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arXiv · 2303.03425

Zero Modes of Fermions Trapped by Giant Vortices

Logan Gates·Alexander A. Penin
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Abstract

Zero-energy solutions of the Dirac equation for the fermions bound to giant vortices of large winding number $n$ are studied in the abelian Higgs and Chern-Simons Higgs models. The case of Jackiw-Rossi theory of the Majorana states in topological superconductors is discussed in detail. By expanding in inverse powers of $n$ we find an analytic result for asymptotically all $n$ solutions required by the index theorem. In the abelian Higgs model the zero modes fill the vortex core and reveal a universal structure independent of fine details of the gauge and scalar field interactions which, in particular, determines the general properties of the large-$n$ superconducting cosmic strings. On the contrary, for the Chern-Simons Higgs vortices the zero modes are localized on the core boundary and the explicit solution is obtained for the supersymmetric couplings in a self-dual background.

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Logan Gates, Alexander A. Penin. 2023-03-06. Zero Modes of Fermions Trapped by Giant Vortices. https://doi.org/10.1007/jhep06(2023)072

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