論文

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2023年4月27日

Why magnetic monopole becomes dyon in topological insulators

  • Shoto Aoki
  • ,
  • Hidenori Fukaya
  • ,
  • Naoto Kan
  • ,
  • Mikito Koshino
  • ,
  • Yoshiyuki Matsuki

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.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:2304.13954
URL
http://arxiv.org/abs/2304.13954v3
URL
http://arxiv.org/pdf/2304.13954v3 本文へのリンクあり
ID情報
  • arXiv ID : arXiv:2304.13954

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