Precise measurement of the configurational energy of bent graphene membranes via three-dimensional force field spectroscopy
Precise measurement of the configurational energy of bent graphene membranes via three-dimensional force field spectroscopy
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通过三维力场光谱精确测量弯曲石墨烯膜的构型能
DOI：
10.1103/physrevb.104.085407
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发表时间：
2021
影响因子：
3.7
通讯作者：
and Roland Wiesendanger
中科院分区：
文献类型：
--
作者：
1.Makoto Ashino;Keita Nishioka;Keiji Hayashi;and Roland Wiesendanger
原子级薄膜的弯曲变形由弯曲刚度和高斯模量决定。在单原子厚的石墨烯膜中，这两个参数需要通过弯曲引起的拓扑结构变化和电子轨道之间的相互作用来确定，这超出了现有的平面石墨烯研究。在这里，我们采用原子力显微镜证明，配置（应变）的能量可以成功地进行评估的基础上，通过三维分析的原子间的吸引力与亚原子分辨率的表面几何形状的变化。一个二次关系的粘附能与单层曲率的滚动和展开的石墨烯导致的发现，探针尖端可以检测空间变化的表面电位由于再杂交效应和弯曲引起的下一个邻居跳跃的变化。尖端诱导的局部应变内石墨烯被发现产生拓扑缺陷，独立于面内拉伸。它们的能量分析和与局部曲率的关系揭示了Helfrich哈密顿量的适用性，并确定了弯曲刚度和高斯模量。在蜂窝晶格的中空部位处评估的那些与各向同性弹性属性一致。在位于尖端诱导凸点的最高中心的一个非均匀碳原子处观察到的非常大的负高斯模量，为由于高斯曲率的拓扑缺陷和几何势引起的电荷不均匀性之间的吸引力相互作用提供了证据。
Flexural deformations of atomically thin membranes are governed by bending rigidity and the Gaussian modulus. In one-atom-thick graphene membranes, these two parameters need to be determined via bending-induced changes in topology and interaction between electron orbitals, going beyond existing studies on flat graphene. Herein, we employ atomic force microscopy to demonstrate that the configurational (strain) energy can successfully be evaluated based on changes in the surface geometry with subatomic resolution via three-dimensional analyses of attractive interatomic forces. A quadratic relation of adhesion energy with monolayer curvatures of rolled and unrolled graphene led to the finding that the probe tip can detect spatially varying surface potentials owing to the rehybridization effects and the change in the next-neighbor hopping caused by bending. The tip-induced local strain inside graphene was found to generate topological defects, independently of in-plane stretch. Their energetic analysis and relationship with local curvatures reveal the applicability of the Helfrich Hamiltonian and determine the bending rigidity and Gaussian modulus. Those evaluated at the hollow sites of the honeycomb lattice are consistent with the isotropic elastic attributes. The remarkably large negative Gaussian modulus, observed at a pyramidalized carbon atom located at the topmost center of the tip-induced bump, provides evidence for attractive interactions between the charge inhomogeneity owing to the topological defects and geometric potentials of the Gaussian curvature.