Why magnetic monopole becomes dyon in topological insulators

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Hauptverfasser: Aoki, Shoto, Fukaya, Hidenori, Kan, Naoto, Koshino, Mikito, Matsuki, Yoshiyuki
Format: Preprint
Veröffentlicht: 2023
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author Aoki, Shoto
Fukaya, Hidenori
Kan, Naoto
Koshino, Mikito
Matsuki, Yoshiyuki
author_facet Aoki, Shoto
Fukaya, Hidenori
Kan, Naoto
Koshino, Mikito
Matsuki, Yoshiyuki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_13954
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Why magnetic monopole becomes dyon in topological insulators
Aoki, Shoto
Fukaya, Hidenori
Kan, Naoto
Koshino, Mikito
Matsuki, Yoshiyuki
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
High Energy Physics - Lattice
High Energy Physics - Theory
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.
title Why magnetic monopole becomes dyon in topological insulators
topic Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
High Energy Physics - Lattice
High Energy Physics - Theory
url https://arxiv.org/abs/2304.13954