Lehrende/r: Univ.-Prof. Dr. Yuriy Mokrousov
Veranstaltungsart: Vorlesung
Anzeige im Stundenplan: 08.128.70001
Semesterwochenstunden: 2
Unterrichtssprache: Englisch
Min. | Max. Teilnehmerzahl: - | -
Voraussetzungen / Organisatorisches: Please register by sending an email directly to ymokrous@uni-mainz.de in case of interest. Possible subjects for master theses will be discussed during the course. The schedule of the course will be adjusted to a most optimal time for all.
Inhalt: The physics and required mathematical background of geometrical and topological phases in non-relativistic quantum physics are discussed in depth, with a particular attention to selected applications in spintronics and magnetism. The course seeks to maintain a balance between presenting mathematical background uncommon to most physicists with profound physical applications. The course aims to be self-contained and requires basic knowledge of mathematics and band theory of solids. The fundamental principles of topology and geometry are applied to selected aspects of magnetic systems such as: topology of spin, Berry phase in spin systems, skyrmions, spin-orbit torque, spin Hall effect and quantized magneto-electric response. The covered material includes the following topics: - Topology of spin systems: dynamics and response to external perturbations - Topology, manifolds, fiber-bundles, connections, gauge theories - Transport properties of spin systems: from Hall effects to spin orbit torque - Homotopy, holonomy and cohomology theory - Characteristic classes and Chern-Simons forms - Magnetic systems: from quantization of charge to skyrmions - Orbital magnetism and magneto-electric phenomena - Topological Magnonics The material is presented in a compact form with a new subject every lecture. The overall aim of the course is to make students familiar with the modern language of the literature on various topological phenomena in solid state physics.
Empfohlene Literatur: M. Nakahara, "Geometry, Topology and Physics", CRC Press (2003) A. Bohm et al. "The Geometric Phase in Quantum Systems", Springer (2003) Xiao, Chang, Niu, "Berry phase effects on electronic properties", Reviews of Modern Physics (2010)
