[论文解读] A Theory for Colors of Strongly Correlated Electronic Systems

Swagata Acharya, Cédric Weber+4 more|arXiv (Cornell University)|Apr 23, 2022

Advanced Chemical Physics Studies被引用 4

一句话总结

该论文基于从头算多体理论，解释了强关联过渡金属氧化物和氟化物（如绿色NiO和粉红色MnF2）的光学颜色。通过结合准粒子GW与Bethe-Salpeter方程（BSE）方法及动力学平均场理论（DMFT），研究发现：在MnF2中，自旋翻转过程（标准微扰GW中缺失）决定了激子的光学亮度；而在NiO中，保持自旋构型的三重态电荷激发解释了其绿色颜色。

ABSTRACT

Many strongly correlated transition metal insulators are colored, even though they have large fundamental band gaps and no quasi-particle excitations in the visible range. Why such insulators possess the colors they do poses a serious challenge for any many-body theory to reliably pick up the interactions responsible for the color. We pick two archetypal cases as examples: NiO with green color and MnF extsubscript{2} with pink color. The body of literature around the collective charge transitions (excitons) that are responsible for the color in these and other strongly correlated systems, often fail to disentangle two important factors: what makes them form and what makes them optically bright. An adequate answer requires a theoretical approach able to compute such excitations in periodic crystals, reliably and without free parameters -- a formidable challenge. We employ two kinds of advanced \emph{ab initio} many body Green's function theories to investigate both optical and spin susceptibilities. The first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, and indeed well describe the dielectric response over the entire frequency spectrum, while the same theory is unable to explain why MnF extsubscript{2} is pink. We show its color originates from higher order spin-flip transitions that modify the optical response. This phenomenon is not captured by low-order perturbation theory, but it is contained in dynamical mean-field theory (DMFT), which has a dynamical spin-flip vertex that contributes to the charge susceptibility. We show that symmetry lowering mechanisms, such as spin-orbit coupling, odd-parity phonons and Jan-Teller distortions, determine how `bright' these excitons are, but are not fundamental to their existence.

研究动机与目标

• 解决强关联绝缘体如NiO和MnF2为何在存在大带隙且可见光范围内无低能准粒子激发的情况下仍呈现可见颜色的问题。
• 分离关联体系中激子形成与光学亮度的物理起源。
• 发展一种无需参数的理论框架，用于计算具有强电子关联性的周期性晶体的介电响应和光学响应。
• 确定标准微扰GW方法是否足以解释光学性质，或是否必须引入高阶关联效应（如自旋翻转顶点）。

提出的方法

• 采用准粒子自洽GW（QS GW）和QS $G\widehat{W}$方法，计算NiO和MnF2的精确电子能带结构与自能修正。
• 使用包含顶点修正的Bethe-Salpeter方程（BSE）计算顺磁相和反铁磁相中的激子态与介电响应。
• 应用动力学平均场理论（DMFT）以引入标准GW中缺失的非微扰自旋翻转顶点贡献，尤其对MnF2至关重要。
• 在顺磁相（准随机自旋无序）和反铁磁相（2×2×2超胞）中进行模拟，比较其光学响应。
• 通过轨道、动量和实空间分解分析激子的空间扩展范围与特征（如d、p、O、Mn、Ni）。
• 对BSE哈密顿量尺寸（最多64个价带和导带）进行收敛性测试，以确保激子本征值的可靠性。

实验结果

研究问题

• RQ1 为何强关联绝缘体如NiO和MnF2尽管具有较大的基本带隙且在可见光范围内无准粒子激发，仍呈现可见颜色？
• RQ2 何种物理机制决定了这些材料中集体电荷激发（激子）的光学亮度？
• RQ3 为何标准微扰GW + BSE无法解释MnF2的粉红色，却能成功解释NiO的绿色？
• RQ4 对称性降低效应（如自旋-轨道耦合、Jahn-Teller畸变）在不影响激子存在的情况下，对激子亮度的影响程度如何？
• RQ5 DMFT能否捕捉解释MnF2光学响应所必需的自旋翻转顶点贡献，而这些在标准GW中缺失？

主要发现

• NiO的绿色来源于t2g与eg轨道之间的三重态电荷激发，其自旋量子数S=1保持不变，该现象可通过低阶GW + BSE良好描述。
• MnF2的粉红色源于高阶自旋翻转跃迁，其改变了电子-空穴顶点，标准微扰GW无法捕捉，但DMFT可包含该效应。
• 在MnF2中，标准GW + BSE下的顺磁相保持透明，仅当通过DMFT引入自旋翻转顶点分量后才呈现颜色。
• NiO（1.6 eV，Eb=2.4 eV）和CrI3（1.1 eV，Eb=1.4 eV）中的激子局域化在约4 Å范围内，而MoS2（1.95 eV，Eb=0.55 eV）中的激子则扩展至数纳米。
• QS $G\widehat{W}$将QS GW的带隙在NiO中减小约1.0 eV，使其更接近实验值（4.0 eV vs. 实测约3.5–4.0 eV），并改善了d-p轨道对齐。
• BSE本征值收敛性在64个价带和64个导带时达到，表明32,768阶矩阵大小足以获得精确的激子谱。