Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect

We consider different schemes for the electrodynamic Aharonov-Bohm (AB) effect introduced in Ref. \[Phys. Rev. A mathbf{108}, 062218 (2023)\], exploring the phenomenon to enhance the understanding of its topological nature in spacetime. In the treated examples, the electric current in a solenoid varies in time, changing its internal magnetic field and producing an external electric field, while a quantum charged particle is in a superposition state inside two Faraday cages in an interferometer. The Faraday cages cancel the electric field at their interiors, such that the particle is always subjected to null electromagnetic fields. We discuss how the AB phase difference depends on the topology of the electric and magnetic fields in spacetime in the different treated situations. In particular, we discuss interesting results when a conducting wire connects the two Faraday cages, with the AB phase depending on the wire position. We also show an amplification of the AB phase when the wire makes several turns around the solenoid, which could enable an experimental verification of the effect.