Interaction of a hydrogenlike ion with a planar topological insulator

An electric charge near the surface of a topological insulator (TI) induces an image magnetic monopole. Here we study the spectra of hydrogenlike ions near the surface of a planar TI, taking into account the modifications which arise due to the presence of the image monopole magnetic fields. In fact, the atom-TI interaction provides additional contributions to the Casimir-Polder potential while the ion-TI interaction modifies the energy shifts in the spectrum, which now became distance dependent. We show that the hyperfine structure is sensitive to the image magnetic monopole fields in states with nonzero angular momentum, and that circular Rydberg ions can enhance the maximal energy shifts. We discuss in detail the energy splitting of the $n$P$_{1/2}$ and $n$P$_{3/2}$ states in hydrogen. We also analyze the Casimir-Polder potential and find that this magnetic interaction produces a large distance repulsive tail for some particular atomic states. A sizable value of the maximum of the potential requires TIs with very low values of the permittivity together with high values of the topological magnetoelectric polarization.