Frustrated Magnets and Unconventional Superconductors: Symmetry and Quantum Mechanics

这项拟议的研究将解决受挫磁体和非传统超导体的基本问题。我将使用新的、基于对称性的分析和计算方法来研究其唯象是长期存在的谜题的系统。几何受阻磁体是磁性离子排列在三角形或四面体晶格中的材料。当每个磁性离子的磁态简并度很小(两个数量级)时，就会产生量子力学效应。量子受挫磁体表现出各种有趣的现象，包括“量子自旋液体”。这项拟议的研究旨在通过解决悬而未决的问题来推进受挫量子磁体的领域，例如确定As量子自旋液体可以存在的条件。该计划的短期目标包括量子磁铁定量模型的推导和量子磁铁物理性质的计算。不同的分析和计算方法将被用来研究这些问题，包括群论(对称性)方法的创新应用。这个研究计划将发展独创的分析方法，导致对量子磁铁的定量描述。量子磁体和量子材料是目前加拿大非常感兴趣的话题，因为它们潜在的技术应用，以及它们提出的具有挑战性的基本问题；该计划的结果将对这一知识分支做出重大贡献。非传统超导体是指除了规范对称性破坏外，点群对称性和/或时间反转对称性也被破坏的超导体。我的主要兴趣是识别非传统超导体的对称性，并利用其不同寻常的量子力学特性。我建议研究几个具体的系统，包括新的铁基超导体家族和迅速增长的非中心对称超导体集合。为了将理论模型和实验结果进行定量比较，还将计算弹性模量、电导率、热容、侵彻深度和点接触电导等物理性质。超导体可以通过点接触隧道效应或邻近效应耦合到正常金属或绝缘体上。在这些装置中，非传统超导体具有不寻常的自旋相关电流。这项工作还试图寻找这种装置的应用，例如构造拓扑超导体。这项研究将是对非传统超导体及其原始应用的深入研究。加拿大在超导研究方面有着深厚的传统，取得了许多重大成就。拟议的研究将加强这一努力，并帮助加拿大保持在这一研究领域的领先地位。

The proposed research will address fundamental problems in frustrated magnets and unconventional superconductors. I will use novel, symmetry-based analytic and computational methods to investigate systems whose phenomenology are long-standing puzzles.Geometrically frustrated magnets are materials with magnetic ions arranged in lattices of triangles or tetrahedra. Quantum mechanical effects arise when the degeneracy of magnetic states of each magnetic ion is small (of the order of two). Quantum frustrated magnets exhibit a variety of interesting phenomena, including "quantum spin liquids". The proposed research aims to advance the field of frustrated quantum magnets by resolving outstanding problems, such as determining the conditions under which as quantum spin liquid can exist. The short-term objectives of this program include the derivation of quantitative models of quantum magnets and calculations of physical properties of quantum magnets. Different analytic and computational approaches will be used to study these problems, including innovative applications of group theory (symmetry) methods.This program of research will develop original methods of analysis that will result in quantitative descriptions of quantum magnets. Quantum magnets and quantum materials in general are topics that are currently of high interest in Canada because of their potential technological applications and because of the challenging, fundamental questions they raise; the results of this program will contribute significantly to this branch of knowledge.Unconventional superconductors are those superconductors for which, in addition to gauge symmetry breaking, the point group symmetry and/or time reversal symmetry are also broken. My primary interests are the identification of the symmetry of unconventional superconductors and the exploitation of their unusual quantum mechanical properties. I propose to examine several specific systems, including the new family of iron-based superconductors and the rapidly growing collection of non-centrosymmetric superconductors. Physical properties, such as elastic moduli, conductivity, heat capacity, penetration depth and point contact conductance, will be calculated in order to make quantitative comparisons between theoretical models and experimental results. Superconductors may be coupled to normal metals or insulators either by point contact tunneling or proximity effect. Unconventional superconductors feature unusual spin-dependent currents in these set-ups. This work also seeks to find applications of such set-ups, such as the construction of a topological superconductor.This research will be a thorough investigation of unconventional superconductors and original applications of them. Canada has a strong tradition of superconductivity research that has resulted in many significant accomplishments. The proposed research will augment this effort and help Canada stay in the forefront of this area of research.