范德华二维材料的层间相互作用：依据能带占据情况的分类研究

近几年，二维材料的层间相互作用研究引起了人们的重视。广泛存在于二维层状材料中的层间准键作用已经被证明对二维材料的电学、磁学、声子以及层间摩擦等各类性质存在影响。通过对层间作用的设计，人们可以控制层状材料的性质，从而得到具有理想性能的二维材料；另一方面，通过层间相互作用可以高效地对层状材料的性质进行调控，进而得到更优异的性能。层间相互作用为二维材料的设计和性能调控提供了新的自由度，并发展出新的研究领域——层间工程。因此，对范德华层状材料层间相互作用的理解和各种应用探索成为研究热点。

最近的研究表明，范德华二维材料的层间相互作用不仅包含van der Waals作用，同时也存在准键作用，其中后者会引起~1 eV量级的能带劈裂和电荷在层间区域的积聚。在本文中，基于密度泛函理论，我们计算并讨论了多种二维材料的层间准键作用带来的能带结构变化，同时，根据层间作用涉及到的能带的占据情况，我们对层间相互作用进行了分类。

首先，我们选择了具有类似几何结构但能带占据类型不同的三种二维材料（砷烯、SnP3和InP3）作为例子进行研究。结构优化的结果表明，SnP3和InP3从单层到双层都存在明显的结构转变。为了排除这种结构变化带来的影响，我们选取了两层结构中的单层作为“中间结构”，讨论了单层到“中间结构”的能带演化；

然后，我们讨论了从“中间结构”到双层由于层间作用带来的能带结构变化；

最后，根据层间准键作用涉及的在费米能级附近能带的不同占据情况，我们将层间相互作用划分为两大类，即大类I：同种占据能带间的相互作用；大类II：不同种占据能带间的相互作用。其中，每一大类中的相互作用类型根据实际能带的占据情况又可以分作不同的小类，如第I大类中两个满占据能带之间的满-满作用；第II大类中空占能带和满占能带之间的满-空作用等。其中，对于第I大类，由于反键态能量升高大于成键态的能量下降，因而是去稳定的，所以有着较弱的层间作用（如砷烯的层间结合能约为20 meV/AA2）。而对于第II大类，能带的变化造成总能量下降增强了稳定性，因而拥有较强的层间作用（如SnP3的层间结合能约为102 meV/AA2）。进一步的计算表明，我们的分类可以推广到一般的二维材料中，并且为判断层间相互作用强弱提供了理论基础。

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