Topological modes in single-species plasmas confined to a two-dimensional surface

Certain mechanical systems with broken time-reversal symmetry are known to have similar properties to topological insulators. In particular, equatorially confined chiral edge modes can emerge, such as those that have been observed in shallow-water waves in the Earth’s oceans. Analogously, a proton plasma confined to the surface of a sphere has the symmetry to support topological vibrational modes when time-reversal symmetry is broken by a constant, axial magnetic field. Starting from the equilibrium configuration of N protons confined to a spherical surface (i.e., solutions of the Thomson problem), we explore this phenomenon using first-order, classical perturbation theory. We benchmark our numerical solutions by comparing them to the analytical solution for N = 2, which one can attain readily by leveraging the extra spatial symmetries of this special case.