Remarks on the Quantum Effects of Screw Dislocation Topology and Missing Magnetic Flux

We revisit the interaction between a point charge and an inhomogeneous magnetic field that yields the magnetic quantum dot system. This magnetic field is defined by filling the whole space, except for a region of radius r0. Then, we assume that there is an impenetrable potential wall located at r0 and discuss the quantum effects of screw dislocation topology and the missing magnetic flux. We first show that Landau levels can be achieved even though there is the presence of an impenetrable potential wall. We go further by discussing the confinement of a point charge to a cylindrical wire. In both cases, we show Aharonov–Bohm-type effects for bound states can be obtained from the influence of the screw dislocation topology and the missing magnetic flux. Later, we discuss the influence of the screw dislocation topology and the missing magnetic flux on the magnetization and the persistent currents.