Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder

We study the Aharonov-Bohm effect in a two-terminal helical ring with long-range hopping in the presence of Rashba spin-orbit interaction. We explore how the spin polarization behavior changes depending on the applied magnetic flux and the incoming electron energy. The most interesting feature that we articulate in this system is that zero-energy crossings appear in the energy spectra at Phi = 0 and also at integer multiples of half-flux quantum values (n Phi(0)/2, n being an integer) of the applied magnetic flux. We investigate the transport properties of the ring using Green's function formalism and find that the zero-energy transmission peaks corresponding to those zero-energy crossings vanish in the presence of Rashba spin-orbit interaction. We also incorporate static random disorder in our system and show that the zero-energy crossings and transmission peaks are not immune to disorder even in the absence of Rashba spin-orbit interaction. The latter prevents the possibility of these helical states in the ring behaving like topological insulator edge states.