Interplay between symmetry breaking, quasiparticles and their topology in quantum condensed matter systems.

非技术总结该奖项支持有关材料的理论研究和教育，这些材料可以被调整以显示物质似乎相互矛盾的性质，例如电绝缘和超导，一种可以在不耗散的情况下导电的电子状态。这项研究的目标是开发一种更好的数学描述，来描述导致同一物理系统观察到的属性出现这种差异的潜在动力学过程。最终的动机是了解系统的组成部分在不同状态下是如何全局组织的，这将有助于改进材料设计和控制，从而利用这些状态之间的接近和相互作用。在一个平行的项目中，PI计划研究一类超导体中的霍尔热传输机制，与简单的元素超导体相比，这类超导体具有不寻常的性质。在磁场存在的情况下，热在材料中发生霍尔传输，并在垂直于磁场的方向上导致样品中的温差。对超导体中这类热传输的实验测量进行分析和解释，可以帮助研究人员区分导致超导的各种可能机制，并澄清它们之间的竞争程度。此外，该项目将通过参与前沿研究来培训和指导年轻科学家。该奖项还支持维基教科书项目的继续，该项目提供由学生根据教师讲稿编写的免费教科书。PI计划在这个项目的基础上进一步扩展到新的课程，成为传播科学知识的工具。技术总结该奖项支持理论研究和教育，旨在为关联量子凝聚态系统中一类鲜为人知的现象开发全面的理论描述，在这些现象中，自发对称性破缺、准粒子及其拓扑有着千丝万缕的联系。这些项目涉及理论模型的分析和数值工作，这些模型平等地展示了自发对称性破裂为相关的非超导状态的倾向，以及在后者附近出现的非传统超导状态。此外，它还探索了Berry相作为非朗道准粒子热霍尔输运的一种新机制，目的是开发一种可靠的工具来从实验数据中提取有价值的光谱信息。目标包括：确定具有不同配对对称性的非传统超导体混合态中准粒子波函数的Berry曲率的能量分布；确定在可能是无间隙系统中控制最近发现的热霍尔电导率热激活尺度的物理过程；发展捕获强关联的涡核模型；建立了一个理论，可以用来研究具有多种干扰有序倾向的模型系统在转变温度上下的物理态；探索与Dirac半金属和反铁磁绝缘体之间的转变有关的量子临界点的电荷掺杂对蜂窝单分子膜的影响；进一步发展物理激励系统中的二维和三维二次带接触理论。所有这些项目的方法都涉及到量子多体和/或场理论的分析和数值方法的结合。该奖项还支持维基教科书项目的继续，该项目提供由学生根据教师课堂讲稿编写的免费教科书。国际和平研究所计划在这一项目的基础上进一步扩大到新的课程，成为传播科学知识的工具。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on materials that can be tuned to display seemingly contradictory properties of matter, such as electrical insulation and superconductivity, an electronic state that can conduct electricity without dissipation. The goal of the research is to develop a better mathematical description of the underlying dynamical processes that cause such differentiation in the observed properties of the same physical system. The ultimate motivation is that understanding how the constituents of the system globally organize in different states will allow improved material design and control that take advantage of the proximity and interplay between these states.In a parallel project, the PI plans to study the mechanisms of Hall transport of heat in a class of superconductors with unusual properties compared to the simple, elemental superconductors. Hall transport of heat occurs in a material in the presence of magnetic field, and results in a temperature difference in the sample in a direction perpendicular to the magnetic field. Analysis and interpretation of experimental measurements of this type of heat transport in superconductors can help researchers distinguish between the various possible mechanisms that can cause superconductivity, and clarify the degree of competition between them. In addition, this project will enable training and mentoring of young scientists via participation in cutting-edge research.This award also supports the continuation of a Wiki textbook project which delivers freely available textbooks written by students based on faculty lecture notes. The PI plans to further build on this project expanding to new courses to become a vehicle for the dissemination of scientific knowledge.TECHNICAL SUMMARYThis award supports theoretical research and education aimed to develop a comprehensive theoretical description for a class of poorly understood phenomena in correlated quantum condensed matter systems, in which spontaneous symmetry breaking, quasiparticles, and their topology are inextricably linked. The projects involves analytical and numerical work on theoretical models that display on equal footing propensity towards spontaneous symmetry breaking into correlated non-superconducting states, as well as unconventional superconducting states that emerge in the vicinity of the latter. In addition, it explores Berry phases as a novel mechanism for thermal Hall transport of non-Landau quasiparticles, with the goal of developing a reliable tool for extracting valuable spectroscopic information from experimental data.Among the objectives are: determining the energy distribution of the Berry curvature of the quasiparticle wavefunctions in the mixed state of unconventional superconductors with different pairing symmetries; identifying the physical processes which control the recently discovered thermal activation scale of thermal Hall conductivity in what may otherwise be gapless systems; development of models of the vortex core which capture strong correlations; constructing a theory which would allow the study of the physical states both above and below the transition temperature in model systems with a multitude of interfering ordering tendencies; exploring the effects of charge-carrier doping of the quantum critical point associated with the transition between the Dirac semi-metal and the antiferromagnetic insulator on the honeycomb monolayer; further development of a theory of two- and three-dimensional quadratic band touching in physically motivated systems. The approach to all of these projects involves a combination of analytical and numerical methods of quantum many-body and/or field theory.This award also supports the continuation of a Wiki textbook project which delivers freely available textbooks written by students based on faculty lecture notes. The PI plans to further build on this project expanding to new courses to become a vehicle for the dissemination of scientific knowledge.