NSF-BSF: Theory of Quantum Materials

非技术总结该奖项支持在所谓的“量子材料”中相互作用的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，两层碳原子层彼此重叠，具有相对扭曲角，以及电子-电子相互作用能与其动能相当或更大的材料。该项目的一个主要重点是解开超导体的神秘特性，电子在一定的临界温度以下一致流动而不会损失任何能量。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，但对非传统超导体（包括高温超导体和碳原子扭曲层）的基本理解仍然是难以捉摸的。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，包括当代凝聚态物理学核心的非常规超导体。这个项目的主题是量子多体问题，它与其他物理学领域有着广泛而深刻的联系，从弦理论到量子信息。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，对该项目中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劳动力的发展，因为它将支持研究生和博士后的研究培训，他们有可能在未来的学术界和工业界占据领先地位。技术概述该奖项支持量子材料中相互作用的电子和声子的微观模型的理论研究。特别注意将支付给中间耦合制度，其中相互作用和动力学项是相当的幅度。当组成粒子形成合适的实空间结构（如维格纳晶体）时，相互作用通常会最小化，而动力学项在动量空间中是对角的。 因此，中间耦合区是量子阻挫最大的地方。PI还将应用Landau-Ginzburg-Wilson有效场论方法来研究存在多种不同有序趋势的问题，有效挫折反映了它们之间的竞争。这种一般类型的具体问题，将是研究的重点是（i）非常规金属制度的可解模型，特别是集中在铜酸盐超导体的教训，（ii）具有多重交织有序趋势的系统的唯象和微观理论，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，和电子自旋秩序，（iii）多谷二维电子气的相关相，（iv）推广不同相的分类，特别是非常规超导相，到准周期系统，包括莫尔材料，其中布洛赫定理不适用，至少必须重新考虑传统的对称性分类。这个项目的主题是身体问题，它与物理学的其他领域有着广泛而深刻的联系，从弦理论到量子信息。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，对该项目中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劳动力的发展，因为它将支持研究生和博士后的研究培训，这些人将来可能在学术界和工业界担任领导职务。该奖项反映了NSF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.