AIMR Math Group Seminar #11
FY2018
Date : Oct 19th (Fri.) 10:00～12:00
Place：3C, AIMR Main Bldg., Katahira campus, Tohoku University
Speaker： Dr. Kei Yamamoto
Title : A topological characterisation of classical waves and the origin of magnetostatic surface spin waves
Abstract：
Recent developments in condensed matter physics have established a remarkable connection between topological invariants of bulk Hamiltonians and edge-localized eigenstates for the corresponding systems with a spatial boundary. Those topological edge states are robust in the sense that continuous perturbations cannot remove them. Despite the comprehensive classification of topologically protected edge states of electrons, a known robust edge-localized excitation of classical waves, magnetostatic surface spin waves (MSSWs), does not appear to fit into the general framework. In this talk, we clarify how an appropriate extension of the topological bulk-edge correspondence can explain features of MSSWs. We first introduce the notion of class CI semimetals. Within this class, Hamiltonians are topologically characterised by a set of vortex lines that act as extended Dirac monopoles. We then show that there is a subclass of classical systems that are class CI semimetals upon identifying the symplectic structure to be a chiral symmetry operator. This identification requires a metric and we discuss this in comparing our characterisation with that of Peano and Schulz-Baldes (2018). We apply this framework to spin waves and predict a topological edge mode that does not appear in a bulk spectral gap, which is consistent with the experimentally observed MSSWs.
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