Frustrated Magnets and Unconventional Superconductors: Symmetry and Quantum Mechanics

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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.