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      Optical imaging of strain in two-dimensional crystals

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          Abstract

          Strain engineering is widely used in material science to tune the (opto-)electronic properties of materials and enhance the performance of devices. Two-dimensional atomic crystals are a versatile playground to study the influence of strain, as they can sustain very large deformations without breaking. Various optical techniques have been employed to probe strain in two-dimensional materials, including micro-Raman and photoluminescence spectroscopy. Here we demonstrate that optical second harmonic generation constitutes an even more powerful technique, as it allows extraction of the full strain tensor with a spatial resolution below the optical diffraction limit. Our method is based on the strain-induced modification of the nonlinear susceptibility tensor due to a photoelastic effect. Using a two-point bending technique, we determine the photoelastic tensor elements of molybdenum disulfide. Once identified, these parameters allow us to spatially image the two-dimensional strain field in an inhomogeneously strained sample.

          Abstract

          Strain is an effective tool to tune the optoelectronic properties of two-dimensional materials. Here, the authors demonstrate that second harmonic generation can be used to extract the full strain tensor of MoS 2 and to spatially image its two-dimensional strain field.

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          Most cited references 53

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          Measurement of the elastic properties and intrinsic strength of monolayer graphene.

          We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.
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            Atomically thin MoS2: A new direct-gap semiconductor

            The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N = 1, 2, ... 6 S-Mo-S monolayers have been investigated by optical spectroscopy. Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure. With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 0.6 eV. This leads to a crossover to a direct-gap material in the limit of the single monolayer. Unlike the bulk material, the MoS2 monolayer emits light strongly. The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 1000 compared with the bulk material.
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              Emerging photoluminescence in monolayer MoS2.

              Novel physical phenomena can emerge in low-dimensional nanomaterials. Bulk MoS(2), a prototypical metal dichalcogenide, is an indirect bandgap semiconductor with negligible photoluminescence. When the MoS(2) crystal is thinned to monolayer, however, a strong photoluminescence emerges, indicating an indirect to direct bandgap transition in this d-electron system. This observation shows that quantum confinement in layered d-electron materials like MoS(2) provides new opportunities for engineering the electronic structure of matter at the nanoscale.
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                Author and article information

                Contributors
                thomas.mueller@tuwien.ac.at
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                6 February 2018
                6 February 2018
                2018
                : 9
                Affiliations
                ISNI 0000 0001 2348 4034, GRID grid.5329.d, Institute of Photonics, , Vienna University of Technology, ; Gußhausstraße 27-29, 1040 Vienna, Austria
                Article
                2830
                10.1038/s41467-018-02830-y
                5802795
                29410470
                © The Author(s) 2018

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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