Bound states and persistent currents in topological insulator rings

We analyze theoretically the bound-state spectrum of an Aharonov Bohm ring in a two-dimensional topological insulator using the four-band model of HgTe quantum wells as a concrete example. We calculate analytically the circular helical edge states and their spectrum as well as the bound states evolving out of the bulk spectrum as a function of the applied magnetic flux and dimension of the ring. We also analyze the spin-dependent persistent currents, which can be used to measure the spin of single electrons. We further take into account the Rashba spin-orbit interaction that mixes the spin states and derive its effect on the ring spectrum. The flux tunability of the ring states allows for coherent mixing of the edge and the spin degrees of freedom of bound electrons, which could be exploited for quantum information processing in topological insulator rings.