Three-dimensional non-Abelian anyons: Degeneracy splitting and detection by adiabatic cooling

Three-dimensional non-Abelian anyons have been theoretically proposed to exist in heterostructures composed of type II superconductors and topological insulators. We use realistic material parameters for a device derived from Bi${}_{2}$Se${}_{3}$ to quantitatively predict the temperature and magnetic field regimes where an experiment might detect the presence of these exotic states by means of a cooling effect. Within the appropriate parameter regime, an adiabatic increase of the magnetic field will result in a decrease of system temperature when anyons are present. If anyons are not present, the same experiment will result in heating.