Speaker: Hidenori Fukaya (Osaka Univ.)
Title: Magnetic monopole and domain-wall fermion Dirac operator
Time/Date: 4:45-6:15pm, May 23 (Tue.), 2023
Room: 126 Math Sci Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)
Abstract: The Witten effect is a theoretical prediction about a monopole that it acquires a fractional electric charge inside topological insulators. In this work, we try to microscopically describe this phenomenon by solving a regularized Dirac equation in the presence of the monopole. In our analysis, the gauge field is smeared within a finite range to remove the short-range singularity and the so-called Wilson term is added to manifestly distinguish the topological and normal insulators. Our findings show that the dense magnetic flux around the monopole induces a strong positive mass shift to the electrons, creating a domain-wall. This small but finite-sized domain-wall localizes chiral zero modes, which is topologically protected by the Atiyah-Singer index theorem. The cobordism invariance of the index is crucial to explain why the electric charge is fractional.