skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

Title: Van der Waals interaction affects wrinkle formation in two-dimensional materials
Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer “bubbles” in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical “Winkler foundation” model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ; ; ; ; ;
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Stacking layers of atomically thin transition-metal carbides and two-dimensional (2D) semiconducting transition-metal dichalcogenides, could lead to nontrivial superconductivity and other unprecedented phenomena yet to be studied. In this work, superconducting α-phase thin molybdenum carbide flakes were first synthesized, and a subsequent sulfurization treatment induced the formation of vertical heterolayer systems consisting of different phases of molybdenum carbide—ranging from α to γ′ and γ phases—in conjunction with molybdenum sulfide layers. These transition-metal carbide/disulfide heterostructures exhibited critical superconducting temperatures as high as 6 K, higher than that of the starting single-phased α-Mo 2 C (4 K). We analyzed possible interface configurations to explain the observed moiré patterns resulting from the vertical heterostacks. Our density-functional theory (DFT) calculations indicate that epitaxial strain and moiré patterns lead to a higher interfacial density of states, which favors superconductivity. Such engineered heterostructures might allow the coupling of superconductivity to the topologically nontrivial surface states featured by transition-metal carbide phases composing these heterostructures potentially leading to unconventional superconductivity. Moreover, we envisage that our approach could also be generalized to other metal carbide and nitride systems that could exhibit high-temperature superconductivity. 
    more » « less
  2. Continuum mechanics break down in bending stiffness calculations of mono- and few-layered two-dimensional (2D) van der Waals crystal sheets, because their layered atomistic structures are uniquely characterized by strong in-plane bonding coupled with weak interlayer interactions. Here, we elucidate how the bending rigidities of pristine mono- and few-layered molybdenum disulfide (MoS 2 ), graphene, and hexagonal boron nitride (hBN) are governed by their structural geometry and intra- and inter-layer bonding interactions. Atomic force microscopy experiments on the self-folded conformations of these 2D materials on flat substrates show that the bending rigidity of MoS 2 significantly exceeds those of graphene or hBN of comparable layers, despite its much lower tensile modulus. Even on a per-thickness basis, MoS 2 is found to possess similar bending stiffness to hBN and is much stiffer than graphene. Density functional theory calculations suggest that this high bending rigidity of MoS 2 is due to its large interlayer thickness and strong interlayer shear, which prevail over its weak in-plane bonding. 
    more » « less
  3. Abstract

    Lengenbachite is a naturally occurring layered mineral formed with alternating stacks of two constituent PbS-like and M2S3-like two-dimensional (2D) material layers due to the phase segregation process during the formation. Here, we demonstrate to achieve van der Waals (vdW) heterostructures of lengenbachite down to a few layer-pair thickness by mechanical exfoliation of bulk lengenbachite mineral. The incommensurability between the constituent isotropic 2D material layers makes the formed vdW heterostructure exhibit strong in-plane structural anisotropy, which leads to highly anisotropic optical responses in lengenbachite thin flakes, including anisotropic Raman scattering, linear dichroism, and anisotropic third-harmonic generation. Moreover, we exploit the nonlinear optical anisotropy for polarization-dependent intensity modulation of the converted third-harmonic optical vortices. Our study establishes lengenbachite as a new natural vdW heterostructure-based 2D material with unique optical properties for realizing anisotropic optical devices for photonic integrated circuits and optical information processing.

    more » « less
  4. Abstract The design and formation of van der Waals (vdW) heterostructures with different two-dimensional (2D) materials provide an opportunity to create materials with extraordinary physical properties tailored toward specific applications. Mechanical exfoliation of natural vdW materials has been recognized as an effective way for producing high-quality ultrathin vdW heterostructures. Abramovite is one of such naturally occurring vdW materials, where the superlattice is composed of alternating Pb 2 BiS 3 and SnInS 4 2D material lattices. The forced commensuration between the two incommensurate constituent 2D material lattices induces in-plane structural anisotropy in the formed vdW heterostructure of abramovite, even though the individual 2D material lattices are isotropic in nature. Here, we show that ultrathin layers of vdW heterostructures of abramovite can be achieved by mechanical exfoliation of the natural mineral. Furthermore, the structural anisotropy induced highly anisotropic vibrational and optical responses of abramovite thin flakes are demonstrated by angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent third-harmonic generation. Our results not only establish abramovite as a promising natural vdW material with tailored linear and nonlinear optical properties for building future anisotropic integrated photonic devices, but also provide a deeper understanding of the origin of structural, vibrational and optical anisotropy in vdW heterostructures. 
    more » « less
  5. Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in plant leaves and animal epithelia and perhaps even the formation of human fingerprints. We elucidate a primary source of this morphological complexity—an incompatibility between an elastically favored “microstructure” of uniformly spaced wrinkles and a “macrostructure” imparted through the wrinkle director and dictated by confinement forces. Our theory is borne out of experiments and simulations of floating sheets subjected to radial stretching. By analyzing patterns of grossly radial wrinkles we find two sharply distinct morphologies: defect-free patterns with a fixed number of wrinkles and nonuniform spacing and patterns of uniformly spaced wrinkles separated by defect-rich buffer zones. We show how these morphological types reflect distinct minima of a Ginzburg–Landau functional—a coarse-grained version of the elastic energy, which penalizes nonuniform wrinkle spacing and amplitude, as well as deviations of the actual director from the axis imposed by confinement. Our results extend the effective description of wrinkle patterns as liquid crystals [H. Aharoniet al.,Nat. Commun.8, 15809 (2017)], and we highlight a fascinating analogy between the geometry–energy interplay that underlies the proliferation of defects in the mechanical equilibrium of confined sheets and in thermodynamic phases of superconductors and chiral liquid crystals.

    more » « less