Theory and Application of Berry Phase Methods in Solids

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TECHNICAL SUMMARY The Division of Materials Research and the Office of Cyberinfrastrcture contribute funds to this award. It supports theoretical research and education on the electronic properties of novel materials in which orbital currents play an important role. The objectives are (i) to develop the formal theory of such systems, making use of mathematical concepts from differential geometry; (ii) to develop accurate, efficient, robust and informative algorithms for computing the associated properties of materials; and (iii) to apply these methods to study actual and as-yet unsynthesized materials, especially ones having potential technological applications. A major thrust of the research program is to make further developments in the theory of the electronic structure of materials in which time-reversal symmetry is broken, for example ferromagnets, and in the theory of topological insulators. Mathematical approaches related to Berry phases and the Wannier representation will be utilized to investigate these more general problems. These techniques have proven useful for understanding electric polarization, orbital magnetization, and the anomalous Hall conductivity. Theoretical investigations will be carried out to better understand two classes of topological insulators. The first is the theoretically simpler but experimentally more elusive "Chern" or "quantum anomalous Hall" insulator, of which no known experimental realizations exist to date some 20 years after a theory describing them appeared. This work should clarify the expected physical properties of such materials and may suggest further avenues for experimental searches. The second are the "Z2 topological insulators," several examples of which have been discovered in the last five years. A second major thrust of the research program concerns the calculation of the linear magnetoelectric couplings of crystalline insulators. Methods for such calculations are still in their infancy, but are ripe for further development. Using first-principles methods, all of the various contributions to the magnetoelectric coupling will be calculated, including purely electronic, lattice-displacement-mediated, and strain-mediated ones, for several prototypical materials. This project is expected to lead to fundamental advances in the understanding of the electronic structure of materials with unusual magnetic or topological order, and to contribute to the development of novel materials that are promising for commercial applications, especially ones involving the coupling of electrical and magnetic responses. This project will also contribute to developing formal theory and methods to enable first principles calculations of the properties of these materials. NON-TECHNICAL SUMMARY The Division of Materials Research and the Office of Cyberinfrastrcture contribute funds to this award. It supports research and education in computational condensed-matter theory, with a focus on obtaining a deeper understanding of novel materials in which orbital currents play an essential role. Magnetic phenomena generally fall into two classes: those explained by a quantum mechanical property of the electron known as spin, and those related to the presence of microscopic currents that flow at the atomic scale. The effects of these latter "orbital currents" are sometimes secondary. For ordinary magnets such as iron, they account for less than 10% of the magnetism. However, in recent years there has been an outpouring of interest in certain novel materials for which the orbital currents play the dominant role. In a series of remarkable developments a few years ago, for example, theoretical predictions of "topological insulators" were quickly followed by experimental confirmations. 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. Essentially, the "topological" organization of the electrons in the bulk enforces a certain corresponding organization of the atomic-scale orbital currents so as to produce a net current at the surface. Such phenomena could have important practical applications; one example might be materials that can convert electrical impulses to magnetic impulses and vice versa. The PI's program is focused on obtaining a detailed understanding of these unusual materials and their magnetoelectric phenomena, with activities spanning from formal theory, development and implementation of new computer algorithms, predictive computer simulations, and pedagogical dissemination of the results.