PERSPECTIVES this work. As noncovalent interactions tend to be weaker than covalent bonds, the steps in a self-assembly process are often reversible—such that errors made are readily “corrected” as the assemblies funnel toward the thermodynamically most favorable arrangement. The reversibility of this type of assembly process lends itself well to the construction of large, intricate structures that would be difficult to access by traditional covalent synthesis. Fukino et al. speculate that the initial nanotube formation from their ferrocene-based building blocks is a stochastic process that does not involve the initial formation of nanorings for entropic reasons but rather doubly-bridged oligomeric units. With respect to the formation of the latter units,

the added Ag+ cations are believed to induce an eclipsed geometry and a bent shape to the molecular building blocks because of metallophilic interactions. The oligomers are then proposed to stack into curved sheets that ultimately form the observed nanotubes. The results reported by Fukino et al. open the door to many fascinating new possibilities. The generation of other shaped molecular precursors and their subsequent dynamic self-assembly is expected to be a fertile field for future discovery. Moreover, the manipulation of noncovalent stacking interactions in the resulting nanostructures and the ability to paste to substrates offer interesting opportunities in nanoscience for both synthesis and patterning.

References 1. T. F. De Greef et al., Chem. Rev. 109, 5687 (2009). 2. M. Yoshizawa, J. K. Klosterman, M. Fujita, Angew. Chem. Int. Ed. 48, 3418 (2009). 3. R. Chakrabarty, P. S. Mukherjee, P. J. Stang, Chem. Rev. 111, 6810 (2011). 4. M. Kastler, W. Pisula, D. Wasserfallen, T. Pakula, K. Müllen, J. Am. Chem. Soc. 127, 4286 (2005). 5. G. R. Whittell, M. D. Hager, U. S. Schubert, I. Manners, Nat. Mater. 10, 176 (2011). 6. J. Zhu et al., Nat. Commun. 4, 2297 (2013). 7. A. H. Gröschel et al., Nat. Commun. 3, 710 (2012). 8. L. A. Fielding et al., Chem. Sci. 4, 2081 (2013). 9. P. A. Rupar, L. Chabanne, M. A. Winnik, I. Manners, Science 337, 559 (2012). 10. T. Fukino et al., Science 344, 499 (2014).; 10.1126/ science.1252120. 11. C. Li et al., J. Am. Chem. Soc. 119, 1609 (1997). 12. Y. Ma, W. -F. Dong, M. A. Hempenius, H. Möhwald, G. J. Vancso, Nat. Mater. 5, 724 (2006). 10.1126/science.1254140

PHYSICS

Nonlinear Optics Pushed to the Edge

The edges of small flakes of atomically thin crystals become directly visible at optical wavelengths by doubling the frequency of input infrared light.

Dragomir Neshev and Yuri Kivshar

N

onlinear optics describes processes in which coherent photons change their properties, such as their frequency, when they pass through a medium. This field traces back to the demonstration of frequency doubling (1)—generating photons with twice the frequency of the input laser light—via second-harmonic generation [(SHG); see the figure, panel A]. Because SHG is a second-order parametric process, the symmetry of the medium must lack inversion symmetry (2). Interfaces between bulk (or three-dimensional) materials can meet this criterion, which has made SHG microscopy an indispensable tool for their study (3). On page 488 of this issue, Yin et al. (4) open a new dimension in second-harmonic microscopy with the optical visualization of the edge modes in two-dimensional (2D), atomically thick materials (5). These 2D materials are composed of single or a few layers of atoms or molecules and include graphene, boron nitride, and transition metal dichalcogenides such as molybdenum disulfide (MoS2). However, when the lateral dimensions of these materials are reduced to create small flakes, structural discontinuities appear at the edges and boundaries between different flakes that break inNonlinear Physics Center, Australian National University, Canberra, ACT 0200, Australia. E-mail: ysk@internode. on.net; [email protected]

plane translational symmetry. These regions support strongly localized electron states that are expected to enhance SHG. Yin et al. used second-order nonlinear optics to study the edges and boundaries of the hexagonal lattice of MoS2 atomic membranes, grown by large-scale chemical vapor deposition techniques. Previous studies have applied SHG spectroscopy to few-layer MoS2 and other 2D materials (6–9). Notably, MoS2 with an odd number of layers lacks inversion symmetry, while for an even number of layers the transverse inversion symmetry is restored. As such, the SHG signal from MoS2 with odd numbers of layers was orders of magnitude more intense than that for even numbers of layers (6–9). This method provides strong contrast between single and bilayer samples. For MoS2 structures with odd numbers of layers, the exact number of layers can also be determined from the strong variation of SHG intensity. For a monolayer of MoS2, the longitudinal phase matching (longitudinal here is in the z direction, and transverse is across the 2D plane, x and y; see the figure, panel B) is not important, and the SHG emission is emitted equally in both the forward and backward directions. However, the strength of emission strongly depends on the transverse symmetry and phase matching (10). The SHG signal also depends strongly on the orientation of the crystal. For example,

for x-polarized pump beams (see the figure, panel B), the SHG signal can have x or y polarization with powers Px2ω ≈ cos 3φ and Py2ω ≈ sin 3φ, respectively, where φ is the angle between the incident polarization and the crystal orientation (see the figure, panel C). The measurement of Px2ω and Py2ω allows the orientation of the crystallographic axes to be determined. Yin et al. performed such a nonlinear optical imaging technique that allows rapid determination of the crystal orientations at a large scale (see the figure, panel B). The presence of constructive or destructive interference of the SHG signal at the boundary between two flakes could even discriminate between two MoS2 flakes with opposite crystal orientations. This purely optical method for characterizing MoS2 requires minimal sample preparation, is noninvasive, and imposes no special environmental requirements. However, the most exciting results arise from the second-order nonlinear susceptibility being highly sensitive to extremely small changes in materials’ electronic properties. If the small MoS2 flakes possess internal energy levels resonant with either the input or SHG radiation (2), these internal resonances will show up in the SHG signal. Such small flakes can be obtained in the chemical vapor deposition process for short growth time and appear as small triangles (see the figure, panel D).

www.sciencemag.org SCIENCE VOL 344 2 MAY 2014 Published by AAAS

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PERSPECTIVES A

B

SHG image

Monolayer MoS2

|e典

ω 2ω ω

y x

|g典

C

Filter and polarizer

D

Zigzag

Armchair



φ S2 Mo 1280 nm

Although rough at the atomic scale, the edges of these monolayer islands are the more energetically favorable termination of MoS2 zigzag edges, and they appear straight and sharp under the optical microscope. These zigzag edges have localized electronic states because they break translational symmetry. As Yin et al. show in proof-of-concept calculations, these edge modes have energies just below the band gap of an infinite MoS2 monolayer. The localized electronic states enhanced in-plane nonlinear polarizability, and the resulting SHG enhancement allowed the direct optical imaging of the atomic edges. Why were Yin et al. the first to optically observe such edge states? Other groups (6–

1300 nm

9) used pump wavelengths of ~800 nm, but Yin et al. tuned their laser precisely at a twophoton resonance with the energy of the edge states, namely at ~1300 nm. They measured a well-pronounced maximum for the SHG from the edge states. Comparing the left and right images in panel D of the figure, even a detuning of 20 nm from the resonant input wavelength causes the signature of the edge states to completely disappear. Edge states play an important role in electron dynamics for the quantum Hall effect and topological insulators, and the understanding of their physics is an important goal in realizing robust topological states in both solids and optics. Optical monitoring of the dynam-

Edges do a frequency-doubled take. (A) In a second-harmonic generation (SHG) process, two photons of frequency ω (red arrows) absorbed by the ground state |g典 combine to form a high-frequency (2ω) photon (green arrow). The proximity of atomic states (or edge states |e典) to the energy 2ω of the output beam strongly enhances the generation of harmonics. (B) The SHG signal depends on the orientation of the MoS2 flakes and the incident polarization of the excitation laser. The SHG image shows flakes of different brightness (encoded with different colors) for different crystal orientations. (C) Two-dimenstional crystal orientation and incident field polarization. (D) Yin et al. show that when the energy of the two pump photons is near the SHG frequency, the harmonic is strongly enhanced, as seen in the edge modes on the right circled in white; scale bar, 20 µm.

ics of such edge states could further clarify the mechanism of electrocatalytic hydrogen evolution (11). The direct mapping of edge states by optical methods developed by Yin et al. is an important step toward these goals. The nonlinear response reveals the structural and symmetry properties of 2D atomic monolayers, and it would allow the exploration of other types of 2D crystalline structures. References 1. P. A. Franken, A. Hill, C. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961). 2. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, ed. 3, 2008). 3. Y. R. Shen, Nature 337, 519 (1989). 4. X. Yin et al., Science 344, 488 (2014). 5. K. S. Novoselov et al., Science 306, 666 (2004). 6. H. Zeng et al., Sci. Rep. 3, 1608 (2013). 7. N. Kumar et al., Phys. Rev. B 87, 161403 (2013). 8. L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, A. M. de Paula, Phys. Rev. B 87, 201401 (2013). 9. Y. Li et al., Nano Lett. 13, 3329 (2013). 10. S. M. Saltiel et al., Phys. Rev. Lett. 100, 103902 (2008). 11. T. F. Jaramillo et al., Science 317, 100 (2007). 10.1126/science.1253531

BOTANY

Limits on Yields in the Corn Belt

Increasing vapor pressure deficit and drought sensitivity will limit future corn yields in the U.S. Midwest.

Donald R. Ort1, 2 and Stephen P. Long2

I

n total global production, corn (maize, Zea mays L.) is the most important food and feed crop. Of the 967 million metric tons produced in 2013, 36.5% were produced in the United States, mostly in the Midwest Corn Belt. The United States is by far the world’s largest corn exporter, accounting for 50% of corn exports globally (1, 2). 1

Global Change and Photosynthesis Research Unit, USDA/ ARS, University of Illinios, Urbana, IL 61801, USA. 2Departments of Plant Biology & Crop Sciences, University of Illinois, Urbana, IL 61801, USA. E-mail: [email protected]

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Until recently, breeding and management have allowed farmers to increase the number of plants per acre without loss of yield per plant. On page 516 of this issue, Lobell et al. (3) use a detailed data set for farms across the Corn Belt, to show that increasing yields have been accompanied by rising drought sensitivity, with important implications for future crop yields. The data set contains yields, environmental variables, and management variables for Midwest corn fields in each year from 1995 to

2012. Lobell et al.’s analysis reveals that while corn yield has increased, drought sensitivity has also increased. This may be explained by the fact that with more plants per acre, less soil water is available to each plant. Yield was most sensitive to water vapor pressure deficit (VPD), a factor that has rarely been included in past analyses but that has major implications for yields as climate change progresses in the Corn Belt. So what is the VPD, and why is it so important to crop production? To assimilate CO2

2 MAY 2014 VOL 344 SCIENCE www.sciencemag.org Published by AAAS

Physics. Nonlinear optics pushed to the edge.

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