Substrate-Induced Nanoscale Undulations of Borophene on Silver

Publication Date (Web): September 22, 2016. Copyright © 2016 ... *E-mail: [email protected]., *E-mail: [email protected]., *E-mail: nguisinger@anl...
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Substrate-Induced Nanoscale Undulations of Borophene on Silver Zhuhua Zhang,† Andrew J. Mannix,‡,§ Zhili Hu,† Brian Kiraly,‡,§ Nathan P. Guisinger,*,‡ Mark C. Hersam,*,§,∥ and Boris I. Yakobson*,† †

Department of Materials Science and NanoEngineering and Department of Chemistry, Rice University, Houston, Texas 77005, United States ‡ Center for Nanoscale Materials, Argonne National Laboratory, 9700 South Cass Avenue, Building 440, Argonne, Illinois 60439, United States § Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208, United States ∥ Department of Chemistry, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: Two-dimensional (2D) materials tend to be mechanically flexible yet planar, especially when adhered on metal substrates. Here, we show by first-principles calculations that periodic nanoscale one-dimensional undulations can be preferred in borophenes on concertedly reconstructed Ag(111). This “wavy” configuration is more stable than its planar form on flat Ag(111) due to anisotropic high bending flexibility of borophene that is also well described by a continuum model. Atomic-scale ultrahigh vacuum scanning tunneling microscopy characterization of borophene grown on Ag(111) reveals such undulations, which agree with theory in terms of topography, wavelength, Moiré pattern, and prevalence of vacancy defects. Although the lattice is coherent within a borophene island, the undulations nucleated from different sides of the island form a distinctive domain boundary when they are laterally misaligned. This structural model suggests that the transfer of undulated borophene onto an elastomeric substrate would allow for high levels of stretchability and compressibility with potential applications to emerging stretchable and foldable devices. KEYWORDS: Boron nanostructure, substrate, two-dimensional material, atomic structure, defect, density functional theory calculation promoted applications in flexible electronics, as demonstrated with graphene12,13 and silicon ribbons,14,15 direct growth of 2D materials with natural wavy configurations would simplify processing and provide additional opportunities for device design and integration. In search for such naturally undulated 2D materials, we are particularly interested in 2D B sheets (i.e., borophenes), which are expected to be structurally flexible16,17 and fluxional.18−20 Theoretical studies have proposed using metal substrates,21,22 such as Ag or Cu, for synthesizing borophenes. Very recently, two independent experiments23,24 reported the synthesis of borophenes on Ag(111), which are one-atom thin and hundreds of nanometers wide. Earlier predictions25−28 suggest that borophenes adopt a triangular lattice with a variable network of hollow hexagons (HHs). Mechanically, the vacancyvoids in the materials may soften the borophenes to ease structural deformations. Indeed, ultrahigh vacuum (UHV) scanning tunneling microscopy (STM) imaging has revealed

wo-dimensional (2D) materials have undergone a flurry of research activities due to a number of outstanding properties and potential applications.1−3 One of their most intriguing properties is their high degree of flexibility against out-of-plane deformation,4−6 as aided by their atomic thickness. This unique property opens opportunities for fabricating flexible electronic devices that enable innovative architectures and enhanced performance.7,8 Yet, successful examples that allow direct incorporation of 2D materials into flexible devices are rather limited. The major issue lies in that ideal flexible electronics must be not only bendable but also stretchable, compressible, and even twistable to form complex shapes during use. However, this is beyond the capability of most existing 2D materials, which are relatively stiff against in-plane deformation.9,10 A promising way to overcome this issue is to configure the 2D materials into 3D “wavy” shapes. In particular, periodically undulated 2D materials adhered to elastomeric substrates should not only remain easy to bend but also can afford large in-plane deformations. Currently, generating such wavy geometry is achieved mainly through mechanical postprocessing methods,11 such as transferring the 2D materials onto a prestretched “sticky” substrate and then releasing the substrate to induce periodic buckling. While this approach has

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© 2016 American Chemical Society

Received: August 9, 2016 Revised: September 19, 2016 Published: September 22, 2016 6622

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Figure 1. Atomic geometry of periodically undulated borophene on Ag(111). (a) Front (top) and side (bottom) views of a planar v1/6 sheet on silver. (b) Front (top) and side (bottom) views of an undulated v1/6 sheet on reconstructed Ag(111). The topmost Ag atoms are colored blue for clarity. (c,d) Schematic continuum models for the (c) planar and (b) undulated v1/6 sheets on a compliant substrate. Insets illustrate slices of charge redistribution between the B sheet (red) and Ag (blue), where dark and light colors represent charge depletion and accumulation (0.001 e/Å3) regions, respectively.

code.32 After the structural research, the 20 most stable structures were selected for higher-precision calculations. Other details regarding the methods and calculations can be found in Supporting Information. Growth Method and Characterization. Our borophenes were grown on single-crystal Ag(111) substrates in ultrahigh vacuum, which were cleaned via repeated cycles of Ar sputtering followed by annealing at ∼820 K. During the course of growth, boron was deposited from an electron beam evaporator (Focus Gmbh) with a boron rod source (ESPI metals, 99.9999%). The deposition rate was set to vary from 0.01 to 0.1 ML/min. Other details of the growth can be found in our previous work.23 To control the undulation coverage in the B sheets, the samples were heated to a temperature varying from 720 to 980 K, by a button heater. STM measurements were conducted in situ under ultrahigh vacuum in an Omicron Nanotechnology VT-SPM at 55 K and an Omicron Cryo-SPM at 2.5 K. No discernible differences in structure or morphology were observed between these systems. STM measurements were acquired in constant current mode, using electrochemically etched W tips degassed in situ. Results and Discussion. Before discussing the sheet undulations, one should determine the most suitable atomic lattice with lowest energy. This can be done efficiently by combining the cluster expansion method33 with first-principles calculations, to search for the global minimum of planar 2D B in vacuum27 or, more recently, on metal substrates,21 including Ag(111) in particular. For convenience, the methods are briefly summarized in the method section and detailed in the Supporting Information. From the plot of total energy per B atom of all symmetry-inequivalent structures as a function of v (Figure S1a), we see that the global minimum appears at v = 1/ 6,21 for a structure denoted as v1/6 sheet (Figure 1a). The v1/6 sheet adheres to Ag(111) with a binding energy of 42 meV/Å2, which is about twice the 22 meV/Å2 for graphene to Cu(111). The binding energy is larger than the 30 meV/Å2 reported in ref 24, where the v1/6 sheet on Ag(111) was stretched by 3% to attain commensurability. The buckled triangular B sheet (v = 0) is also reproduced as a local minimum at an energy that is 42 meV/atom higher than the v1/6 sheet and thus is less stable. The triangular sheet has been proposed for the planar phase,23 on the basis of simulated STM images that resemble experiments. Yet, the simulated STM image of the v1/6 sheet

borophene phases that show one-dimensional striped patterns.23 The origin of this apparently corrugated structure remains an open question, especially since dissimilar atomic models16,23,24 have been proposed for planar borophenes. Here, we present comprehensive theoretical and experimental analyses of this corrugated phase, whose atomic lattice is well presented as a monolayer B sheet with parallel HH rows, with a HH concentration of v = 1/6 (defined as v = n/N, where n is the number of HH among N triangular lattice sites). We find that, in contrast to existing 2D materials, the v1/6 sheet favors periodic nanoscale undulations on a reconstructed Ag substrate, permitted by a synergic effect of enhanced chemical binding to substrate and its exceptionally small bending stiffness along the HH rows. Geometric features of the lowest energy undulated v1/6 sheet, as well as an alternative model of a sheet first rippled by compression, both show excellent agreement with atomic-scale UHV STM characterization of the undulated phase in terms of topography, wavelength, Moiré pattern, and specific structural defects. Since the undulated B sheet is still weakly bound to the underlying substrate, it should be viable to transfer the electrically conductive monolayer onto an elastomeric substrate while preserving the undulation. In this manner, mechanical flexibility will be preserved in the transferred borophene layer as is required for stretchable electrodes and displays. Theoretical Calculations. The calculations were performed by employing ultrasoft pseudopotentials for the core region and spin-unpolarized density functional theory (DFT) based on the generalized gradient approximation of Perdew− Burke−Ernzerhof functional, as implemented in Vienna Ab initio Simulation Package (VASP) code.29,30 A kinetic energy cutoff of 400 eV was chosen for the plane-wave expansion. In all structures, the vacuum region between two adjacent periodic images was fixed to 12 Å to eliminate spurious interaction. The positions of metal atoms of the topmost three layers plus the step Ag atoms and the entire B sheet were fully relaxed using the conjugate-gradient method until the force on each atom is less than 0.01 eV/Å. Dipole correction was included in calculating the total energies. Scanning tunneling microscopy (STM) images were simulated in constant current mode and rendered with Hive software. 31 The structural search calculations based on cluster expansion method were implemented in ATAT (alloy theoretical automated toolkit) 6623

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and EAg are total energies of the entire system and relaxed reconstructed Ag substrate within the same supercell, respectively, and NB is the number of B atoms. Counterintuitively, such an undulated v1/6 sheet is more stable, with the energy ∼20 meV/atom lower than the planar form shown in Figure 1a. Better stability of the undulated 2D B is also supported by its lower formation energy, calculated as Ef = (Esyst − NBEB − NAgEAg)/NB, where EB and EAg are the energy per atom of a freestanding planar v1/6 sheet and a flat Ag substrate, respectively, and NAg is the number of Ag atoms. Still, Ef of the undulated v1/6 sheet is 7 meV/atom lower than that of the planar form. The Ag(111) surface reconstruction is essential for stabilizing the B sheet undulations. Without the protruding Ag rows, the undulated B sheet is unstable and naturally flattens. Any trial modifications to the Ag rows (e.g., changing the inter-row distance or adding more Ag atoms) lead to higher energy and thus are unfavorable (Figure S2). Note that similar reconstructed rows have been found on noble metal surfaces35−37 (i.e., Au, Pt, and Ir) as well as on Ag(110) decorated with alkali metals38,39 or oxygen40 because the reconstructions can efficiently relieve surface stress. It is also notable that the HH rows tend to be located at the troughs of the undulations, and no stable structure can be identified when placing HH rows at the crest. This configuration is favorable because the HH rows are more reactive on the convex side giving stronger binding with Ag, as supported by charge redistribution analysis (Figure 1c,d, insets). To better understand why the undulations are favored, we consider the competition between the energy cost Ebend of bending the sheet, and the energy reduction Ebind due to B−Ag binding, enhanced by the undulations and Ag reconstruction. The Ebind of the undulated v1/6 sheet on reconstructed Ag(111) is calculated to be 152 meV/atom, greater than 122 meV/atom for the planar sheet on flat Ag(111), whereas Ebend is as little as 11 meV/atom due to the very small D, overall resulting in an energy reduction of 19 meV/atom from the planar sheet. Apparently, the small Ebend is a key for favoring the undulations, which do not occur with other 2D materials on the same substrate. Taking graphene (D = 1.5 eV) and h-BN monolayer (D = 0.97 eV, close to early values41) as examples, we find both are decoupled from the reconstructed substrate (Figure S3) and their ground state remains planar since they are stiffer to bending and interact more weakly with the substrate. Geometrically, the undulated sheet has higher areal density than the planar geometry, indicating that some compression could occur during the growth process, caused by boron oversaturation or thermal mismatch with the substrate. In fact, the initial undulation could even be triggered by such small compression of an elastic sheet. Its in-plane stiffness C = 189 N/m, bending stiffness D = 0.39 eV, and interaction with the substrate described by a “spring constant” per unit area k = 0.032 eV/Å 4 , can all be obtained from DFT energy computations. The resulting Euler undulation threshold42 is as small as εEu = 2(kD)1/2/C ≈ 1.9% (see Supporting Information). Furthermore, the wavelength estimated for this instability is λEu = 2π(D/k)1/4 = 11.8 Å, which agrees well with the 13.9 Å determined in atomistic calculations above and with the 12.9 ± 0.7 Å measured in experiments. After this instability begins, its wavelength does not change, while the amplitude grows until the in-plane compression is fully relaxed; the undulation amplitude fully accommodating ε0 = 9.5% mismatch can be found from basic length/material conservation and is

captures the features observed in experiments too (Figure S1b), as also noted in ref 24. It is worth mentioning that another v1/5 sheet on Ag (denoted24 as χ3), albeit unrelated to the B phases discussed here, is nearly as stable as the v1/6 sheet (i.e., the energies agree within 2 meV/atom). We find, however, that all these planar B sheets (Figures 2a, S1, and S4) fail to agree with

Figure 2. Characterization of undulated borophene on Ag(111). (a) STM topography image of an undulated B sheet (Vsample = 0.1 V, It = 1.0 nA). (b) Experimental (top) and simulated (bottom) STM images. Vsample is 1.0 V for simulation and 0.2 V for experiment, It = 3.0 nA. λ, λ′, and λ″ mark three length scales in the model and experimental image. (c) Simulated Moiré pattern of the undulated B sheet on Ag(111), compared to (d) experimental image.

experimental characterization of the striped-undulated phase, suggesting that its pattern originates from actual undulations in the structure, rather than from electronic heterogeneities. This motivates us to explore geometric off-plane distortions of borophenes. We also assess the rigidity of borophenes against off-plane undulations by calculating their bending stiffness, D. For the v1/6 sheet, we find D = 0.39 eV along the HH rows (about onefourth of the 1.5 eV for graphene), which can accommodate one-dimensional off-plane undulations along the HH rows. According to our calculations,34 other borophenes have markedly higher D (>0.55 eV, e.g. D is 0.63 eV for the α sheet17). In particular, for the buckled triangular sheet D = 4.92 eV across the ridges, so the energy cost of bending undulations is prohibitively high in the absence of negative frequency phonon mode-induced instabilities.23 Since the very flexible v1/6 sheet also fits the planar phase, we will focus on this candidate for the undulated 2D B. When searching for the energetically optimal structure of the undulated v1/6 sheet on Ag(111), we considered a number of configurations with different wavelengths λ and amplitudes h/2, and then compared the total energy per B atom. Since the undulated B phase is realized at high temperatures (∼980 K),23 both flat and reconstructed Ag(111) surfaces were considered. Figure 1b presents the optimal configuration of the undulated v1/6 sheet, formed on reconstructed Ag(111). The distance between B and Ag ranges from 2.23 to 2.63 Å, with the minimum at the wave trough and the maximum at its crest. First, the stability of the B sheets is evaluated by their total energy per B atom, defined as EB = (Esyst − EAg)/NB, where Esyst 6624

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Figure 3. Partially undulated borophene. (a) STM topography image of a partially undulated B sheet synthesized at ∼800 K (Vsample = 0.2 V, It = 1.0 nA). The inset shows structural failure at the end of undulations. (b) Side (top) and front (bottom) views of a partially undulated v1/6 sheet with four crests on Ag(111). (c) Simulated (top) and experimental (bottom) STM images of the partially undulated sheet. Vsample is set to 1.0 V for simulation.

Isolated ridges and flat regions are found to coexist within the same B sheet, sharing the same periodicity along the ridges. The lattice appears to be coherent across the interface between the undulated and flat regions, suggesting that the undulated phase is an elastic distortion of the flat phase. Local failure discontinuities can be seen at the end of each ridge (Figure 3a, inset), due to mismatch strain thereof, further suggesting that the undulation is structural. These results are further elucidated by simulations. Figure 3b shows the atomic geometry of a partially undulated B sheet with four crests, which is more favorable than the fully planar B sheet. Simulated STM images of the partially undulated sheets reproduce the experimental results (Figures 3c and S5). The partially undulated B sheets are intermediate states between the fully undulated and planar B sheets, all being local minima reachable by thermally driven relaxation. The temperature-dependence of the undulations suggests a nucleation barrier, mainly due to the energy cost of forming the Ag steps and bending the B sheet. It also enables us to understand why no undulation is observed in the experiments24 by Feng et al. First, their growth temperatures are below 680 K, too low to activate the undulations. Second, their B islands are limited to tens of nanometers, so that the undulations are suppressed by dominant edges that are likely to bind more strongly to the substrate. We also observe a high density of dark point-defects in the undulated 2D B, most of which appear to be vacancies (Figure 2a). To better interpret these defects, we simulated monovacancies in the undulated v1/6 sheet by examining all inequivalent sites, labeled by 1−8 in Figure 4a. The formation energies of monovacancies are in the range of Ef = 1.18−2.09 eV, much lower than the vacancy formation energy of ∼7.5 eV in graphene44,45 and ∼3 eV in most metals.46 Therefore, monovacancies are anticipated to form easily in undulated borophene, in accord with experimental observations. The optimal monovacancy is shown in Figure 4b, created by removing a B atom from site 1; its Ef is 1.18 eV, lower by at least 0.4 eV than those for other monovacancies (Figure S6). This monovacancy spontaneously reforms into a complex of an empty octagon and a pentagon filled with a B atom. Such reconstruction efficiently passivates the dangling bonds near the defect, which thereby has low chemical reactivity. Indeed, no remarkable out-of-plane distortion is found near the defect or on the substrate (Figure 2b, bottom). This contrasts the normally high reactivity of monovacancies in other 2D materials.47−50 A simulated STM image of the optimal monovacancy closely resembles the experimental image of defects observed most frequently (Figure 4c). We also examine

calculated to be h/2 = 1.15 Å (see Supporting Information), close to the 1.35 Å obtained from atomistic calculations. Both key characteristics, λ and h, can also be obtained by minimizing the energy per unit area of a compressed slab on an elastic substrate, expressed as f = C[ε0 − (hπ /λ)2 /4]2 /2 + D(hπ 2/λ 2)2 + kh2 /16 (1)

The related details are provided in the Supporting Information. It is worth mentioning that, while a clean Ag(111) surface does not favor reconstruction, a coverage of 2D B may facilitate the reconstruction by charge exchange in a manner similar to that for O-adsorbed Ag surfaces.40,43 The experimental characterization of the striped undulated phase agrees well with a notion of it being structurally transformed from the planar v1/6 sheet (experimental details are provided in the method section). Figure 2a shows a STM topography image of a typical 2D B sample grown at 980 K, which displays parallel stripes. The striped pattern is robust against changing bias voltage, suggesting that it cannot originate from electronic heterogeneities of a planar lattice but is rather due to actual ripple undulations of the sheet. The wavelength of the undulation is measured to be λ = 12.9 ± 0.7 Å, between the theoretical values of λatom = 13.9 Å from atomistic DFT calculations and λEu = 11.8 Å from continuum elasticity. The two marks of length scales in Figure 2b are λ′ = 4.2 ± 0.2 Å and λ″ = 2.5 ± 0.1 Å, respectively, in agreement with theoretical values (4.48 and 2.40 Å). Moreover, the high-resolution STM image agrees well with the simulated image, as also shown in Figure 2b. Within a period of undulation, we can identify three substripes, with the middle one wider than the two on the periphery. Assuming that these substripes are equally wide preceding undulation, their widths allows us to estimate the height of undulation based on the projected lateral dimensions. The measurements result in a height of h ≈ 3.5 Å, close to the 2.7 Å determined from the atomic model. The agreement between theory and experiment is confirmed further at larger length scales. Figure 2c presents a simulated Moiré pattern of an undulated v1/6 sheet overlaid on reconstructed Ag(111), which has a rhombic supercell with edge length of L = 7.8 nm and angle of θ = 62°. The simulation reproduces the experimental Moiré pattern shown in Figure 2d, in which L ≈ 8 nm and θ ≈ 64°. The coverage of undulations varies with growth temperature. The B sheet is nearly fully undulated at 980 K but remains almost flat below 720 K. A STM topography image of a partially undulated B sheet grown at 820 K is shown in Figure 3a. 6625

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to follow the centers of the rhombuses of the Moiré pattern (Figure 2a), arising in the bright regions, where the Ag−B interaction should be stronger than that in the dark regions. The domain wall observation further corroborates that the striped STM patterns originate from a structural undulation, not merely an electronic effect of a nonundulated planar sheet. After identifying and realizing the naturally undulated borophenes, the next issue will be separating them from the substrate, which so far remains an experimental challenge. To assess feasibility, we calculated the adhesion energy between the undulated v1/6 sheet and reconstructed Ag substrate. The adhesion energy of 52 meV/Å2 remains roughly 2-fold higher than that for graphene on Cu(111) but is less than one-third of that (173 meV/Å2) for silicene on Ag(111). Thus, a recently developed encapsulated delamination transfer method,51 which has been successfully applied to separate silicene from Ag(111), may be adopted to transfer the undulated B sheet. Instead of using Al2O3 as a capping layer, an elastomeric substrate, such as poly(dimethylsiloxane) is suggested to preserve the undulation, which should prove useful for the development of novel flexible electronics. We have verified that the electronic structure of borophene is robust against structural undulation (Figure S8); in particular, its metallicity is well preserved in the undulated form, a prerequisite for potentially fabricating stretchable devices with robust performance. We note that the borophene on Ag(111) remains reactive, to the extent that it covalently binds to an additionally overlaid B monolayer (Figure S9). However, there is no evidence of the formation of multilayer borophenes in our experiments.23 Conclusions. We have combined comprehensive theoretical analyses with atomic-resolution UHV STM experiments to show that borophene can energetically favor periodic undulations on reconstructed Ag(111). This behavior proves to be unique to borophene with hollow hexagon concentration of v = 1/6, due to its record small bending stiffness and enhanced chemical interaction with silver. Furthermore, the geometry of the “wavy” configuration can be well described by elastic plate theory. Our atomistic model also shows excellent agreement with high-resolution characterization of undulated borophene epitaxially grown on Ag(111) in terms of topography and Moiré pattern. We also reveal that vacancy defects are easily accommodated in undulated borophene, yet show low chemical reactivity distinct from other 2D materials. Moreover, although the lattice structure can be coherent throughout an entire borophene island, the undulations nucleated on different sides of the island can be misaligned to form distinctive domain boundaries. These spontaneous undulations and unusual structural disorder reveal borophenes as an entirely new class of 2D material that will likely broaden the spectrum of applications in the atomically thin limit.

Figure 4. Structural disorder in undulated borophene. (a) Formation energy for creating a monovacancy on sites 1−8 (circles), as scaled by the bottom color bar from the lowest site 1 to the highest site 8. (b) Front (top) and side (bottom) views of the atomic geometry of the most favorable monovacancy, created by removing a B atom from site 1 in a. (c) Simulated STM image of the preferred monovacancy, compared to an experimental STM image (bottom) of the most frequently observed defect. (d) Atomic geometry of a domain boundary connecting misaligned undulations. (e) Experimental STM image of the domain boundary, compared to (f) a simulated STM image. Vsample = 0.2 V for experiments and 1.0 V for simulations.

double-vacancies, among which the optimal one has Ef = 1.13 eV (Figure S7a), even lower than that of monovacancy and about one-eighth of that for a double-vacancy in graphene.44,45 A simulated STM image of the optimal double-vacancy supports its existence in experiments (Figure S7b). The undulation decreases the Ef of defects since in a planar v1/6 sheet on Ag the Ef value is greater than 1.8 eV for a monovacancy and 2.4 eV for a double-vacancy. The v1/6 sheet possesses strong bending anisotropy, with easy bending along the HH rows and harder bending in the transverse direction (D = 0.56 eV). This anisotropy dictates that the undulations orient in the same direction in a B island, a behavior observed in experiments (Figures 2a and 3a). However, during the course of growth, the undulations can initially nucleate randomly across the island, via the formation of Ag steps and concerted local bending of the B sheet. It is thus possible that undulations nucleated at different sites are misaligned. If two misaligned undulated patterns have nucleated far from each other, they can grow large and not align with one another upon coalescence, resulting in a domain wall in the undulated phase (see Figure 4d). Experimental evidence reveals such a domain boundary (Figure 4e), where the array of crests shifts laterally. A simulated STM image (Figure 4f) of the domain wall with a large-scale atomic model (containing 1000+ atoms of Ag and B) agrees well with the experimental data. Interestingly, the domain walls are observed

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b03349. Details of theoretical and experimental methods, detailed discussion of the analytical model, results of the structural search of 2D B on Ag(111), energy comparison of differently undulated 2D B sheets, compressed graphene and h-BN on reconstructed Ag(111), simulated STM images of two planar 6626

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borophenes, simulations of partially undulated borophenes, and monovacancy and double-vacancy defects in the undulated B sheet are collected. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computer resources were provided by XSEDE under allocation TG-DMR100029 and TG-DMR150082 and the DAVinCI cluster. This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility under Contract No. DE-AC0206CH11357. A.J.M., B.K., M.C.H., and N.P.G acknowledge support by the U.S. Department of Energy SISGR (contract no. DE-FG02-09ER16109), the Office of Naval Research (grant no. N00014-14-1-0669), and the National Science Foundation Graduate Fellowship Program (DGE-1324585 and DGE0824162). Z.Z., Z.H., and B.I.Y. acknowledge support by the US DOE Office of Science grant DE-SC0012547. Z.Z. and B.I.Y. are grateful to Kevin Kelly for helpful discussions.

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DOI: 10.1021/acs.nanolett.6b03349 Nano Lett. 2016, 16, 6622−6627