基于GW近似的二维材料多体效应计算方法研究

Since the discovery of graphene materials, new types of 2D materials have emerged, including transition metal sulfides and monolayers of black phosphorus, which with their special electrical and optical properties have attracted the attention of researchers from all of the world. The main source of its characteristics is the strong many-body effect caused by the reduction of dimensions. The gold standard for calculating material many-body effects is the GW method. However, this method is too computationally expensive to calculate two-dimensional materials, making it difficult to study. At present, the two acceleration methods proposed for this problem, that is, the low-order expansion analysis method and the special sampling method, are expected to solve the above problems. The main research goal of this project is to compare and study the reliability and universality of two newly proposed accelerating methods in detail and the advantages and disadvantages of the two methods or to use the three-dimensional computing method on the parameter sets in which there’s error cancellation to do the two-dimensional material research. Furthermore, the many-body effect of two-dimensional material will be calculated to a deeper iteration under the framework of GW, revealing a more profound many-body effect and laying a foundation for the research and design of two-dimensional material electronic and optical devices.

自石墨烯材料发现以来，新型二维材料不断涌现，包括过渡金属硫化物，单层黑磷等，他们以其特殊的电学和光学特性吸引着各界研究者的目光。而其特性的主要来源就是因维度降低而导致的强烈多体效应。计算材料多体效应的黄金标准是GW方法。但该方法在计算二维材料时计算量过大使得其研究难以进展。目前针对该问题提出的两种加速方法即低阶展开解析式方法和特殊抽样法有望解决上述问题。本项目主要的研究目标就是详细比较研究两种新提出的加速方法在更大范围内的可靠性和普适性以及两种方法的优劣，或者通过误差相消的参数集采用三维计算方法对二维材料展开研究。进而，将二维材料的多体效应计算到GW框架下更深层次的迭代，从而揭示更为深刻的多体效应，为二维材料的电子和光学器件的研究和设计打下基础。

随着二维材料和其新奇特性被广泛关注，其电子结构尤其是能带以及光吸收谱等性质的计算成为了重点。使用库仑截断加密集K点分布采样的方法一直以来在处理三维材中有着不错的表现但在二维材料计算中却因为收敛速度太慢而遭遇瓶颈。本项目采用新近提出的低阶展开解析式法和特殊抽样法对二维材料的激发态电子结构进行了计算，并且详细探究了低阶展开解析式法的适用条件、收敛参数使用范围、以及该方法和其他内嵌于GW方法计算时的近似方法的兼容型，详细分析了二维介电常数随着真空层厚度和应变的关系，尝试对比了低阶展开解析式法和特殊抽样法在GW计算和GW+BSE的异同，为后续在二维材料上更大规模的激发态电子结构计算奠定了基础。