Hiroshi Teramoto (Hokkaido University, Sapporo, Japan)
Classification of Band Geometries in a neighborhood of a Band Crossing
Transportation properties of crystals can be understood by geometrical and topological structures of bands of crystals. Thanks to the developments of experimental technologies, band structures can be directly observed by techniques like ARPES and they can be manipulated by changing material properties of crystals. Having these developments in mind, it is natural to ask whether it is possible to control transportation properties of crystals by manipulating their material properties. Since bands cannot change their topology without closing their band gaps, it is important to understand what types of geometric and topological changes can happen when the band gaps close. Aiming at the understanding, we have developed a fully automatic method to classify local geometrical structures of bands on the verge of band collisions based on comprehensive Groebner basis and try to understand how the band gap closing trigger global topological changes of bands that may be characterized by K-theory.