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Why magnetic monopole becomes dyon in topological insulators
- Publication Year :
- 2023
-
Abstract
- The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon, as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in continuum and numerically on a lattice, by adding the Wilson term and smearing the gauge field within a finite range to regularize the short-distance behavior of the system. Our results reveal that the Wilson term induces a strong positive mass shift, creating a domain-wall around the monopole/vortex. This small, yet finite-sized domain-wall localizes the chiral zero modes and ensures their stability through the Atiyah-Singer index theorem, whose cobordism invariance is crucial in explaining why the electric charge is fractional.<br />Comment: 40 pages, 10 figures, minor corrections, references added, published version
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.13954
- Document Type :
- Working Paper