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Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional Van Der Waals Interfaces

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Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional Van Der Waals Interfaces pubs.acs.org/NanoLett Letter Stochastic Stress Jumps Due to Soliton Dynamics in Two- Dimensional van der Waals Interfaces SunPhil Kim, Emil Annevelink, Edmund Han, Jaehyung Yu, Pinshane Y. Huang, Elif Ertekin, and Arend M. van der Zande* Cite This: https://dx.doi.org/10.1021/acs.nanolett.9b04619 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simu- lations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 μm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines. KEYWORDS: Solitons, Dislocation, Graphene, NEMS, Nanomechanics, Nonlinear Mechanics he atomic-scale thickness of two-dimensional (2D) interfaces are superlubric,14,22 allowing free sliding between T materials like graphene and molybdenum disulfide, layers. Interlayer solitons are mobile, creating and annihilating combined with their high mechanical strength and flexibility, themselves at high temperatures,23 under electrostatic field,24 and excellent electronic properties, open up new opportunities by a local mechanical stress,25,26 and their presence leads to for low power, highly tunable, and highly sensitive nano- changes in local electrical21 and optical20 states. These solitons − electromechanical systems.1 4 Examples include speakers and should affect the mechanical properties of the membranes, yet 5,6 See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. ffi Downloaded via UNIV ILLINOIS URBANA-CHAMPAIGN on January 27, 2020 at 19:24:26 (UTC). microphones from atomic membranes, highly tunable are di cult to measure because of their discrete nature and the filters,7 oscillators,8 mass/force sensors,9,10 and piezotronics.11 lack of techniques to deterministically manipulate them. For In many cases, micro and nanoelectromechanical systems need example, interlayer shear stress has been measured in bilayer more than one layer to connect mechanics to transduction.12 graphene with a pressurized bubble test.27 Similarly, the For example, in 2D material heterostructures, there are now inelastic slip between layers in 2D multilayers and hetero- many emerging technologies being explored utilizing mechan- structures have been observed through nanoindentation − ical deformations ranging from twistronics13 15 to origami studies, leading to a lower effective elastic modulus28,29 and bimorph nanomachines16 to deformable electronics from conductance modulations.30 Due to the large forces and low bent17 or crumpled membranes.18 In these structures, the sensitivity, these studies probe the continuum level of many weak interlayer bonding and stacking orientation at the van der dislocations. Due to their low mass and high tunability, Waals (vdW) interface dramatically affect the mechanics of 2D resonators from 2D materials are exceptionally responsive to membranes and electromechanical coupling, providing a new degree of freedom for engineering 2D mechanical systems. For Received: November 8, 2019 example, commensurate graphene layers relax interfacial Revised: January 14, 2020 stresses through the presence of solitons, local changes in Published: January 16, 2020 stacking registry from AB to BA (also known as dislocations or − domain walls),19 21 while twisted or incommensurate © XXXX American Chemical Society https://dx.doi.org/10.1021/acs.nanolett.9b04619 A Nano Lett. XXXX, XXX, XXX−XXX Nano Letters pubs.acs.org/NanoLett Letter perturbations and are being explored as ultrahigh sensitive mass and force sensors.10,31 Here, we utilize this intrinsic sensitivity to probe the mechanics of 2D interfaces directly and detect the creation and annihilation of a single soliton in bilayer graphene. In this study, we probe the influence of solitons on the mechanics of 2D membranes by directly comparing the electrostatic tuning of resonance frequency in nanoelectro- mechanical drumhead resonators from CVD grown monolayer graphene (MLG) and commensurate, Bernal stacked bilayer graphene, twisted bilayer graphene, and few-layer graphene. We observe new behaviors in the Bernal stacked bilayer graphene of sudden stochastic jumps in the resonance frequency tuning, which can be either positive or negative, are irreversible and whose magnitude is independent of the initial or electrostatically induced stress of the membrane. Using atomistic simulations, we establish a theory that relates these frequency jumps to changes in stress, resulting from stochastic slip events during the creation and annihilation of solitons. Supporting this theory, twisted bilayer graphene resonators, which have been shown to have superlubric interfaces,14,22 show no evidence of frequency jumps, while few-layer graphene resonators show many frequency jumps. We develop a simple model relating the magnitude of the Figure 1. Structure of the 2D material atomic membrane drumhead stress induced by soliton dynamics across length scales, ranging resonator. (a) Schematic drawing of a suspended 2D membrane from <0.01 N/m for the measured 5 μm diameter to ∼1.2 N/ circular drumhead resonator and the electronic actuation and optical m for the 38.7 nm simulations. These results demonstrate the detection scheme. The suspended membrane is electrostatically sensitivity of 2D resonators is sufficient to probe the nonlinear actuated, while the mechanical motion is detected by dynamic changes in reflection. (b) An optical image of a Bernal stacked bilayer mechanics of single dislocations in an atomic membrane and graphene (BS-BLG) membrane suspended as a 5 μm circular provide a model to understand the nonlinear mechanics of drumhead. The crystal structure is the inset. (c) Raman spectra of different kinds of van der Waals interfaces under stress. monolayer graphene (MLG, black) and Bernal Stacked bilayer Figure 1a shows a schematic of the 2D material resonators graphene (BS-BLG, red), corresponding with the black and red used in this study as well as the electrical circuit used for points indicated in panel b. (d) First fundamental resonance of BS- V μ V actuation and tuning. Figure 1b shows a corresponding optical BLG at g = 2.4 V, laser power = 50 W, and RF = 1 mV. image of one such resonator made from BS-BLG. To fabricate the resonators, 2D atomic membranes composed of monolayer narrow Lorentzian line shape of the 2D peak with fwhm = 28.6 graphene (MLG), Bernal stacked (commensurate) bilayer cm−1, and a 2:1 ratio of 2D to G peak intensities.34 In contrast, graphene (BS-BLG), twisted (incommensurate) bilayer the bilayer shows a reduction in 2D band intensity (2D to G ≅ graphene (T-BLG), and few-layer graphene (FLG) are 1) and a wider 2D peak width, typical of a commensurate transferred and suspended over circular holes with a 5 μm bilayer (BS-BLG).34 Figures S2 and S3 compare the diameter and a depth of 230 nm in a 285 nm thick silicon spectroscopic characterization of T-BLG and FLG, respec- oxide layer on a degenerately doped silicon substrate (Figure tively, and Figure S4 compares the AFM topography for each S1). The transferred layer is then electrically contacted by membrane type. evaporating Cr/Au through a shadow mask (see Supporting To probe the mechanical resonance of the graphene Information, Section 1). We use bilayer and few-layer graphene drumhead resonators, we utilize established electrostatic − islands grown by chemical vapor deposition.32 Previous studies actuation and optical detection techniques,35 37 shown in have shown these bilayer islands may be either Bernal stacked Figure 1a and detailed in the Supporting Information, Section or twisted, and the Bernal stacked layers contain a higher 1. Figure 1d shows the first fundamental mode of the BS-BLG fi V density of solitons when compared with exfoliated sam- resonator from Figure 1b with the Lorentz t (red) at g = 2.4 ples.19,23,33 The use of as-grown bilayer graphene ensures the V. The resonance frequency and the quality factor are 18.2 interface will be atomically clean. In total, we measured 10 MHz and 42, respectively, similar to other 2D material resonators including two monolayer graphene (MLG) and drumhead resonators.1,7,38 three commensurate, Bernal stacked bilayer graphene, two In Figures 2a,b, we compare the electrostatic tuning twisted bilayer graphene, and
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