外加电磁场下周期性体系的第一性原理计算方法

First-principles calculation method for periodic system under external electromagnetic field

电磁场对物质性质的影响和调控一直是科学研究的核心议题.然而,在计算凝聚态物理领域,由于传统的密度泛函理论并不能轻易推广至含有外加电磁场的情景,且外场往往会破缺周期性体系原本具有的平移对称性,从而使得布洛赫定理失效.因此,利用第一性原理方法计算外场作用下的物质性质并非易事,特别是在外场不能被视为微扰的情况下.在过去的二十年中,许多计算凝聚态物理学者致力于构建和发展适用于有限外场下周期性体系的第一性原理计算方法.本文旨在系统地回顾这些理论方法及其在铁电、压电、铁磁、多铁等领域的应用.本文首先简要介绍现代电极化理论,并阐述基于此理论以及密度泛函理论,构建出两种用于有限电场下计算的方法.然后探讨将外磁场纳入密度泛函理论,并对相关的现有计算手段以及所面临的挑战进行讨论.接着回顾了被广泛用于研究磁性、铁电和多铁体系的第一性原理有效哈密顿量方法,以及该方法在考虑外场时的延伸.最后,介绍了当下备受瞩目的利用机器学习中的神经网络方法构建有效哈密顿量模型的发展成果及在考虑外场下的拓展.

The influence of electromagnetic field on material characteristics remains a pivotal concern in scientific researches.Nonetheless,in the realm of computational condensed matter physics,the extension of traditional density functional theory to scenarios inclusive of external electromagentic fields poses considerable challenges.These issues largely stem from the disruption of translational symmetry by external fields inherent in periodic systems,rendering Bloch's theorem inoperative.Consequently,the using the first-principles method to calculate material properties in the presence of external fields becomes an intricate task,especially in circumstances where the external field cannot be approximated as a minor perturbation.Over the past two decades,a significant number of scholars within the field of computational condensed matter physics have dedicated their efforts to the formulation and refinement of first-principles computational method adopted in handling periodic systems subjected to finite external fields.This work attempts to systematically summarize these theoretical methods and their applications in the broad spectrum,including but not limited to ferroelectric,piezoelectric,ferromagnetic,and multiferroic domains.In the first part of this paper,we provide a succinct exposition of modern theory of polarization and delineate the process of constructing two computation methods in finite electric fields predicated by this theory in conjunction with density functional theory.The succeeding segment focuses on the integration of external magnetic fields into density functional theory and examining the accompanying computational procedures alongside the challenges they present.In the third part,we firstly review the first-principles effective Hamiltonian method,which is widely used in the study of magnetic,ferroelectric and multiferroic systems,and its adaptability to the case involving external fields.Finally,we discuss the exciting developments of constructing effective Hamiltonian models by using machine learning neural network methods,and their extensions according to the external fields.