NSF-BSF: Theory of Quantum Materials

该奖项支持在所谓的“量子材料”中相互作用电子和离子的原子尺度模型的理论研究。量子材料的一些例子包括高温超导体，两层碳原子片以相对扭曲的角度相互叠加，以及电子-电子相互作用能与其动能相当或大得多的材料。这个项目的一个主要焦点是揭示超导体的神秘特性，在超导体中，电子在低于某个临界温度的情况下一致流动，而不损失任何能量。虽然量子力学使科学家能够理解和预测“传统”超导体的大多数特性，但对非常规超导体（包括高温超导体和扭曲的碳原子层）的基本理解仍然难以捉摸。在这个项目中，PI和他的团队将研究一系列关于材料系统和主题的原子尺度模型，包括非传统超导体，这是当代凝聚态物理学的核心。量子多体问题是这个项目的主题，它与从弦理论到量子信息的其他物理学领域有着广泛而深刻的联系。此外，量子材料对基础科学和技术都产生了巨大的影响，因此，对本项目所要研究的问题的更多理解有可能影响科学和技术的更广泛发展。该奖项还将有助于科学队伍的发展，因为它将支持研究生和博士后的研究培训，这些研究生和博士后将来可能在学术界和工业界担任领导职务。该奖项支持量子材料中电子和声子相互作用微观模型的理论研究。将特别注意中间耦合制度，其中的相互作用和动力学项是相当的大小。当组成粒子形成合适的实空间结构（如维格纳晶体）时，相互作用通常是最小的，而动力学项在动量空间中是对角的。因此，中间耦合状态是量子受挫最大的状态。PI还将应用Landau-Ginzburg-Wilson有效场理论方法来研究存在多个不同排序趋势的问题，并且有效挫折反映了它们之间的竞争。这类将成为研究重点的具体问题是：(i)非常规金属体制的可解模型，特别是铜超导体的经验教训；（ii）具有多种相互纠缠的有序趋势的系统的现象学和微观理论，包括多种可能的均匀超导秩序，对密度波秩序，电荷和自旋密度波秩序，以及电子向列秩序；（iii）多谷二维电子气体的相关相，以及（iv）将不同相的分类，特别是非常规超导相的分类推广到准周期系统，包括moir<s:1>材料，其中不适用布洛赫定理，至少必须重新考虑传统的对称分类。量子多体问题是这个项目的主题，它与从弦理论到量子信息的其他物理学领域有着广泛而深刻的联系。此外，量子材料对基础科学和技术都产生了巨大的影响，因此，对本项目所要研究的问题的更多理解有可能影响科学和技术的更广泛发展。该奖项还将有助于科学队伍的发展，因为它将支持研究生和博士后的研究培训，这些研究生和博士后将来可能在学术界和工业界担任领导职务。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 theoretical research on atomic scale models of interacting electrons and ions in so-called "quantum materials". Some examples of quantum materials include high-temperature superconductors, two layers of carbon atom sheets on top of each other with a relative twist angle, and materials in which the electron-electron interaction energies are comparable or much larger compared to their kinetic energies. A major focus of this project is to unravel the mysterious properties of superconductors through which electrons flow in unison without losing any of their energy below a certain critical temperature. While quantum mechanics has allowed scientists to understand and predict most properties of "conventional" superconductors, achieving a fundamental understanding of unconventional superconductors, which include high-temperature superconductors and twisted layers of carbon atoms, has remained elusive. In this project, the PI and his team will study an array of atomic scale models on material systems and topics, including unconventional superconductors, that are at the heart of contemporary condensed matter physics.The quantum many-body problem that is the topic of this project has diverse and deep connections to other fields of physics, from string theory to quantum information. In addition, quantum materials have had a tremendous impact on both fundamental science and technology, and hence, an increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology. This award will also contribute to the development of the scientific workforce, as it will support the research training of graduate students and postdocs, who are likely to take leading positions in academia and industry in the future.TECHNICAL SUMMARYThis award supports theoretical research on microscopic models of interacting electrons and phonons in quantum materials. Particular attention will be paid to the intermediate coupling regime, where interactions and kinetic terms are of comparable magnitude. Interactions are generally minimized when the constituent particles form suitable real-space structures, such as a Wigner crystal, while kinetic terms are diagonal in momentum space. Hence, the intermediate coupling regime is where quantum frustration is maximal. The PI will also apply a Landau-Ginzburg-Wilson effective field theoretical approach to study problems in which multiple distinct ordering tendencies are present, and the effective frustration reflects the competition between them. Specific problems of this general sort that will be the focus of study are (i) Solvable models of unconventional metallic regimes, particularly focusing on lessons for cuprate superconductors, (ii) Phenomenological and microscopic theories of systems with multiple intertwined ordering tendencies, including multiple possible uniform superconducting orders, pair-density-wave order, charge and spin density wave order, and electron nematic order, (iii) Correlated phases of multi-valley two-dimensional electron gases, and (iv) Generalizing the classification of distinct phases, especially unconventional superconducting phases, to quasi-periodic systems including Moiré materials in which Bloch's theorem does not apply and conventional symmetry classifications at the very least must be reconsidered.The quantum many-body problem that is the topic of this project has diverse and deep connections to other fields of physics, from string theory to quantum information. In addition, quantum materials have had a tremendous impact on both fundamental science and technology, and hence, an increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology. This award will also contribute to the development of the scientific workforce, as it will support the research training of graduate students and postdocs, who are likely to take leading positions in academia and industry in the future.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.