New Phases and Non-Equilibrium Transport in Topological Mesoscopic Superfluids

该奖项支持对液体和固体中出现的不寻常物质状态的理论研究，当它们被限制在非常小的空间维度时。在一些特殊的材料中，如超导和超流凝聚体，基本粒子以步调一致的方式相互作用，消除碰撞并形成一种新的物质相，这对从无损电力传输到量子计算的新技术非常重要。通过将超流相限制在非常小的空间区域内，可以增加这种超流相的复杂性，使得超流与其限制边界的相互作用可以导致表面现象的出现，这可能有助于设计在大块材料中未观察到的物质的新相。这些新的物质相有可能推动未来的量子技术。在这个项目中，PI将与研究生研究人员合作，开发理论和计算工具，以推进对超导相与受限几何中边界相互作用的基本理解。该项目将提供关键知识，推动超导体中新的边界诱导表面态的发现，以及调整这些状态以实现理想物理特性的方法的发展。该研究将连接过去、正在进行和未来的小尺度环境中超流体实验工作。该项目将培养研究生掌握先进的量子物理、理论和数值技术以及复杂的数值代码。PI还将让本科生参与一些研究项目。PI将继续在地区学校开展推广活动，在那里他将展示低温物理学，量子力学和材料之间的联系，以激发学生对现代科学的可能性，并向他们展示材料如何改变我们的社会。 该奖项支持对强约束几何中非常规费米子凝聚体基本性质的理论研究。 它旨在通过创建一套工具来严格模拟实际实验环境，并提供边界效应的定性分析描述，从而在理论和实验之间建立可靠的联系。该项目旨在为正在进行的非常规超导体和超流体氦3实验提供理论联系。分析和数值方法，准经典量子场论的基础上，将被用来获得本地化的Andreev准粒子态的现实光谱。一个重点将是建立在多个实验探针，包括热力学和非平衡响应，以及在微观限制的几何形状的非局部效应的表面状态的特征签名。本研究的主要内容有：1. PI将探索边界条件，超电流和外部场对多组分超流体中新对称性破缺相形成的影响。2. PI将追求磁散射边界条件的发展，包括自旋翻转动力学及其对具有纠缠自旋和轨道自由度的超导体表面态的影响。这些研究将包括在界面区域的自旋电流产生的调查。 3.热能输运有望成为研究拓扑材料表面态（包括电荷中性模式）的有力工具。PI将建立一个理论的表面热传输的束缚态在一个有限的几何形状和域壁。 该项目将培养高级量子物理学，理论和数值技术以及复杂数值代码的研究生。PI还将让本科生参与一些研究项目。PI将继续在地区学校开展推广活动，在那里他将展示低温物理学，量子力学和材料之间的联系，以激发学生对现代科学的可能性，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评估，被认为值得支持。影响审查标准。

NONTECHNICAL SUMMARY This award supports theoretical research on unusual states of matter that appear in liquids and solids when they are confined to very small spatial dimensions. In some special materials, such as superconducting and superfluid condensates, the fundamental particles interact with each other in such a way they move in lockstep, eliminating collisions and forming a new phase of matter that is of great importance to new technologies from lossless electricity transfer to quantum computing. It is possible to increase the complexity of such superfluid phases by confining them to very small regions of space so that the interaction of the superfluid with its confining boundary can lead to the emergence of surface phenomena which could be useful for engineering new phases of matter that are not observed in the bulk material. These new phases of matter have the potential to drive future quantum technologies.In this project, the PI will work with graduate student researchers to develop theoretical and computational tools that will advance the fundamental understanding of the interaction of superconducting phases with their boundaries in confined geometries. The project will provide critical knowledge that will drive the discovery of new boundary-induced surface states in superconductors as well as the development of ways to tune these states to achieve desirable physical properties. The research will bridge past, ongoing, and future experimental work on superfluids in small-scale environments.This project will train graduate students in advanced quantum physics, theoretical and numerical techniques, and complex numerical codes. The PI will also involve undergraduate students in some of the research projects. The PI will continue with his outreach activities at regional schools, where he gives presentations that demonstrate the connections between low-temperature physics, quantum mechanics, and materials to excite students about the possibilities in modern science, and shows them how materials transform our society. TECHNICAL SUMMARY This award supports the theoretical investigation of the fundamental properties of unconventional fermionic condensates in a strongly confined geometry. It aims to build a reliable connection between theory and experiment by creating a set of tools to both rigorously model actual experimental environments, and to supply qualitative analytic descriptions of boundary effects. This project is designed to provide a theoretical link for ongoing experiments on unconventional superconductors and superfluid Helium 3. Analytical and numerical methods, based on the quasi-classical quantum field theory, will be used to obtain realistic spectra of localized Andreev quasiparticle states. One emphasis will be on establishing characteristic signatures of the surface states in multiple experimental probes that include thermodynamic and non-equilibrium responses as well as non-local effects in microscopically confined geometries. The central topics of the research are:1. The PI will explore the effects of boundary conditions, supercurrents, and external fields on the formation of phases with new broken symmetries in multi-component superfluids. 2. The PI will pursue the development of magnetic scattering boundary conditions involving spin-flip dynamics and their effects on surface states in superconductors with entangled spin and orbital degrees of freedom. These studies will include the investigation of spin-current generation in interface regions. 3. Thermal energy transport promises to be a powerful tool to study surface states, including charge-neutral modes of topological materials. The PI will build a theory of surface heat transport by bound states in a confined geometry and domain walls. This project will train graduate students in advanced quantum physics, theoretical and numerical techniques, and complex numerical codes. The PI will also involve undergraduate students in some of the research projects. The PI will continue with his outreach activities at regional schools, where he gives presentations that demonstrate the connections between low-temperature physics, quantum mechanics, and materials to excite students about the possibilities in modern science, and shows them how materials transform our society.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.