Intrinsic Charge Separation and Tunable Electronic Band Gap of

Letter pubs.acs.org/JPCL

Intrinsic Charge Separation and Tunable Electronic Band Gap of Armchair Graphene Nanoribbons Encapsulated in a Double-Walled Carbon Nanotube Liangzhi Kou,*,† Chun Tang,‡,§ Thomas Frauenheim,† and Changfeng Chen‡ †

Bremen Center for Computational Materials Science, University of Bremen, Am Falturm 1, 28359 Bremen, Germany Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States § School of Engineering, University of California, Merced, California 95343, United States ‡

S Supporting Information *

ABSTRACT: Recent synthesis of nanocomposite structures of graphene nanoribbons (GNRs) encapsulated in a carbon nanotube (CNT) has opened a new avenue for exploring new functionalities for applications in nanotechnology. This new class of carbon nanocomposites is expected to possess electronic properties beyond those offered by the constituent parts of nanotubes and nanoribbons; unveiling such new properties and understanding the underlying physics are among the most pressing issues in the study of these promising materials. Here, we report on first-principles calculations of the electronic properties of armchair GNRs encapsulated in a zigzag double-walled CNT. This unique structural configuration produces an intrinsic charge separation with electrons and holes localized in the outer tube and the ribbon, respectively, while the inner tube remains charge-neutral, forming an n-type/intrinsic/p-type semiconducting heterojunction due to the staggered lineup of the band structures of the constituent parts. The electronic band gap of the nanocomposite can be tuned sensitively by the changing width of encapsulated GNRs. Such intrinsic charge separation and widely tunable electronic properties without doping or an external field make this class of new carbon nanocomposites promising candidates for photovoltaic and electronics applications. SECTION: Physical Processes in Nanomaterials and Nanostructures

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using carbon nanopeapods as starting materials, where the inner CNT was formed by C60’s coalescence under electron beam irradiation.19,20 It is thus expected that a GNR encapsulated inside of a DWCNT is feasible by using the same experimental procedures. The additional CNT in the DWCNT compared to that for the SWCNT provides extra space for charge (re)distribution in the composite system, which may produce electronic properties that are suitable for designing new functionalities in applications. In the present work, we investigate the structural and electronic properties of GNR@DWCNTs and explore the underlying physics to gain insights for understanding these new materials. CNT-based hybrid composites are ideal for photovoltaic applications because of the feasibility to engineer and tailor their optical and electronic properties by controlling the material size, shape, and surface. Recent theoretical predictions of polymer/fullerene or polymer/CNT blends indicate that a type-II heterojunction is formed at the interface between P3HT

raphene nanoribbons (GNRs) and carbon nanotubes (CNTs) are among the most important one-dimensional carbon materials because of their promise for applications in next-generation nanoscale electronic devices.1−3 Depending on the size and chirality, they exhibit metallic or semiconducting behavior.4,5 Both systems have been extensively studied, but the investigation of their hybrid composites has been relatively rare despite some seamless three-dimensional CNT−graphene hybrid materials already being fabricated.6−8 Recently, a novel carbon hybrid nanocomposite,9−11 consisting of a GNR encapsulated inside of a single-walled CNT (GNR@ SWCNT), has been synthesized from a random mixture of molecular precursors (fullerene or polycyclic aromatic hydrocarbon molecules) within a SWCNT, similar to the synthesis of nanopeapods and nanonuds.12,13 In contrast to SWCNTs or GNRs alone, the hybrid composites possess advantageous electronic and magnetic properties, which are promising for photovoltaic and spintronic applications.14 The microscopic dynamic formation procedure and structural stability of the hybrid GNR@SWCNT have been investigated via molecule dynamics simulation and ab initio studies.15−18 Similarly, double-walled CNTs (DWCNTs) also can be synthesized © XXXX American Chemical Society

Received: January 7, 2013 Accepted: April 7, 2013

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dx.doi.org/10.1021/jz400037j | J. Phys. Chem. Lett. 2013, 4, 1328−1333

The Journal of Physical Chemistry Letters

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has been shown that the LDA/GGA is able to reproduce the interlayer spacing and the binding energy.32 To clarify these issues for the present work, we have calculated the electronic properties of the hybrid structures using the VASP (GGA), which considers the vdWs interaction. Our results indicate that the LDA calculations using the SIESTA code capture the essential physics and provide the correct qualitative trends (see below for more details). Consequently, we present below our analysis and discussions on the results obtained using the LDA method. We now define the notations and specify the nanocomposite configurations studied in this work. We use An−H2GNR to denote the H-passivated armchair GNR with n C dimers along the width while using Zm−Zh−CNT to denote (m, 0)@(h, 0) zigzag DWCNTs. Thus, a nanocomposite complex of An− H2GNR encapsulated inside of Zm−Zh−DWCNT is denoted as An−H2GNR@Zm−Zh−CNT. To examine the size effect, two zigzag DWCNTs (Z16−Z25−CNT and Z20−Z29−CNT; the interwall distance between the inner and outer CNT is ∼3.4 Å, which is the equilibrium distance of the vdWs interaction) are chosen as host CNTs with diameters in the range of 12−23 Å, and encapsulated armchair GNRs with widths of comparable sizes are considered. Two hybrid composites of A6−H2GNR@ Z16−Z24−CNT and A6−H2GNR@Z15−Z24−CNT are studied to check the effect of semimetallic CNTs on the electronic properties. Before examining the electronic properties, we first evaluate the structural stability of various geometric configurations of fully relaxed An−H2GNR@ Zm−Zh−CNT. From results shown in Figure 1, one can see that elastic deformation is relatively

and a semiconducting CNT, thus separating excitons to different parts and facilitating charge collection, which is highly desirable for photovoltaic application.21,22 We also found that excitons are well-separated in different locations due to electrostatic potential variation when an armchair GNR is encapsulated inside of a semiconducting zigzag CNT.14 However, there is a significant possibility for recombination of dissociated excitons owing to the absence of a buffer layer, and this greatly reduces the efficiency of these materials in solar cell applications. Tian et al. reported coaxial SiNWs solar cells with an n-doped core and p-doped shell structure.23 Their work revealed that the introduction of an i-layer, namely, an intrinsic Si buffer layer, yields much better quality diodes with the p−i− n junction. In fact, the intrinsic buffer layer has been confirmed to improve solar cell efficiency, where surface recombination and current leakage are drastically suppressed.24 In the GNR@ DWCNT studied in the present work, the introduction of an additional (inner) CNT as a buffer layer is expected to improve the performance of the solar cell made of such materials. It could offer a solution that is more realizable than the general stragies based on the type-II band edge arrangement, such as coaxial heterojunction nanowires (Si/Ge, ZnO/ZnS), radial p− n doped nanowires, and polymer/semiconductor solar cells,25−28 which remain as great technical challenges in terms of nanoscale fabrication and precise control of doping. In this work, we investigate the stability and the structural and electronic characteristics of the GNR@DWCNT nanocomposites by first-principles calculations. We find that the physical properties are very sensitive to the size and matchup of the constituent GNR and DWCNT components. When Hpassivated armchair GNRs are encapsulated inside of a semiconducting zigzag DWCNT, the electronic band gap exhibits oscillating behaviors with the changing width of the inserted GNRs. On the other hand, when one (either inner or outer) CNT is semimetallic, the entire system becomes metallic. Due to the staggered band edge arrangement (band offset) after encapsulation, armchair GNRs in a semiconducting CNT can lead to type-II heterojunctions and a well-separated spatial distribution of electrons and holes localized in the outer CNT and GNR, respectively. These results offer key insights for understanding the emergent properties of armchair GNR@ DWCNTs, which establish a roadmap for guiding design and synthesis of specific nanocomposite configurations with tailored properties for nanoelectronic and photovoltaic applications. We performed our calculations using the SIESTA package29 with the local density approximation (LDA) for the exchange− correlation (XC) function.30 The double-ζ polarized numerical atomic orbital basis sets for C and H are used in all of the calculations. All atoms are allowed to relax until the force on each atom is less than 0.02 eV/Å. The Brillouin integration is sampled with 1 × 1 × 10 Monkhorst meshes. An equivalent plane wave cutoff of 300 Ry is chosen in the simulations. Vacuum layers of at least 10 Å are chosen except in the axial direction. We note that while standard DFT calculations underestimate quasiparticle gaps and neglect excitonic effects, they are expected to capture the rearrangement of electron density at interfaces that is important for predicting trends in electronic-level alignment and band offsets.31 In this work, the DFT calculations provide a reliable estimate of the trends, provided that the predicted band offset that develops from potential variation is significant compared with typical exciton binding energies. In general, LDA-type XC functionals do not describe accurately van der Waals (vdWs) forces. However, it

Figure 1. (a) Relaxed atomic structures of armchair GNRs encapsulated in DWCNTs. (b) Calculated deviation of the CNT diameter along the direction parallel to the GNR plane (dashed lines with open symbols) or normal to the GNR plane (solid lines with filled symbols). The black, red, blue, and green lines are for Z16−CNT, Z25−CNT, Z20−CNT, and Z29−CNT, respectively.

small when the width of the GNR is comparable to the diameter of the inner CNT (center panel), and it becomes more significant as the size of the encapsulated GNR increases or decreases. For instance, both the inner (16,0) CNT and outer (25,0) CNT remain in nearly circular shape when an A6− H2GNR is encapsulated. These tubes, however, deform into an elliptical configuration when A5−H2GNR or A7−H2GNR is 1329



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encapsulated, which induces a large elastic deformation of the CNTs. The elastic energy induced by the deformation raises the corresponding formation energies of the composite system. However, the energies are lowered by the vdWs interaction between the edges of the GNR and the walls of the CNT and between the walls of the inner and outer CNTs, which is proportional to the overlap area between the constituent parts of the nanocomposites. The equilibrium structure of the GNR encapsulated in the DWCNT is determined by the subtle balance between the vdWs interaction and elastic deformation. This leads to a nontrivial dependence of the equilibrium GNR@DWCNT on the width of the GNR and diameter of the DWCNT (see Figure 1). The interspaces between the GNR edges and the CNT walls and those between the inner and outer CNTs all keep at a distance of about 3.3−3.4 Å. We plot in Figure 1b the geometric characteristics of the deformed DWCNTs, which clearly show that the deviation of the crosssectional dimensions of the DWCNT is very sensitive to the width of the encapsulated GNR. For A5−H2GNR, both the inner Z16−CNT and outer Z25−CNT shrink by 0.5−1.0 Å along the direction parallel to the plane of the GNR, while they dilate by 0.5−1.0 Å along the direction normal to the GNR plane, and the deformation of the outer CNT is larger than that of the inner CNT. These trends reverse for A7−H2GNR@Z16− Z25−CNT. Meanwhile, the deformations of both the inner and outer CNTs are relatively small for encapsulated A6−H2GNR; this is because the initial distance between the edges of A6− H2GNR and the walls of the inner CNT is close to the equilibrium distance of 3.4 Å. The same pattern of structural deformation is observed in the An−H2GNR@Z20−Z29−CNT series, as also shown in Figure 1b. For a quantitative assessment of structural stability, we have calculated the encapsulation energy Eenc, which is defined as the difference between the energy of the nanocomposite and those of the isolated constituent parts Eenc =

Figure 2. (a) Encapsulation energy of the GNR@DWCNT. The blue asterisk is the value for A6−H2GNR@Z16−Z24−CNT. (b) Band gap of An−H2GNR encapsulated inside of a DWCNT as a function of the GNR width; the corresponding values of An−H2GNR and An− H2GNR@SWCNT are also presented for comparison.

We now turn our attention to the electronic properties of GNR@DWCNT and compare them with those of the corresponding isolated constituent parts studied here, which are all semiconductors [the band gaps of Z16−CNT, Z20−CNT, Z25−CNT, and Z29−CNT are 0.6, 0.52, 0.39, and 0.21 eV, respectively, while armchair GNRs have an oscillating gap with their width; see Figure 2b]. A previous study indicated that a DWCNT consisting of two semiconducting zigzag CNTs with small diameters (Z7−CNT@Z16−CNT) is metallic due to the curvature effect and difference in the downward shift of the π and π* electron states between the inner and outer tubes.33 However, the DWCNTs investigated here, Z16−CNT@Z25− CNT and Z20−CNT@Z29−CNT, are semiconductors with band gaps of 0.47 and 0.22 eV, respectively, because of the weak σ−π rehybridization. For structures with additional armchair GNRs introduced in the center of the cavity, the obtained results are summarized in Figure 2b. The value of the electronic band gap is sensitive to the structural details of the constituent parts and is smaller than the gaps of either of the individual constituents due to the staggered band edge states (i.e., the effect of band offset). For example, the electronic band gap of A7−H2GNR@Z20−Z29−CNT is 0.17 eV, although the corresponding values of the freestanding A7−H2GNR, Z20− CNT, and Z29−CNT are 1.6, 0.52, and 0.21 eV, respectively. With increasing width of the encapsulated An−H2GNRs, the gap ΔEn of An−H2GNR@DWCNT undergoes an oscillating variation, which is similar to the results for the freestanding An− H2GNR and An−H2GNR@SWCNT. The electronic band gap of the composites exhibits three distinct families of behaviors depending on the widths of An−H2GNRs with ΔE3p+1 > ΔE3p > ΔE3p+2 (p is an integer).5 Therefore, these gaps as a function of the GNR width are well-separated into three different categories (or family structures). We also calculated the electronic behavior of GNR@SWCNT and found that the gap of An−H2GNR@Z16−CNT follows almost the same trend as that of An−H2GNR@Z16−Z25−CNT, but the gap is significantly reduced in An−H2GNR@Z20−Z29−CNT com-

(EGNR@DWCNT − EGNR − E innCNT − EoutCNT) L

where L is the lattice constant of the unit cell. The encapsulation energy of GNR@DWCNT decreases with increasing width of GNR at first, but it then increases as the width further increases, as shown in Figure 2a. When the distance between the GNR edges and the walls of the inner CNT is in the range of the equilibrium distance by the vdWs interaction, which is about 3.4 Å, the encapsulation energy is at the minimum because both of the CNTs are in nearly undeformed shape, producing a minimal elastic energy. As the width of the GNR becomes wider or smaller, the encapsulation energy rises due to the increasing elastic deformation of the CNTs, as shown in Figure 1. Generally, the calculated encapsulation energies are about 2 eV/Å lower than those of the corresponding [email protected] The large negative energy is mostly related to the excess energy of the vdWs attraction between the inner and outer CNTs, while the increase in the elastic energy of the outer CNT is negligibly small. This can be verified by evaluating a different form of encapsulation energy defined as E*enc = (EGNR@DWCNT − EGNR − EDWCNT)/L. Here, the results (see the dashed lines shown in Figure 2a) are comparable to those for the GNR@SWCNT. The lower encapsulation energies in a DWCNT with a larger diameter (see Figure 2a, Z20−Z29−CNT) can also be attributed to the larger overlap area between the inner and outer CNTs, which leads to stronger vdWs interaction. 1330



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pared with that for An−H2GNR@Z20−CNT. This result is attributed to the small band gap of Z29−CNT, which reduces the gap of GNR@Z20−CNT owing to the band offset. To examine the influence of the weak interaction between the walls and edges of GNRs and check the robustness of the above results, we performed complementary calculations for all of the structures studied here using ab initio density functional theory in conjunction with the all-electron projector augmented wave potential and the Perdew−Burke−Ernzerhof generalized gradient approximation (PBE-GGA) to the electronic exchange and correction, as implemented in VASP. The other parameters of calculations are the same as those in SIESTA, except the introduction of vdWs. The vdWs interactions are incorporated by adding a semiempirical dispersion potential to the conventional KS DFT energy, through a pairwise force field following Grimme’s DFT-D2 method.34 The obtained results are presented in the Supporting Information, Figures S4 and S5. The structural characters of the optimized An−H2GNR@ Z16−Z25−CNT are preserved as those in Figure 1. Meanwhile, the band gap variation as a function of the GNR’s width is basically the same, as shown in Figure 2, although the magnitudes of the values are generally larger than those without considering the vdWs interactions. The band structures of An−H2GNR@Z16−Z25−CNTs calculated by VASP (PBE +vdW) are also qualitatively the same as those obtained using the SIESTA calculation (LDA method; see Figures 3 and 4). These results indicate that the vdWs interaction between the walls of the CNTs and the edges of the GNRs can affect the electronic properties of the hybrid structures to some degree, but it does not play a dominant role, and the calculations based on the LDA can capture the physical essence of the properties studied here. Below, we present our analysis and discussions of our results obtained from the LDA calculations. To understand the underlying physics of the electronic structure variations, we have studied the density of state (DOS), electrostatic potential, and electron transfer of A7− H2GNR@Z16−Z25−CNT as a typical example, and the obtained results are shown in Figure 3. Because all of the GNRs and CNTs are direct gap semiconductors, the hybrid composite also has a direct gap of 0.25 eV at the Γ point (see Figure 3a), but the band gap is significantly reduced compared to that of the corresponding isolated constituent parts. We plot in Figure 3b the radially resolved projected density of states (RDOS) obtained by summing up the DOS of all atoms of each constituent, and the results indicate that the states near the Fermi level are coming from different parts. The first peak below the Fermi level (the VBM state) originates from the encapsulated GNR, while the first peak above the Fermi level (the CBM state) comes from the outer CNT. This is corroborated by the spatial distribution of their wave functions shown in the insets of Figure 3b. It is interesting to note that the VBM and CBM states are completely localized at the GNR and the outer CNT, respectively, leading to well-separated electron and hole states localized in different constituent parts of the nanocomosite. The same phenomena are also observed in A7−H2GNR@Z16−Z26−CNT (where the outer CNT is replaced by a Z26−CNT to explore the effect of interwall distance). All of the band structures, the band edge alignments near the Fermi level, and the distribution of the wave functions are the same as those of A7−H2GNR@Z16−Z25−CNT shown in Figure 3, although the interwall distance between the inner and outer CNTs has increased (see the Supporting Information). The charge separation is also observed with the

Figure 3. (a) Band structure of A7−H2GNR@Z16−Z25−CNT. (b) Resolved DOS of constituent parts of the nanocomposite. (c) DOS of freestanding constituent parts, where red, blue, and green lines are for the GNR, inner CNT, and outer CNT, respectively. The same color scheme is used in the following figures. The arrows in (c) indicate the shift of the states of the constituent parts compared with the freestanding counterparts, which is highly correlated with the variation of the electrostatic potential after encapsulation (d). The colors of the arrows correspond to the DOS. The wave function distributions of the band edge states are shown in the insets of (b). The panel in (e) shows the electron transfer (pink: electron accumulation; cyan: electron loss; 0.001 e/Å3).

electron (hole) localized at the outer CNT (GNR). This result indicates a high degree of robustness of the physical phenomena revealed in the present work. In contrast to previously predicted charge separations in GNR@SWCNT, here, there is a buffer layer (the inner CNT) between the encapsulated GNR and the outer CNT. This greatly reduces the possibility of exciton recombination, which is a key requirement for photovoltaic applications. An intrinsic buffer layer has been experimentally demonstrated to improve solar cell efficiency.23 To have a clear understanding of the shifting energy levels after encapsulation, we present the DOS of each isolated corresponding constituent part for comparison in Figure 3c. All of the states of the GNR move upward, whereas those of the outer CNT move downward. For the inner CNT, we find that the valence band levels shift upward while the conduction bands shift downward. These different band movements stem from the variations of the electrostatic potential after the encapsulation of GNRs, which is defined as the difference between the electrostatic potential of the hybrid composite and that of each constituent. Results plotted in Figure 3d show that the electrostatic potential of the outer CNT decreases, but that of the GNR (especially at the edges) increases. The potential variation of the inner CNT is more diverse; the potential of the region close to the edge of the GNR rises while the other part drops. These intriguing potential variations explain the movements of the energy levels 1331



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states are gradually delocalized, which is in contrast to the localization of the VBM states on the GNR. For A6−H2GNR@ Z16−Z25−CNT, a small part of the CBM states resides at the inner CNT, although most of them are localized at the outer CNT. The CBM states are distributed throughout the whole composite in A5−H2GNR@Z16−Z25−CNT due to different electrostatic potential variations when ribbons with different widths are encapsulated. The same phenomenon occurs in GNRs in a large DWCNT (Z20−Z29−CNT) (see the Supporting Information). The most significant charge separation is observed in the An−H2GNR@Z20−Z29−CNT with n = 7 and 10. It is worth pointing out that the hybrid composite becomes metallic with the valence band crossing the Fermi level for the case of A8−H2GNR@Z20−Z29−CNT because of the small band gap of A8−H2GNR and Z29−CNT and the realignment of the Fermi level. In general, the most remarkable charge separation occurs in hybrid composites An−H2GNR@ Zm−Zh−CNT with n(mod)3 = 1 and (m × h)(mod)3 ≠ 0. Such sensitive size dependence of the electronic properties provides a highly desirable approach to tuning the physical behavior for applications in nanodevices with high efficiency. The semiconducting properties and charge separation no longer hold when a metallic constituent is introduced. To illustrate this point, we choose A6−H2GNR@Z16−Z24−CNT and A6−H2GNR@Z15−Z24−CNT as representative examples to examine the effect of a semimetallic CNT on the electronic properties of the nanocomposite, where isolated Z15−CNT and Z24−CNT have very small band gaps of only several meVs. As indicated in Figure 5, the introduction of the semimetallic CNT, whether placed at the position of the inner or outer CNT, gives rise to a metallic hybrid composite. The RDOS analysis indicates that the states crossing the Fermi level come not only from the Z15−CNT or Z24−CNT but also from the semiconducting GNR and CNT due to the electrostatic potential variation. The metallization also leads to the disappearance of charge separation in the nanocomposite. These results indicate that semimetal CNTs should be avoided in fabricating the hybrid nanocomposites for photovoltaic applications where the semiconducting nature and intrinsic charge separation are required. In summary, we have investigated the structural characteristics and stability, electronic band structure, and intrinsic charge separation of a new class of hybrid nanocomposites GNR@DWCNT. We find that the geometric configuration and encapsulation energy are determined by the balance of the

after encapsulation. Consequently, a type-II heterojunction with staggered band edge arrangements forms, leading to an intrinsic band gap modulation (reduction) and charge separation. For comparison, we decompose the A 7 − H2GNR@Z16−Z25−CNT into two GNR@SWCNTs, A7− H2GNR@Z16−CNT and A7−H2GNR@Z25−CNT, and investigate the electronic properties. It is interesting to note that the same band edge alignments near the Fermi level due to electrostatic potential variation are found in A7−H2GNR@ Z16−CNT, giving rise to charge separation. However, the states of A7−H2GNR@Z25−CNT are simply a superposition of the two constituent parts; both band edge states are from the CNT because of the large distance and weak interactions between them (see the Supporting Information). Meanwhile, electron transfer after the encapsulation is insignificant (see Figure 3e), with the transfer mainly from the π orbitals of both the inner and outer tubes and the edges of the GNR to the spacious region between the constituents. The accumulated electrons are mainly distributed in the interwall region, leaving both the inner and outer CNTs slightly electron-depleted. The direct band gap characteristics of the host DWCNT are preserved when the A5−H2GNR or A6−H2GNR is encapsulated, but the size of the band gap is reduced, as shown in Figure 4. However, the wave function distributions of the CBM

Figure 4. Band structures of (a) A5−H2GNR@Z16−Z25−CNT and (b) A6−H2GNR@Z16−Z25−CNT. The insets are wave function distributions of the CBM (green) and VBM (red) states.

Figure 5. Band structure (left) and RDOS (right) of (a) A6−H2GNR@Z15−Z24−CNT and (b) A6−H2GNR@Z16−Z24−CNT. 1332



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(17) Lebedeva, I. V.; Popov, A. M.; Knizhnik, A. A.; Khlobystov, A. N.; Potapkin, B. V. Nanoscale 2012, 4, 4522−4529. (18) Chamberlain, T. W.; Biskupek, J.; Rance, G. A.; Chuvilin, A.; Alexander, T. J.; Bichoutskaia, E.; Kaiser, U.; Khlobystov, A. N. ACS Nano 2012, 6, 3943−3953. (19) Smith, B. W.; Monthioux, M.; Luzzi, D. E. Nature 1998, 396, 323−324. (20) Sloan, J.; et al. Chem. Phys. Lett. 2000, 316, 191. (21) Kanai, Y.; Grossman, J. C. Nano Lett 2008, 8, 908−912. (22) Ren, S.; Bernardi, M.; Lunt, R. R.; Bulovic, V.; Grossman, J. C.; Gradecak, S. Nano Lett 2011, 11, 5316−5321. (23) Tian, B.; Zheng, X.; Kempa, T. J.; Fang, Y.; Yu, N.; Yu, G.; Huang, J.; Lieber, C. M. Nature 2007, 449, 885. (24) Pallarès, J.; Schropp, R. E. I. J. Appl. Phys. 2000, 88, 293. (25) Ng, M.-F.; Tong, S. W. Nano Lett. 2012, 12, 6133−6138. (26) Nduwimana, A.; Wang, X.-Q. Nano Lett. 2009, 9, 283−286. (27) Nduwimana, A.; Musin, R. N.; Smith, A. M.; Wang, X.-Q. Nano Lett. 2008, 8, 3341−3344. (28) Yang, S.; Prendergast, D.; Neaton, J. B. Nano Lett. 2010, 10, 3156−3162. (29) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (30) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (31) Wu, Z.; Neaton, J. B.; Grossman, J. C. Nano Lett. 2009, 9, 2148−2422. (32) Björkman, T.; Gulans, A.; Krasheninnikov, A. V.; Nieminen, R. M. Van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations. Phys. Rev. Lett. 2012, 108, 235502. (33) Okada, S.; Oshiyama, A. Phys. Rev. Lett. 2003, 91, 216801. (34) Bučko, T.; Hafner, J.; Lebégue, S.; Á ngyán, J. G. J. Phys. Chem. A 2010, 114, 11814−11824.

vdWs interaction and elastic deformation of CNTs. The complex of armchair GNRs encapsulated in a semiconducting DWCNT exhibits an oscillating electronic band gap with changing GNR width. Furthermore, an intrinsic charge separation occurs with a well-separated spatial distribution of electrons and holes localized in the CNT and GNR components, respectively. These results offer key insights for understanding and predicting electronic properties of GNR@ DWCNT; they also establish a roadmap for guiding design and synthesis of specific nanocomposite configurations with tailored properties for nanoelectronic and photovoltaic applications.

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ASSOCIATED CONTENT

S Supporting Information *

Band structure and wave function distributions of band edge states of An−H2GNR@Z20−Z29−CNT (n = 7−10), A7− H2GNR@Z16−Z26−CNT and GNR@SWCNT, as well as VASP results. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.K. acknowledges the financial support by the Alexander von Humboldt Foundation of Germany. C.F.C. was supported by the Department of Energy through Cooperative Agreement DE-FC52-06NA26274.

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REFERENCES

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Intrinsic Charge Separation and Tunable Electronic Band Gap of

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