Linear and nonlinear exciton dynamics with time-dependent density-functional theory

非技术总结光和物质的相互作用在科学和技术中具有基础性的重要性：它通过光学光谱确定材料的特征，形成光伏作为可再生能源的基础，并在量子信息领域开辟新技术。该奖项支持研究和教育活动，旨在开发比现有方法更准确、更高效地建模光-物质相互作用的理论和计算方法。当光被材料吸收时，电子被激发到更高的状态，留下带正电荷的“空穴”状态。电子和空穴可以排列在一起形成激子对，这会产生独特的光谱特征，并经常主导材料的光学性质。激子效应的理论和计算描述具有挑战性，因为电子-空穴对存在于由多个电子组成的固态环境中，并且受到它们之间微妙的相互作用效应的影响。这个项目将特别关注二维材料中的这种相互作用。这个项目将利用一种称为含时密度泛函理论的量子力学方法，该方法在物理、化学和材料科学的许多领域中已经非常成功地描述了相互作用的电子系统的动力学。在这个理论框架内，PI将发展新的方法来解释二维材料中多电子系统的量子行为。另一个重点将是对光-物质相互作用的实时描述，它明确地解释快速动力学效应，允许模拟在非常短的时间尺度上在2D材料中探索激子动力学的实验。研究活动将与教育努力齐头并进，重点放在研究生和博士后的培训和指导以及创新教学方法的发展上。将开发一个计算机模拟的开源图书馆，作为密度泛函理论入门课程的教学工具。这显然需要让来自不同背景的学习者更容易接触到这些高级量子力学主题。技术总结该奖项支持理论和计算研究和教育活动，旨在开发和应用基于时间相关的密度泛函理论(TDDFT)的方法来研究线性和非线性区域中的激子。第一个研究目标是扩展基于长程修正和介电屏蔽的混合泛函方法来描述有限动量和二维材料中的激子。这就需要发展在倒易空间中具有显式矩阵形式的长程修正的交换相关泛函，以及使用动量依赖的介电屏蔽模型的混合泛函。这些方法将被应用于描述暗激子，这是未来量子信息设备中潜在的量子比特候选。第二个目标是通过固体的含时Kohn-Sham方程实时描述超快和非线性激子效应。这将通过长程修正的交换关联泛函的时间相关版本来实现，该版本被适当地修改以实施所谓的零力定理，并通过具有明确的时间相关介电屏蔽的混合泛函来实现。这些方法将在2D模型系统的帮助下开发和测试，并将在INQ和八达通两个代码中实现。应用将涉及2D材料中激子的形成和动力学，动态Franz-Keldysh效应，以及高次谐波产生中的激子效应。研究活动将与教育工作齐头并进，重点放在对研究生和博士后的培训和指导以及创新教学方法的开发上。将开发一个基于Python的计算机模拟的开源库，作为密度泛函理论入门课程的教学工具。这个奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为是值得支持的。

NON-TECHNICAL SUMMARYThe interaction of light and matter is of fundamental importance in science and technology: it determines the characterization of materials through optical spectroscopy, forms the basis of photovoltaics as a renewable energy resource, and opens up new technologies in the area of quantum information. This award supports research and education activities with an aim to develop theoretical and computational methods for modeling light-matter interactions that are more accurate and efficient than existing approaches.When light gets absorbed in a material, electrons are excited into higher states, leaving positively charged “hole” states behind. The electrons and holes can team up and form pairs, called excitons, which give rise to characteristic spectroscopic features and often dominate the optical properties of materials. The theoretical and computational description of excitonic effects is challenging, since the electron-hole pairs exist within a solid-state environment of many electrons, and are influenced by subtle interaction effects between them. This project will especially focus on such interactions in two-dimensional materials.This project will utilize a quantum-mechanical method called time-dependent density-functional theory, which has been very successful in describing the dynamics of interacting electronic systems in many areas in physics, chemistry and materials science. Within this theoretical framework, the PI will develop new ways of accounting for the quantum behavior of many-electron systems in two-dimensional materials. Another focus will be on a real-time description of light-matter interactions that explicitly accounts for fast dynamical effects which allow the simulation of experiments probing exciton dynamics on very short time scales in 2D materials.The research activities will go hand in hand with educational efforts focusing on the training and mentoring of graduate students and postdocs and the development of innovative teaching methods. An open-source library of computer simulations will be developed, to be used as teaching tools for introductory courses in density-functional theory. This addresses a clear need to make these advanced quantum mechanical topics more accessible to learners from various backgrounds.TECHNICAL SUMMARYThis award supports theoretical and computational research and education activities with an aim to develop and apply time-dependent density-functional theory (TDDFT) based approaches for excitons in the linear and nonlinear regime. The first research goal is to extend the long-range corrected and the dielectrically screened hybrid functional based approaches to describe excitons at finite momentum and in two-dimensional (2D) materials. This requires the development of long-range corrected exchange-correlation functionals with explicit matrix form in reciprocal space, and of hybrid functionals that use momentum-dependent dielectric screening models. These methods will be applied to describe dark excitons, which are potential candidates for qubits in future quantum information devices. The second goal is to describe ultrafast and nonlinear excitonic effects in real time via the time-dependent Kohn-Sham equation for solids. This will be accomplished through a time-dependent version of the long-range corrected exchange-correlation functional, suitably modified to enforce the so-called zero-force theorem, and via hybrid functionals with explicitly time-dependent dielectric screening. These methods will be developed and tested with the help of 2D model systems, and they will be implemented in two codes, INQ and Octopus. Applications will address exciton formation and dynamics in 2D materials, the dynamical Franz-Keldysh effect, and excitonic effects in high-harmonic generation. The research activities will go hand in hand with educational efforts focusing on the training and mentoring of graduate students and postdocs and the development of innovative teaching methods. An open-source library of Python-based computer simulations will be developed, to be used as teaching tools for introductory courses in density-functional theory. This addresses a clear need to make TDDFT more accessible to learners from various backgrounds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.