Topological characterization of classical waves; The Topological origin of magnetostatic surface spin waves

古典波動現象のトポロジーによる特徴付け; 静磁スピン波表面モードのトポロジカルな起源

山本 慧   ; Thiang, G. C.*; Pirro, P.*; Kim, K.-W.*; Everschor-Sitte, K.*; 齊藤 英治*

Yamamoto, Kei; Thiang, G. C.*; Pirro, P.*; Kim, K.-W.*; Everschor-Sitte, K.*; Saito, Eiji*

We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class of classical systems that includes spin waves driven by dipole-dipole interactions, we show that the topology is characterized by vortex lines in the Brillouin zone in such a way that the symplectic structure of Hamiltonian mechanics plays an essential role. We define winding numbers around these vortex lines and identify them to be the bulk topological invariants for a class of semimetals. Exploiting the bulk-edge correspondence appropriately reformulated for these classical waves, we predict that surface modes appear but not in a gap of the bulk frequency spectrum. This feature, consistent with the magnetostatic surface spin waves, indicates a broader realm of topological phases of matter beyond spectrally gapped ones.