  We study Aharonov-Bohm effect in a two-terminal helical ring with long-range
hopping in 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 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 absence of
Rashba spin-orbit interaction. The latter prevents the possibility of behaving
these helical states in the ring like topological insulator edge states.
