Successful PhD defense of Elena Derunova!
Congratulations to Elena Derunova!
Title: "Fermi surface local geometry and anomalous quantum transporty"
Recently topological quantum physics exploded onto the scene after the experimental realization of Topological Insulators in 2007. This opened doors for mathematics mixed with material science to become an important fundamental and technological topic for researching novel physical phenomena. In the present work the computational methods of topological physics have been merged with the results from modern geometry on Riemannian manifolds. The Fermi surface, which is a surface made off electrons’ momentum, as a Reimenaian manifold can be classified locally into 3 geometrical types: elliptic, hyperbolic and Euclidian. In semiclassical transport approach, Fermi surface is used to predict transport properties of materials in a response to applied fields, therefore its geometrical type fundamentally defines a type of the response, including non-trivial responses like observed in Hall effects. Particularly, the correlations between hyperbolic type and the anomalous Hall effect have been found. An index, HF , was created for describing the concentration of locally hyperbolic areas of the FS, and it shows a universal correlation (R2 = 0.97) with the experimentally measured intrinsic anomalous Hall effect of 16 different compounds spanning a wide variety of crystals, chemical, and electronic structure families. This work lays the foundation for developing a complete theory of geometrical understanding of electronic structure, beginning with Fermi Surfaces. In analogy to the broad impact of topological physics, the concepts begun here will have far reaching consequences in the understanding of electron transport, moving it to include geometrical properties of the E vs k manifold.