稳态强磁场下STM/STS图像的数值计算模拟

Currently, STM images have been realized technically under 27 tesla at uniform strong magnetic field scientific center in China. This brings forth the requirement for STM/STS image calculations and theoretical analysis of materials under uniform strong magnetic field. For a direct first-principles calculation for system under strong magnetic field, now there are still unsolved methodology problems. Basing on our abundant research experience in the first-principles calculations and maximum localized Wannier functions (MLWF) approach, we try to build up a new theoretical research framework for STM/STS image calculation under uniform strong magnetic field. Taking topological insulator Bi2Se3 as an example, research contents are included: 1) Obtaining the effective Hamiltonian parameters for system without magnetic field by using the MLWF approach in combination with the first-principles calculations; 2) The effect of external magnetic field is introduced by perturbation theory. Here, the on-site energies and hopping parameters of system under a uniform steady magnetic field are expressed as a combination of those in the absence of magnetic field and an additional phase factor induced by magnetic field. Further, the spin-orbital coupling correction needs to be introduced in Hamiltonian under magnetic field. Diagonalizing the final Hamiltonian, one can get electronic structure and surface local density of states; 3) Based on Hamiltonian parameters of bulk system and slab system under magnetic field, one can obtain semi-infinite surface Green functions and surface local density of states by using iteration method. Eventually, high-precision STM/STS image can be obtained by Tersoff-Hamann approach.

目前稳态强磁场中心已经实现在27 T强场下的STM成像。这就对强磁场下材料STM/STS图像的计算和理论分析提出了要求。当前，第一性原理方法在强磁场下的应用还有很多方法上的问题没有解决。基于在密度泛函计算和最大局域化瓦尼尔函数应用方面的经验，本项目拟发展具有第一性原理精度的强磁场下STM/STS图像模拟的新框架。以拓扑绝缘体Bi2Se3为研究对象，拟展开以下研究：1)通过最大局域化瓦尼尔函数计算，得到基于第一性原理计算的无磁场下的有效哈密顿参数。2)采用微扰展开方法引入强磁场效应，把磁场中的哈密顿参数展开为无磁场时的哈密顿参数，以及磁场相关的相因子的组合。进一步在哈密顿中引入自旋-轨道耦合修正。3)基于获得的磁场下的三维体结构和二维表面的哈密顿参数，使用迭代方法计算出半无限表面格林函数和表面局域态密度，通过Tersoff-Hamann近似得到拓扑绝缘体Bi2Se3表面的STM/STS图像。

目前稳态强磁场中心已经实现在27 T强场下的STM实验研究。这就对强磁场下材料电子结构的计算和理论分析提出了要求。基于微扰理论，我们解析地推导了在周期性体系中引入了强磁场效应的理论框架，其中同时严格考虑了磁平移对称性的约束和晶格的周期性边界条件，得到了存在磁场时的有效哈密顿的普适表达式。结合密度泛函理论和最大局域化瓦尼尔函数方法，我们将考虑磁场效应的解析公式程序化，完成了整套计算代码的编写工作，并最终建立了一个针对强磁场下物性研究的新的理论研究框架。这套代码框架一方面可避免传统第一性原理方法对磁场中的周期性体系的算力限制，另一方面可利用最大局域化瓦尼尔函数方法最大程度地保留第一性原理方法的精确性。在解析推导和代码编写的同时，我们也积极地和强磁场实验团队开展合作研究。目前在本项目资助下，除了强磁场下代码设计和编写，也在国际期刊上发表SCI论文6篇，另有2篇在投。

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