We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a $S$-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.

• Received 22 July 2022
• Accepted 22 February 2023

DOI:https://doi.org/10.1103/PhysRevD.107.065007

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Published by the American Physical Society