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Fermi surface local geometry and anomalous quantum transport

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Derunova,  Elena
Nano-Systems from Ions, Spins and Electrons, Max Planck Institute of Microstructure Physics, Max Planck Society;

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Citation

Derunova, E. (2022). Fermi surface local geometry and anomalous quantum transport. PhD Thesis, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale).


Cite as: https://hdl.handle.net/21.11116/0000-0010-8008-4
Abstract
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 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, so its geometrical type defines a type of the response. Particularly, the correlations between hyperbolic type and the anomalous Hall effect have been found and presented in this work. An index, HF describing the concentration of locally hyperbolic areas of the FS, and it shows a universal correlation with the experimentally measured intrinsic anomalous Hall effect of 16 different compounds spanning a wide variety of crystals. This work lays the foundation for developing a complete theory of geometrical understanding of electronic structure, beginning with Fermi Surfaces.