Transport and Superconductivity in Strongly Correlated Quantum Matter

非技术性总结该奖项支持旨在理解系统的电子和输运性质的理论研究，其中电子之间的强相互作用导致高温超导性等紧急行为。在超导体中，电子导电而没有任何损失，但这通常只发生在低温下。由于电力损失占所有电费的很大一部分，室温超导体将代表电力传输的重大进步。PI的工作重点是理解1987年发现的一类高温超导体，这些超导体在1957年由Barthel，库珀和Schrieffer提出的所谓BCS理论中无法理解。 主要的困难是，虽然BCS理论适用于金属，如铝，其中电子之间的相互作用可以忽略不计，但对于高温超导体来说，情况并非如此，其中超导性是通过掺杂材料而发生的，这些材料是由于电子之间的强烈排斥而形成的绝缘体。PI已经为这样的系统提出了一个精确可解的模型，并展示了超导性是如何出现的。由于该模型是完全可解的，一个清晰的画面出现，如何BCS理论必须修改。 PI将致力于量化这些材料中的差异，并构建超导性的普遍特征，这些材料在标准BCS理论中无法描述。该奖项还支持培养攻读理论物理博士学位的研究生。PI将参与其他教育和推广活动，例如继续修订他在理论固态物理学方面的研究生教科书，在著名科学期刊的编辑委员会任职，在物理学和种族的交叉点推进美国物理学会的倡议，并致力于增加科学劳动力的多样性。技术总结该奖项支持理论研究，重点是新的方法，强关联电子系统的输运和超导性质，通过使用精确可解模型、数值计算和重整化技术来建立强耦合不动点的存在。精确可解的模型使人们对掺杂莫特绝缘体（如高温超导体）中的超导性问题有了新的认识。 我们的目标是确定莫特物理学在超导状态下出现了什么新的特征。 精确可解模型的另一个目标是确定它们所体现的物理学是否受一个新的强耦合不动点的支配，就像费米液体理论支配简单金属物理学一样。 这方面的成功可以为强关联电子物质的物理学提供一个组织原则。 最后，通过数值计算确定周期性势作用下稀电子气的相图，旨在为新的实验提供信息，这些实验揭示了打破莫尔双层系统平移对称性的新型绝缘态。该奖项还支持培养攻读理论物理学博士学位的研究生。PI将参与其他教育和推广活动，例如继续修订他在理论固态物理学方面的研究生教科书，在著名科学期刊的编辑委员会任职，在物理学和种族的交叉点推进美国物理学会的倡议，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响评审标准。

NONTECHNICAL SUMMARYThis award supports theoretical research aimed at understanding electronic and transport properties of systems in which strong interactions between electrons lead to emergent behavior such as high temperature superconductivity. In a superconductor, electrons conduct electricity without any loss, but this typically happens only at low temperatures. As electrical loss represents a significant portion of all electrical bills, a room temperature superconductor would represent a major advance in power transmission. The PI's work is focused on understanding a class of high-temperature superconductors discovered in 1987 that have defied understanding within the so-called BCS theory proposed in 1957 by Bardeen, Cooper, and Schrieffer. The primary difficulty is that while the BCS theory works fine for metals such aluminum where the interaction between the electrons can be ignored, this is not the case for the high-temperature superconductors where superconductivity occurs by doping materials which are insulators due to strong repulsion between electrons. The PI has advanced an exactly solvable model for such systems and shown how superconductivity emerges. Since the model is exactly solvable, a clear picture emerges as to how the BCS theory must be modified. The PI will work to quantify the differences and construct the universal features of superconductivity in these materials that have defied description in terms of the standard BCS theory.This award also supports training of graduate students seeking their PhD degrees in theoretical physics. The PI will be involved with other educational and outreach activities, such as continuing to revise his graduate textbook in theoretical solid state physics, serving on the Editorial Boards of prominent scientific journals, advancing initiatives within the American Physical Society at the intersection of physics and race, and working to increase diversity in the scientific workforce.TECHNICAL SUMMARYThis award supports theoretical research focused on new methods for the transport and superconducting properties of strongly correlated electron systems by using exactly solvable models, numerical calculations, and renormalization techniques to establish the existence of strongly coupled fixed points. The exactly solvable models allow new insight into the 35-year old problem of superconductivity in doped Mott insulators such as the high-temperature superconductors. The goal is to ascertain what new features emerge from Mott physics in the superconducting state. Another goal of the exactly solvable models is to determine if the physics they embody is governed by a new strongly coupled fixed point in much the same way Fermi liquid theory dictates the physics of simple metals. Success here could provide an organizing principle in the physics of strongly correlated electron matter. Finally, the focus on numerical calculations to determine the phase diagram of the dilute electron gas in the presence of a periodic potential is aimed at informing new experiments that have revealed novel insulating states that break translational symmetry in Moire bilayer systems.This award also supports training of graduate students seeking their PhD degrees in theoretical physics. The PI will be involved with other educational and outreach activities, such as continuing to revise his graduate textbook in theoretical solid state physics, serving on the Editorial Boards of prominent scientific journals, advancing initiatives within the American Physical Society at the intersection of physics and race, and working to increase diversity in the scientific workforce.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.