Theory and Application of Berry Phase Methods in Solids

点击翻译按钮获取中文摘要

NON-TECHNICAL SUMMARYIn the last two decades, there has been a growing appreciation that certain mathematical concepts from differential geometry and topology are sometimes central to the understanding of the behavior of electrons in crystalline solids. The electrons are described by quantum-mechanical wavefunctions, and the manner in which these vary with momentum encodes many kinds of information about the solid, especially its electrical and magnetic responses and their coupling with each other. When the wavefunctions become twisted in momentum space, this results in so-called "topological insulator" states, which have been the focus of intense research interest in the last decade. By definition, electric currents cannot flow in the interior of an insulator, but a topological insulator has the unusual property that there are guaranteed to be current-carrying channels at the surfaces. The present research program is designed to further develop the formal theory of such effects, to invent robust and efficient computational algorithms for computing the related properties of solids, and to carry out a computational search for materials displaying new or enhanced properties. The project will lead to the development of algorithms that will ultimately be implemented in open-source code packages and made available to the wider electronic-structure community. It will also contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. Training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.TECHNICAL SUMMARYThis research program is focused on the electronic properties of topological insulators or other materials in which orbital currents play an important role. The objectives are (i) to further develop the formal theory of such systems, making use of the mathematical concepts of Berry phase, Berry curvature, and Chern number from differential geometry; (ii) to invent accurate and efficient computational methods for computing materials properties related to these mathematical concepts; and (iii) to use computational methods to identify promising new materials or structures in which these properties can manifest themselves, potentially leading to technological applications. While much recent work has concentrated on time-reversal invariant topological insulators such as Bi2Se3, the emphasis here will be on quantum anomalous Hall or Chern insulators, axion insulators, and Weyl semimetals, in which time-reversal symmetry is spontaneously broken. While the possibility of the Chern-insulator state was pointed out already 25 years ago, it has only recently been demonstrated experimentally, and that only at low temperature. Strategies will be developed for theoretically identifying possible two-dimensional Chern-insulator states accessible to experimental synthesis, with gaps and Curie temperatures large enough to approach room-temperature operation. A second and overlapping thrust will be on the theory and calculation of materials properties that involve macroscopic orbital currents, including bulk and surface anomalous Hall effects, orbital magnetization, and orbital magnetoelectric couplings. As a cross-cutting theme, computational materials search strategies will be used to identify promising candidate materials and structures that may exhibit the desired topological or magnetoelectric properties, especially including two-dimensional Chern-insulator states at surfaces of normal magnetic insulators and their interfaces with time-reversal-invariant topological insulators.The project will lead to the development of algorithms that will ultimately be implemented in open-source code packages and made available to the wider electronic-structure community. It will also contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. Training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.