Article pubs.acs.org/JPCC
Structural, Electronic, and Optical Properties of Bulk Graphdiyne Guangfu Luo,†,‡ Qiye Zheng,† Wai-Ning Mei,§ Jing Lu,*,† and Shigeru Nagase*,‡,∥ †
State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, P. R. China Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan § Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266, United States ‡
S Supporting Information *
ABSTRACT: Graphdiyne is a newly discovered 2D carbon allotrope with many special features. Using density functional theory plus van der Waals (vdW) density functional, we investigate the structural, electronic, and optical properties of several possible graphdiyne bulk structures. We find that bulk graphdiyne can be either a semiconductor or a metal, depending on its stacking configuration. The interlayer vdW force red shifts the optical absorption peaks of bulk graphdiyne relative to those of the monolayer, and spectra of different stackings display notable differences in the energy range below 1 eV. Finally, combining with previous electrical and optical experiments, we identify the structure of the recently synthesized graphdiyne film.
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INTRODUCTION Graphdiyne, as illustrated in Figure 1a, is a 2D carbon allotrope with hexagonal carbon rings connected by diine linkages (−CC−CC−). Its large-area multilayer films have been fabricated in recent experiments.1,2 Compared with graphene, which is impermeable to standard gases including helium owing to its very small hexagonal holes,3 graphdiyne has ca. 4.7 times larger holes (each with an area of ca. 25 Å2). It can therefore be used to filter small molecules, such as hydrogen gas.4 In a recent study,5 we showed that graphdiyne has a very large Young’s modulus of 412 GPa within the plane but can be distorted easily along the out-of-plane direction. Because of its 1.1 eV direct quasiparticle band gap,5 graphdiyne is superior to the zero-band gap graphene in the application to semiconductor devices and more advantageous than the indirectband gap silicon in terms of light absorption. Also, graphdiyne exhibits interesting excitons with both Wannier−Mott and Frenkel exciton characteristics.5 Furthermore, its nanoribbons are predicted to have the same level of charge carrier mobility as graphene.6 In view of the above-mentioned special features, graphdiyne together with its similar form, such as graphyne,7−10 has been attracting growing attention. Previous studies have shown us that multilayer graphene and graphite exhibit differences in many aspects as compared with the monolayer, for example, the band structure, Raman spectra,11,12 infrared spectra,13,14 and optical absorption spectra.15 Therefore, we anticipate a similar trend in bulk graphdiyne. Recently, we have studied the structural and electronic properties of bilayer and trilayer graphdiyne and explored the possibility of tuning their band gap using external electric field.16 However, the stacking style and its effects on the electronic and optical properties of bulk graphdiyne remain an open question. © XXXX American Chemical Society
We present our study on the electronic and optical properties of differently stacked bulk graphdiyne by using the density functional theory (DFT) with inclusion of the van der Waals (vdW) correction. We demonstrate that the electronic properties and the low-energy optical absorption spectra strongly depend on the stacking, and the vdW correction is essential for computing the binding energy and low-energy optical spectra.
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MODEL AND METHODS It is well known that the local density approximation (LDA) and generalized gradient approximation (GGA) to the exchange−correction functional of DFT are not appropriate to describe the vdW force in layered compounds due to lack of nonlocal ingredients. In recent years, two schemes have been developed to modify this drawback: one approach empirically introduces to DFT a C6R−6 form of dispersion correction, the so-called DFT-D scheme, whereas the other adds a nonlocal correlation term to the known DFT functional, namely, the vdW-DFT scheme.17 Previous applications of the two methods to both molecules18 and extended systems17,19−21 yielded considerable improvements, but overestimation in binding energy or poor prediction of structure were also occasionally noticed.20,21 Therefore, to identify a functional suitable for our system, we test different methods using graphite as a touchstone. As presented in Table 1, vdW-DFT with the optimized Perdew−Burke−Ernzerhof exchange energy, vdWoptPBE, describes best the structure and binding energy of graphite compared with the advanced theories (the quantum Received: March 4, 2013 Revised: June 2, 2013
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dx.doi.org/10.1021/jp402218k | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
sampled with a Monkhorst−Pack grid spacing of 0.02 Å−1 in ground-state calculations and 0.006 Å−1 in the optical spectrum calculations. Increasing the parameters to a 900 eV energy cutoff, a 700 eV PAW pseudopotential, and a 0.01 Å−1 k-point spacing changes the lattice lengths and binding energies by less than 0.002 Å and 0.2 meV/atom, respectively. The structures are optimized until the force on each atom is
