogues have been proposed, as exemplified by a recently experimentally realized graphene/BN superlattice. 16 Using the CVD process and transfer methods, 17,18 the width of the well (graphene) and barrier (BN) can be controlled to the precision of the sub-nanoscale by determining the atomic layer number, 16 which enables the exploration of superlattices in nano photonics and electronics. However, to the best of our knowledge, only a few theoretical studies have focused on the bandgap tunability in the graphene/BN super- lattice, 19,20 and further insight into the engineering of quantized energy states is demanded. Moreover, less investigation has been done on the layered superlattices of graphene and its derivatives (CH, CF, C 4 F, etc.), which may lead to a range of new super- lattice concepts. a Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, P. R. China. E-mail: shishenglin@zju.edu. cn; jackluo@zju.edu.cn b Cyrus Tang Center for Sensor Materials and Applications, Zhejiang University, Hangzhou 310027, P. R. China c College of Nanoscale Science and Engineering, State University of New York, Albany, New York 12203, USA. E-mail: byu@albany.edu † Electronic supplementary information (ESI) available. See DOI: 10.1039/c2jm35652j ‡ These authors contributed equally to this work. This journal is ª The Royal Society of Chemistry 2012 J. Mater. Chem., 2012, 22, 23821–23829 | 23821 Dynamic Article Links C < Journal of Materials Chemistry Cite this: J. Mater. 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