Building on recent developments in electronic-structure methods, we define and calculate the flexoelectric response of two-dimensional (2D) materials fully from first principles. In particular, we show that the open-circuit voltage response to a flexural deformation is a fundamental linear-response property of the crystal that can be calculated within the primitive unit cell of the flat configuration. Applications to graphene, silicene, phosphorene, boron nitride, and transition-metal dichalcogenide monolayers reveal that two distinct contributions exist, respectively of purely electronic and lattice-mediated nature. Within the former, we identify a key metric term, consisting in the quadrupolar moment of the unperturbed charge density. We propose a simple continuum model to connect our findings with the available experimental measurements of the converse flexoelectric effect.

中文翻译：

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二维材料中的正反柔电性

基于电子结构方法的最新发展，我们完全从第一原理定义和计算二维 (2D) 材料的挠曲电响应。特别是，我们表明对弯曲变形的开路电压响应是晶体的基本线性响应特性，可以在平面配置的原始晶胞内计算。石墨烯、硅烯、磷烯、氮化硼和过渡金属二硫属化物单层的应用表明存在两种不同的贡献，分别是纯电子和晶格介导的性质。在前者中，我们确定了一个关键指标项，包括未扰动电荷密度的四极矩。我们提出了一个简单的连续模型，将我们的发现与可用的逆挠曲电效应实验测量值联系起来。