  We study the helical edge states of a two-dimensional topological insulator
without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of
axial spin symmetry can lead to so-called generic helical edge states, which
have energy-dependent spin orientation. This opens the possibility of inelastic
backscattering and thereby nonquantized transport. Here we find analytically
the new dispersion relations and the energy dependent spin orientation of the
generic helical edge states in the presence of Rashba spin-orbit coupling
within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for
a finite width ribbon. In the single-edge case, we analytically quantify the
energy dependence of the spin orientation, which turns out to be weak for a
realistic HgTe quantum well. Nevertheless, finite size effects combined with
Rashba spin-orbit coupling result in two avoided crossings in the energy
dispersions, where the spin orientation variation of the edge states is very
significantly increased for realistic parameters. Finally, our analytical
results are found to compare well to a numerical tight-binding regularization
of the model.
