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arXiv · 2304.13954

Why magnetic monopole becomes dyon in topological insulators

Shoto Aoki·Hidenori Fukaya·Naoto Kan·Mikito Koshino·Yoshiyuki Matsuki
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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.

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Shoto Aoki, Hidenori Fukaya, Naoto Kan, Mikito Koshino, Yoshiyuki Matsuki. 2023-04-27. Why magnetic monopole becomes dyon in topological insulators. https://arxiv.org/abs/2304.13954

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