Topological insulator ring with magnetic impurity

Topological insulator edges contain gapless states that are topologically protected by time-reversal symmetry. However, several materials considered as typical candidates for topological insulators (such as Bi₂Se₃ and Sb₂Te₃) contain spinful nuclei or other types of magnetic impurities that break the time-reversal symmetry. We model a topological insulator quantum ring and address the problem of spin coupling of the edge states to a magnetic impurity on the ring. We present an analytical solution for scattering states and band structure. Furthermore, we discuss the consequences of placing the ring inside a magnetic field and use the Aharonov-Bohm effect to link the tunable parameters that control the band structure to the magnetic flux threading the ring. We further analyze the electron-impurity entanglement entropy of the system, which reveals maximal entanglement at the band edges.