Pairing of Incoherent Fermions in Quantum-Critical Metals

非技术总结该奖项支持量子材料中电子基本性质的理论研究和教育。带负电荷的电子通过通常的库仑相互作用相互排斥。然而，在材料中存在某些情况，其中这种排斥相互作用被屏蔽并且在某些距离处变得有吸引力，这可以导致电子对和超导性的形成。然而，同样的屏蔽库仑相互作用也倾向于散射电子，从而破坏它们的相干运动，这反过来又对超导性具有破坏性。本项目的关键目标是了解这两种竞争趋势之间的微妙相互作用。PI将分析与当前实验相关的特定模型，目的是了解超导状态何时最稳定，以及如何提高超导性被破坏的温度，从而扩展对应用有用的温度范围。这样的理解可能会导致关于材料中电子复杂行为的一般性结论，也与超导的实际应用有关，例如能量存储，磁悬浮列车，超导电力线，MRI成像和粒子加速器。PI提出要研究的问题相当普遍，并且引起了广泛的物理学家社区的兴趣。该项目可能会对数学和高能物理等其他几个科学领域产生影响。该项目的一个主要组成部分是指导和培训研究生谁将参与研究的各个方面。技术总结该奖项支持强关联电子系统的理论研究和教育，这是在凝聚态物理的实验和理论活动的中心。该PI将解决与量子临界点（QCP）附近的物理学相关的几个基本问题，其中与临界玻色子的相互作用引起强关联和非费米液体行为。考虑的问题包括费米子非相干性与库珀配对的强烈趋势之间的竞争，非相干费米子配对与超导性之间的相互作用，分析理论与量子蒙特卡罗数据的比较，以及临界点附近后向散射的特殊作用。在自旋或电荷有序的QCP附近，序参量的软涨落相互作用破坏了整个费米面或其中某些（热）部分的费米相干性，同样的相互作用也倾向于将费米束缚成库珀对。PI的计划是分析这两种趋势之间的竞争。特别是，他将解决的问题，是否可以得到一个非费米液体行为下降到T=0，不间断的配对。他接下来将研究非相干费米子的配对是否会导致真正的超导性，或者由于超导序参数的强烈波动而导致预形成对的伪能隙行为。他的具体目标是理解频率依赖能隙的形状波动的作用，因为这些“纵向”波动可能至少在某些量子临界系统中变得柔软。为此，PI将导出完整的Luttinger-Ward泛函，其最小化产生Eliashberg方程。他将分析远离最小值的这个泛函的轮廓，并验证纵向波动的刚度在QCP处是否具有额外的小性。如果是这样的话，应该存在一个中间温度范围，在那里配对间隙已经发展，但费米子仍然不相干，不超导。这应该回答了关于QCP附近金属行为的最基本问题。PI提出要研究的问题是相当普遍的，并且对广泛的物理学家社区感兴趣。该项目可能会对数学和高能物理等其他几个科学领域产生影响。该项目的一个主要组成部分是指导和培训研究生，他们将参与研究的各个方面。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 and education on fundamental properties of electrons in quantum materials. Electrons, carrying negative charge, repel one another via the usual Coulomb interaction. However, there are certain circumstances within materials where this repulsive interaction is screened and becomes attractive at certain distances, which can lead to the formation of electron pairs and superconductivity. Yet, the same screened Coulomb interaction also tends to scatter electrons and thereby destroy their coherent motion, which in turn is destructive for superconductivity.The key goal of this project is to understand the delicate interplay between these two competing tendencies. The PI will analyze specific models relevant to current experiments with the aim to understand when a superconducting state is most stable, and how to increase the temperature at which superconductivity is destroyed, thereby extending the temperature range that is useful for applications. Such understanding could lead to general conclusions about the complex behavior of electrons in materials and is also relevant for practical uses of superconductivity in, for example, energy storage, magnetically levitated trains, superconducting power lines, MRI imaging, and particle accelerators.The problems the PI proposes to study are quite general and are of interest to a broad community of physicists. The project could have an impact on several other areas of science, such as mathematics and high-energy physics. A major component of this project is the mentoring and training of graduate students who will be involved in all aspects of the research.TECHNICAL SUMMARYThis award supports theoretical research and education on strongly correlated electron systems, which are at the center of experimental and theoretical activities in condensed-matter physics. The PI will address several fundamental problems related to physics near a quantum critical point (QCP), where interaction with a critical boson gives rise to strong correlations and non-Fermi-liquid behavior.The problems considered include the competition between fermionic incoherence and a strong tendency towards Cooper pairing, the interplay between pairing of incoherent fermions and superconductivity, the comparison of analytical theory with Quantum Monte Carlo data, and the special role of backscattering near a critical point. Near a QCP towards spin or charge order, the interaction with soft fluctuations of the order parameter destroys fermionic coherence either on the whole Fermi surface or in some (hot) portions of it. The same interaction also tends to bind fermions into Cooper pairs. The PI's plan is to analyze the competition between these two tendencies. In particular, he will address the issue whether one can get a non-Fermi-liquid behavior down to T=0, uninterrupted by the pairing. He will next study whether the pairing of incoherent fermions leads to true superconductivity or to pseudogap behavior of preformed pairs due to strong fluctuations of a superconducting order parameter. His specific goal is to understand the role of fluctuations of the shape of the frequency dependent gap, as these "longitudinal" fluctuations likely become soft at least in some quantum-critical systems. To do this, the PI will derive the full Luttinger-Ward functional, whose minimization yields Eliashberg equations. He will analyze the profile of this functional away from the minimum and verify whether the stiffness of longitudinal fluctuations has extra smallness at a QCP. If this is the case, there should exist an intermediate temperature range where the pairing gap is already developed, but fermions remain incoherent and do not superconduct. This should answer the most fundamental questions about the behavior of a metal near a QCP. The problems the PI proposes to study are quite general and are of interest to a broad community of physicists. The project could have an impact on several other areas of science, such as mathematics and high-energy physics. A major component of this project is the mentoring and training of graduate students who will be involved in all aspects of the research.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.