CDS&E: Computational Studies of Weyl Semimetals: Disorder, Correlations and Topological Properties

该奖项支持对发现和研究新的Weyl半金属性质的计算和理论研究和教育。这些都是最近在理论上提出的新型材料，现在正开始被发现。它们在体积上是非常差的导体，但具有高导电性的金属表面。这些材料的特殊之处在于它们的表面享有所谓的拓扑保护，这意味着它不能在不破坏大块材料的情况下改变。在大多数材料中，表面可以发生化学改变，因为它们倾向于从环境中吸收杂质，这反过来会干扰材料的导电方式，这是任何电子设备应用的关键特征。然而，Weyl半金属的拓扑保护表面对杂质是稳健的。该研究项目旨在开发寻找新的Weyl半金属的方法，并使用基于计算机的模拟来了解它们的性质。这些材料中不同自由度的电子之间的紧密竞争使得他们的研究特别具有挑战性，但也为新功能带来了巨大的希望。这项研究将带来新的方法、算法和软件，这些方法、算法和软件将增强和简化我们进行特定材料研究的能力，并通过计算机辅助设计促进材料的逐步改进，从而缩短目前昂贵而低效的试错过程。开发科学软件工具，将计算机程序整合到用户友好的界面中，降低了对量子材料特性的计算探索的门槛。这些用户友好界面的开发也将促进高等本科和研究生层次拓扑材料基本理论的教学，从而提高大学课程。该奖项支持基于密度泛函理论与动态平均场和微扰理论相结合的计算方法的发展，这将允许发现新的拓扑半金属并研究它们的单粒子光谱、输运、磁性和超导性质。以晶体结构与已知体系拓扑特征的相似性为指导，实现了不同宇称电子态之间的能带反转机制、部分填充强相关态与填充或空拓扑能带之间的杂化效应、化学价态论证和物理直觉。高通量筛选材料的拓扑性质将执行在无限空间的化学允许化合物使用计算机为基础的模拟。这些发现将允许识别新的拓扑材料，如Weyl半金属，特别是那些只有Weyl节点而没有其他费米表面态的材料。这些发现可以激发手性异常和拓扑超导性的进一步实验研究。预测和研究这些系统中复杂行为的理论和计算方法将潜在地影响依赖于状态拓扑保护的具有独特特性的量子材料的设计，这是材料科学的前沿。这项研究将带来新的方法、算法和软件，这些方法、算法和软件将增强和简化我们进行特定材料研究的能力，并通过计算机辅助设计促进材料的逐步改进，从而缩短目前昂贵而低效的试错过程。开发科学软件工具，将计算机程序整合到用户友好的界面中，降低了对量子材料特性的计算探索的门槛。这些用户友好界面的开发也将促进高等本科和研究生层次拓扑材料基本理论的教学，从而提高大学课程。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports computational and theoretical research and education towards discovering and studying the properties of new Weyl semimetals. These are new types of materials that have been recently proposed theoretically and are now beginning to be discovered. They are very poor conductors in their bulk but have highly conductive metallic surfaces. These materials are special in that their surface enjoys what is called topological protection, meaning that it cannot be changed without destroying the bulk material. In most materials, surfaces can be chemically altered as they tend to pick up impurities from the environment, which in turn interfere with how materials conduct electricity, a crucial feature for applications in any electronic device. However, the topologically protected surfaces of Weyl semimetals are robust to impurities. This research project aims to develop methods for finding new Weyl semimetals, and for understanding their properties using computer-based simulations. The close competition between various degrees of freedom of the electrons in these materials makes their study particularly challenging, but also holds great promise for new functionalities.The research will lead to new methods, algorithms, and software that will enhance and simplify our ability to carry out material-specific studies and to promote the gradual improvement of materials by computer-aided design, thus shortening currently expensive and inefficient trial-and-error procedures. Developing scientific software tools that incorporate computer programs into a user-friendly interface lowers the barrier to entry for the computational exploration of the properties of quantum materials. The development of these user-friendly interfaces will also facilitate the teaching of elementary theories of topological materials at advanced undergraduate and graduate levels, thereby enhancing University curricula.TECHNICAL SUMMARYThis award supports the development of computational approaches that are based on density-functional theory combined with dynamical-mean-field and perturbation theories, which will allow finding new topological semimetals and studying their single-particle spectra, transport, magnetic, and superconducting properties. Guided by similarities between crystal structures and topological features of known systems, realizations of the band inversion mechanism between electronic states of different parity, hybridization effects between partially filled strongly correlated states with filled or empty topological energy bands, chemical valence arguments and physical intuition, a high-throughput screening of materials for their topological properties will be performed in the infinite space of chemically allowed compounds using computer-based simulations.These findings will allow identifying new topological materials, such as Weyl semimetals, and, in particular, those with only Weyl nodes and no other Fermi surface states. Such discoveries could motivate further experimental studies of the chiral anomaly and topological superconductivity. Theoretical and computational approaches to predict and study complex behavior in these systems would potentially influence the design of quantum materials with unique characteristics that rely on topological protection of states, which are at the frontier of materials science.The research will lead to new methods, algorithms, and software that will enhance and simplify our ability to carry out material-specific studies and to promote the gradual improvement of materials by computer-aided design, thus shortening currently expensive and inefficient trial-and-error procedures. Developing scientific software tools that incorporate computer programs into a user-friendly interface lowers the barrier to entry for the computational exploration of the properties of quantum materials. The development of these user-friendly interfaces will also facilitate the teaching of elementary theories of topological materials at advanced undergraduate and graduate levels, thereby enhancing University curricula.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.