Why magnetic monopole becomes dyon in topological insulators
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913354978689024 |
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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 |