Berry-Phase Approaches to Electronic Structure Theory and their Applications

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This grant is for fundamental theoretical research on the electronic and dielectric properties of materials, with special emphasis on the development of novel techniques for the computation and analysis of these properties. The objectives are (i) to continue the development of accurate, efficient, robust and informative algorithms for computing the electronic structure of complex materials, and (ii) to apply these methods to study several important material systems.One major thrust of the proposed work will be to make further developments in the theory of the electronic structure of materials in which time-reversal symmetry is broken (e.g., ferromagnets), in a way that leads to new methods for computing the orbital magnetization, anomalous Hall conductivity, and related electronic properties in these systems. Mathematical approaches related to Berry phases and the Wannier representation, which have proved useful for understanding electric polarization and for treating orbital magnetization in insulators, will be utilized to investigate these more general problems. Applications will be made first to itinerant ferromagnets such as Fe, Ni, and Co. Theoretical investigations will also be carried out to better understandthe physics of Chern insulators, a class of magnetic insulators having unusual properties including a quantized transverse Hall conductivity.A second major thrust will concern the dielectric properties of (mostly non-magnetic) crystalline insulators. Methods will be developed for mapping the energy vs. polarization landscape, and thereby determining the electric equation of state of a given dielectric or ferroelectric material, and for using this information to determine the matching of electrical boundary conditions at interfaces and in superlattices. The non-linear dynamic response of polar semiconductors to a terahertz-frequency applied electric field will be calculated using first-principles methods, as will the dielectric and piezoelectric properties of Mg-doped wurtzite ZnO. The lattice contribution to the dielectric response of antiferromagnetic insulators will also be studied.Intellectual MeritThe project is expected to lead to fundamental advances in the understanding of the electronic structure of magnetic crystals, and in particular, to the development of algorithms for computing such important properties as the orbital magnetization and the intrinsic anomalous Hall conductivity. The project will also include the formulation and testing of novel approaches for studying the linear and nonlinear dielectric properties of insulating materials by direct application of electric fields. These areas are at the forefront of current advances in the capabilities of computational electronic-structure theory.Broader ImpactsThe project will lead to the development of algorithms which 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. Finally, training and mentorship of junior researchers (graduate students and postdocs) will take place, contributing to scientific workforce development.