Letter pubs.acs.org/NanoLett
Dynamic Optical Tuning of Interlayer Interactions in the Transition Metal Dichalcogenides Ehren M. Mannebach,† Clara Nyby,‡ Friederike Ernst,§,# Yao Zhou,† John Tolsma,∥ Yao Li,§ Meng-Ju Sher,⊥,∓ I-Cheng Tung,∇ Hua Zhou,∇ Qi Zhang,∇ Kyle L. Seyler,○ Genevieve Clark,○ Yu Lin,⊥,◆ Diling Zhu,¶ James M. Glownia,¶ Michael E. Kozina,§,⊥ Sanghoon Song,¶ Silke Nelson,¶ Apurva Mehta,¶ Yifei Yu,□ Anupum Pant,△ Ozgur Burak Aslan,§ Archana Raja,§,# Yinsheng Guo,▽ Anthony DiChiara,∇ Wendy Mao,⊥,#,◆ Linyou Cao,□ Sefaattin Tongay,△ Jifeng Sun,⬡ David J. Singh,⬡ Tony F. Heinz,§,⊥,# Xiaodong Xu,○ Allan H. MacDonald,∥ Evan Reed,†,# Haidan Wen,∇ and Aaron M. Lindenberg*,†,⊥,# †
Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States Department of Chemistry, Stanford University, Stanford, California 94305, United States § Department of Applied Physics, Stanford University, Stanford, California 94305, United States ∥ Department of Physics, University of Texas, Austin, Austin, Texas 78712, United States ⊥ Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States ∓ Department of Physics, Wesleyan University, Middleton, Connecticut 06459, United States # PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States ∇ Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States ○ Department of Physics, University of Washington, Seattle, Washington 98195, United States ◆ Department of Geological Sciences, Stanford University, Stanford, California 94305, United States ¶ SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States □ Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States △ School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, Arizona 85287, United States ▽ Department of Chemistry, Columbia University, New York, New York 10027, United States ⬡ Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211-7010, United States ‡
S Supporting Information *
ABSTRACT: Modulation of weak interlayer interactions between quasi-twodimensional atomic planes in the transition metal dichalcogenides (TMDCs) provides avenues for tuning their functional properties. Here we show that abovegap optical excitation in the TMDCs leads to an unexpected large-amplitude, ultrafast compressive force between the two-dimensional layers, as probed by in situ measurements of the atomic layer spacing at femtosecond time resolution. We show that this compressive response arises from a dynamic modulation of the interlayer van der Waals interaction and that this represents the dominant lightinduced stress at low excitation densities. A simple analytic model predicts the magnitude and carrier density dependence of the measured strains. This work establishes a new method for dynamic, nonequilibrium tuning of correlation-driven dispersive interactions and of the optomechanical functionality of TMDC quasi-two-dimensional materials. KEYWORDS: 2D materials, interlayer van der Waals interactions, ultrafast, Casimir effect, femtosecond X-ray scattering
T
ransition metal dichalcogenide materials exhibit a host of novel optoelectronic functionalities in the monolayer limit, including the emergence of a direct band gap,1 piezoelectric response,2 nonlinear optical properties,3 and valley selection rules.4 In the few-to-multilayer limit, the relatively weak interlayer coupling provides new means of © 2017 American Chemical Society
Received: September 14, 2017 Revised: November 7, 2017 Published: November 9, 2017 7761
DOI: 10.1021/acs.nanolett.7b03955 Nano Lett. 2017, 17, 7761−7766
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Nano Letters modulating and controlling their electronic band structure, optoelectronic properties, and atomic-scale structure through intercalation, pressure, temperature, and stacking of layers.5−8 van der Waals forces that determine the interlayer spacing arise from correlated fluctuating dipoles coupled by electromagnetic fields between the atomic planes and are closely related to Casimir forces in which dressed photon states lead to attractive forces driven by quantum fluctuations. A general theory by Lifshitz describes both effects.9,10 In particular, this interaction depends upon how fields are screened at each layer (or equivalently, on the frequency-dependent layer conductivity). A number of experimental and theoretical efforts in recent years have focused on attempts to tune and engineer the Casimir interaction through modification of material dielectric functions with both attractive and repulsive interactions possible in the retarded and nonretarded limits.11−17 Mechanisms by which the Casimir interaction can be tuned18,19 and its behavior in the nonequilibrium or excited state limit, where direct comparison between experiment and theory is difficult to achieve,20 are topics of current interest. In this work, femtosecond-resolution X-ray scattering techniques are used to record optically induced changes in interlayer spacing as a direct and in situ probe of the effective time-dependent interlayer pressure. In contrast to expected thermally induced expansive effects, we find that carrier excitation leads to large-amplitude compressive strains with this response representing the dominant contribution to the interlayer coupling at low light excitation densities. We show that this effect is observable within most of the prototypical TMDC materials known today, including MoS2, MoSe2, MoTe2, and WSe2, with peak observed pressures approaching 0.1 GPa. We further show that a simple analytical model based on a carrier-induced modulation of the dielectric function quantitatively matches the experimental trends and results and is supported by a more detailed many-body treatment. Our study thus demonstrates ultrafast all-optical modification of the near-field Casimir/van der Waals interaction and of the associated interlayer spacing in van der Waals materials. Measurements were carried out at the Linac Coherent Light Source, the Stanford Synchrotron Radiation Laboratory, and the Advanced Photon Source using focused hard X-ray beams to probe single TMDC domains/flakes. See the Supporting Information for further details regarding the different experimental setups. Figure 1a shows a schematic of the pump−probe geometry used in this study in which an abovebandgap optical pulse from a femtosecond laser excites a singlecrystal TMDC flake which is then probed by a femtosecond Xray pulse. Figure 1b shows a series of diffraction images from the (004) Bragg peak of MoS2 at several different pump−probe time delays for an absorbed pump fluence of 20 mJ/cm2 (see Supplementary Movie 1 for the full sequence). Analysis of the center-of-mass motion of the diffracted spot enables extraction of the interlayer d-spacing with quantitative details on this analysis in the Supporting Information.21 The thickness of each flake was measured from the thickness fringes, seen as satellite peaks in the diffraction patterns in Figure 1 and Figure S7, and was confirmed by atomic force microscopy. Figure 2a shows the extracted time-dependent interlayer strain along the c-axis, ηc, in a 50 nm MoS2 sample for absorbed fluences of 0.3 mJ/cm2 and 20 mJ/cm2. In these measurements, the strain is directly extracted from the shift in peak position: ΔQ ηc = − Q . Immediately after excitation, instead of thermally
Figure 1. Schematics of the time-resolved experiment and data collection. (A) Schematic showing the optical pump/X-ray probe experimental setup wherein a TMDC flake is probed by an X-ray pulse (black) following ultrafast above-bandgap optical excitation (red). Changing the carrier density via optical excitation increases the magnitude of the attractive interlayer van der Waals forces. (B) Diffraction images of the (004) Bragg spot of MoS2 at selected probe delay times for an absorbed pump fluence of 20 mJ/cm2. The vertical direction corresponds to the momentum transfer Qz in units of Å−1. (C) The thickness of the sample can be extracted from the spacing of the thickness fringes that lie along the Qz direction: d = 2π/ΔQz.
expanding the MoS2 layers initially and transiently compress. In Figure 1b, this effect appears at short times as a deflection of the diffraction peak center of mass to higher momentum transfer Qz at a probe delay time of ∼10 ps. We observe a similar compressive effect in MoSe2, MoTe2, and WSe2 (Supporting Information, Figure S8). In contrast, at low fluences we find that this compressive response dominates over any thermal effect (Figure 2a, bottom panel). Also observed is a coherent breathing mode response where the period of oscillation is determined by the acoustic round trip time in the flake.22 Under the assumption that the mechanically exfoliated domain is weakly bound to the surface (determined by the van der Waals gap between the flake and substrate), this period is simply 2d/v, where d is the overall thickness of the flake, and v is the longitudinal sound velocity in the cross-plane direction.23 In MoS2, we extract an interlayer speed of sound of 7762
DOI: 10.1021/acs.nanolett.7b03955 Nano Lett. 2017, 17, 7761−7766
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expansion effects, which scale linearly with pump fluence but turn on after the initial compressive ones. This is consistent with an electronic, nearly instantaneous origin for the compressive stress, in contrast to a thermal stress which would develop on electron−phonon coupling time-scales of order a few picoseconds.29,30 Further support for an electronic origin of the compressive feature is found by comparing the lifetime of the compressive response at low fluences, a few hundred picoseconds in MoS2, to time-domain terahertz spectroscopic measurements of the lifetime of photoexcited carriers, where good agreement is obtained between the two (Figure 3a). Both the terahertz (THz) studies and the X-ray
Figure 3. Comparison of the free-carrier lifetime with the lifetime of the optically induced compressive effect. Normalized transient THz transmission following optical pumping (top) and transient interlayer strain (bottom) in MoS2 (A) and ReS2 (B); note the difference in time scales. Decreased THz transmission corresponds to an increase in the density of free carriers. The time-resolution of the X-ray measurements in (A, bottom) is ∼50 ps. The inset in (B, bottom) shows the longertime response in ReS2 at a higher pump fluence. In the top panels, the open circles are data points, and solid lines are exponential fits to the data. In MoS2, the lifetime of the compressive strain follows the response time seen in the THz transmission measurements determined by the free carrier population. In ReS2, the free carrier lifetime is not long enough to induce a measurable compressive strain; only a thermal expansive strain is seen.
Figure 2. Photoinduced strain effects in exfoliated MoS2. (A) Interlayer strain in MoS2 following above-bandgap optical pumping. The bottom panel shows the gray shaded region of the top panel. In MoS2 (as well as MoSe2, MoTe2, and WSe2, see Figure S3), the material initially compresses (ηc, σc < 0) following photoexcitation before thermally expanding. Echoes of the compressive response can be seen every ∼40 ps in MoS2, corresponding to an acoustic breathing of the 50 nm thick flake. The right axis shows the effective stress needed to achieve the experimentally measured strains. The inset shows a representative histogram of the spread of strains measured at each delay point, showing the effective sensitivity of the measurement. Error bars on the measurement are indicated by the shaded regions. (B) The fluence dependence of the compressive strain in MoS2 shows a nonlinear response, scaling roughly as the square root of the carrier density/pump fluence. The black points are experimental values, and the red dashed line is the result of the analytical model of the compressive strain described by eq 1. See the Supporting Information for discussion of the calculation of the error bars.
studies show a lifetime that depends on the carrier density, as would be expected for Auger-type relaxation processes (Supporting Information Figure S10). In contrast, multilayer ReS2, a direct band gap material where the free carrier lifetime is much shorter (∼1.5 ps) such that the applied electronic stress turns off almost instantaneously, does not exhibit the nonlinear compressive response observed in the Mo- and Wdichalcogenides (Figure 3b). Taken together, these observations consistently imply a carrier-driven electronic origin for the compressive response. To obtain an understanding of the electronically driven compressive strain associated with a modification of the interlayer bonding forces, we consider from a microscopic perspective how the attractive van der Waals forces responsible for this interaction depend on carrier density. Lifshitz developed a theory in which the force between two thick slabs separated by a distance l is related to their frequencydependent dielectric functions. The Casimir interaction represents a special case of this theory valid for the limit of
∼2500 m/s, in agreement with previous measurements obtained from the bulk C33 elastic constant.24 We note that prior theoretical studies have pointed toward the possibility for compressive features in quasi-2D systems under direct vibrational excitation25 and previous experimental studies have indicated possibilities for compressive responses in other van der Waals bonded materials at high excitation fluences.26−28 The fluence dependence of the compressive effect (Figure 2b) is strongly sublinear, even down to the lowest measured pump fluences of ∼5 μJ/cm2, corresponding to induced carrier densities of ∼1018 cm−3 and extending over approximately 3 orders of magnitude in fluence. At higher pump fluences, the initial transient compressive feature is dominated by thermal 7763
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Figure 4. Comparison of the simulated average strain with the measured strain in MoS2. Simulated strain profiles in a 50 nm MoS2 flake with carrier densities of 2 × 1020 cm−3 (A) and 1022 cm−3 (B), corresponding to the pump fluences in Figure 2a. Blue shading corresponds to compression, while red corresponds to rarefaction. (C) Time-dependent average strains in the MoS2 flake, where the left and right panels correspond to the low and high carrier densities, respectively, comparing experiment to the theoretical Lifshitz model described in the text.
large l and perfect metal slabs. In the limit of small spacing between two plates, the effective pressure predicted by this theory can be written as ΔF =
ℏ 8π 2l 3
∫0
2 − 1⎞ ⎜ ⎟ dξ ⎝ ε(iξ) + 1 ⎠
why the electronic effect dominates over the usual thermal response (scaling linearly with n) at low carrier densities. More detailed first-principles models, including both interband and intraband excitations and the full dielectric function, give similar behavior with carrier density, as described in the Supporting Information. This suitably defined Lifshitz model has been found to give vdW interaction energy to within 8−20% of the adiabatic-connection fluctuation−dissipation theorem within random phase approximation (ACFDT-RPA) calculations for a variety of layered semiconducting heterostructures.33 DFTbased approaches modeling the vdW interaction in MoSe2 using the method of ref 33 further support the arguments made here, showing that the attractive contribution arising from the electronic polarizability dominates over expansive effects that would arise from excitation into antibonding orbitals. Finally, a many-body calculation described in the Supporting Information shows from a different perspective how quantum fluctuations between optically excited electrons and holes lead to compressive effects. It also quantifies the role of near field effects neglected in the Lifshitz approximation that are expected to become important when the layer separation is small compared to the carrier Fermi wavelength. This more detailed treatment (see in particular equation S19) yields eq 2 above at small Fermi wavelengths (up to a factor of 2/π) and further confirms the basic physical model presented above. Further support for this model can be obtained by considering the balance between the electronic and thermal contributions. One can write the net light-induced, timedependent interlayer stress as the sum of two terms representing the electronic (σe) and thermal (σth) pressures with σe = −α√n and σth = C33αcΔT = C33αc(ℏω − Eg)n/C. Here, α is the prefactor in eq 2, C33 is the interlayer elastic constant, αc is the c-axis thermal expansion coefficient, ΔT is the photoinduced temperature jump, ℏω − Eg is the photon energy minus the band gap (i.e., the excess photon energy), and C is the specific heat. Assuming the sample is homogeneously pumped, the time-dependent stress at short times can then be written as
∞ ⎛ ε(iξ)
(1)
where ε is the frequency dependent dielectric function evaluated at complex values, ℏ is the reduced Planck constant, and the integral is over all frequencies.9,12 Although this model is not intended to be accurate for atomic scale separations, comparison with more detailed models based on electronic structure calculations suggests that it captures the essential physics of the response for some semiconducting 2D materials.31 As a simple approximation to simulate our experimental conditions, we assume a Drude model for the dielectric function, ε(iξ) = 1 +
ωp2 ξ(ξ + γ )
, where ωp is the plasma
frequency (proportional to the square root of the photoexcited carrier density n), and γ is the Drude damping term. The timedomain THz conductivity measurements support this assumed Drude-like response of the photoexcited electron gas.32 Previous studies investigating modifications to the Casimir force driven by doping or other modifications of the dielectric constants have used similar approaches.11−13 In this approximation, the integral in eq 1 can be evaluated analytically. The Supporting Information has further details on this calculation. In the limit ωp ≫ γ, which is relevant for our experimental conditions, this effective pressure can be written as ΔF(n) ≈
ℏωp 32 2 πl 3
=
ℏe n 32 2mϵ0 πl 3
(2)
where m is the effective mass of the electron gas, and ϵ0 is the vacuum permittivity. Evaluation of this expression based on the Mo-to-Mo layer separation l = 6.2 Å gives pressures of order 10 MPa at a carrier density of n = 1021 cm−3. To compare with the experimental data, we make use of the known absorption coefficients of the materials to convert the applied pump fluence into a carrier concentration. We then calculate the strain induced by the electronic force using the interlayer bulk modulus. In this approximation, only nearest layer interactions are considered, a reasonable approximation given the 1/l3 scaling of the force. As can be seen in Figure 2b (dashed line) for MoS2, good quantitative agreement in both magnitude and carrier-density dependence is achieved despite the simplicity of this model. Moreover, the n1/2 scaling explains
σ(t ) ∝ −α n H(t ) + βnH(t )(1 − e−t/ τep)
(3)
where β = C33αc(ℏω − Eg)/C, H(t) is the Heaviside step function representing an instantaneous turn-on of the free carrier population, and τep is the effective electron−phonon coupling time which gives rise to the observed delayed onset of the thermal response. This simple model accurately predicts the experimentally observed crossover fluence, FT, at which the 7764
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transmission measurements were performed on a separate apparatus with a 960 Hz laser chopped at 480 Hz. The optical pump parameters were 40 fs pulses at 650 nm (1.9 eV) from an optical parametric amplifier driven by an amplified Ti:sapphire laser at the Linac Coherent Light Source (LCLS), 2 ps pulses at 400 nm (3.1 eV) from a frequency-doubled Ti:sapphire laser at the Advanced Photon Source (APS), 500 fs pulses at 515 nm (2.4 eV) from a frequency-doubled Yb-doped fiber laser at the Stanford Synchrotron Radiation Lightsource (SSRL), and 100 fs pulses at 400 nm from a frequency-doubled Ti:sapphire laser for the THz transmission measurements. The polarization of the pump light was in the plane of the X-ray scattering. The pump beam was roughly collinear with the probe beam for the LCLS, SSRL, and THz transmission measurements and was perpendicular to the probe beam for the APS experiments. Time-resolved diffraction experiments were carried out at the X-ray Pump−Probe (XPP) instrument at LCLS at beamline 14ID-B at APS and at beamline 10-2 at SSRL. All measurements were performed in a vertically scattering geometry. The LCLS experiments used 9.5 keV photons at a repetition rate of 120 Hz and the Cornell-SLAC Pixel Array Detector (CS-PAD). The APS experiments used 12 keV photons at a repetition rate of 1 kHz and a gated Pilatus 100 K detector. The SSRL experiments used 15 keV photons at a repetition rate of 1.28 MHz and a gated Pilatus 100 K detector. All X-ray probes were monochromatized to a bandwidth of a few electronvolts and focused onto the sample to probe a single domain TMDC flake. THz pulses were generated via a two-color laser-induced gas plasma. The THz beam transmitted through the samples was detected by electro-optic sampling in a 1 mm thick ZnTe crystal. A lock-in amplifier was used to record the differential signal changes of the transmitted THz beam induced by photoexcitation. These measurements average over many flakes in contrast to the X-ray probes.
thermal and electronic effects become comparable in magnitude, determined quantitatively in terms of the above coefficients by FT =
α 2ℏω β 2αA
∼ 100 μJ/cm2, where αA is the
optical absorption coefficient. Following this time-dependent stress, the film responds by launching strain waves from the free 1 and buried interfaces of the form ε(z , t ) = ρv 2 σ(t − z /v).34 A more detailed model presented in the Supporting Information predicts how these strain waves are reflected at both the free and buried interfaces with the observed period 2d/v signifying a quasi-free surface at the substrate interface, in agreement with recent studies of exfoliated flakes van der Waals bonded to a substrate.35 The results of this second model are shown in Figure 4 with good agreement to experimental results. We note that additional modifications to the repulsive part of the interlayer potential and to interlayer orbital hybridization may also be occurring under carrier excitation; separation of these effects from the modulations discussed above is the subject of future work. Carrier/exciton diffusion processes are not likely to play a significant role in the observed response given the quasi-homogeneous excitation conditions used here. Additionally, one can rule out the role of radiation pressure effects or other related stresses which only act during the presence of the incident electromagnetic wave, in contrast to the above considered carrier-induced stresses which stay on for time-scales corresponding to recombination/trapping timescales. In summary, we demonstrate that light can be used to tune interlayer van der Waals/Casimir interactions in quasi-twodimensional transition metal dichalcogenides on ultrashort time scales. This arises from a strong carrier-driven modulation in the polarizability, which leads to attractive interlayer bonding, increasing this interaction strength. The square rootlike scaling with fluence corresponds to an effectively divergent response function (with increasing slope at low carrier densities) and potentially enables new opportunities for nano-optomechanical devices driven by low light excitation densities.25 For example, in a TMDC structure with volume of order a few nm3 a single absorbed photon is predicted to generate an effective compressive strain of ∼0.1−1% and enable new optical means for modifying band structures and associated electronic properties. In addition to the pulsed excitation used here, an additional direction for exploration may involve photoexcitation in the continuous wave limit for tuning 2D layer interactions. Optical control of the van der Waals interaction may also open up new means of optically modulating exciton transfer processes governed by resonant energy transfer.36 Finally, measurements in a tailored heterostructure architecture with stacked layers of different dielectric functions may enable the observation of the converse effect, namely carrier-induced repulsive interlayer interactions, opening new means for dynamic optical tuning of nanoscale stiction effects. Methods. Samples were prepared via mechanical exfoliation from bulk crystals onto c-axis sapphire substrates. The thickness of each flake was measured from the thickness fringes, seen as satellite peaks in the diffraction patterns in Figure 1 and Figure S7, and was confirmed by atomic force microscopy. The thicknesses of the flakes investigated were between 30−150 nm. For all experiments, the samples were pumped above their optical band gaps. The repetition rates of the pump lasers in the time-resolved diffraction measurements were matched to the repetition rate of the relevant X-ray source; the THz
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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.7b03955. First-principles modeling of the vdW interaction; electron−hole fluid superlattice model of compressive strain; analytical Lifshitz model; extraction of strain from time-dependent diffraction images; response of other TMDCs; THz conductivity measurements; acoustic model (PDF) Full sequence of diffraction images from the (004) Bragg peak of MoS2 at several different pump−probe time delays (AVI)
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (A.M.L.)
[email protected]. Phone: 650-725-2640. ORCID
Ehren M. Mannebach: 0000-0002-1236-187X Yu Lin: 0000-0001-5174-9546 Michael E. Kozina: 0000-0002-4747-345X Apurva Mehta: 0000-0003-0870-6932 Linyou Cao: 0000-0002-7834-8336 Sefaattin Tongay: 0000-0001-8294-984X Aaron M. Lindenberg: 0000-0003-3233-7161 7765
DOI: 10.1021/acs.nanolett.7b03955 Nano Lett. 2017, 17, 7761−7766
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E.M., C.N., F.E, M.S., I.T., H.Z., Q.Z., K.S., Y.L., D.Z., J.G., M.K., S.S., S.N., A.M., A.D., W.M., T.H., X.X., H.W., and A.L. carried out the experiments. Y.Z., J.T., Y.L., A.H.M., E.R., J.S., D.J.S., and A.L. carried out the theoretical work. K.S., G.C., Y.Y., A.P., O.A., A.R., Y.G., L.C., S.T., and X.X. were responsible for sample growth. A.L. conceived the experiment. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under contract DE-AC02-76SF00515. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Use of BioCARS was also supported by the National Institute of General Medical Sciences of the National Institutes of Health under Grant R24GM111072. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The time-resolved setup at Sector 14 was funded in part through a collaboration with Philip Anfinrud (NIH/NIDDK). C.N. acknowledges support from the NSF through a Graduate Research Fellowship (DGE114747). F.E. gratefully acknowledges Grant LPDS 2013-13 from the German National Academy of Sciences Leopoldina. I.T., Q.Z., K.S., G.C., X. X., and H.W. acknowledge the support from the Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-SC0012509. D.J.S. and J.S. acknowledge support from the Department of Energy, Office of Science, Computational Materials Science Program, MAGICS Center, award DE-SC0014607. S.T. acknowledges funding from DMR 1552220.
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DOI: 10.1021/acs.nanolett.7b03955 Nano Lett. 2017, 17, 7761−7766
