  We explore the spin and charge properties of electrons in wurtzite
semiconductor nanowires where radial and axial confinement leads to tubular or
ring-shaped quantum structures. Accounting for spin-orbit interaction induced
by the wurtzite lattice as well as a radial potential gradient, we analytically
derive the corresponding low-dimensional Hamiltonians. It is demonstrated that
the resulting tubular spin-orbit Hamiltonian allows to construct spin states
that are persistent in time and robust against disorder. We find that these
special scenarios are characterized by distinctive features in the optical
conductivity spectrum, which enable an unambiguous experimental verification.
In both types of quantum structures, we discuss the dependence of the occurring
persistent charge and spin currents on an axial magnetic field and Fermi energy
which show clear fingerprints of the electronic subband structure. Here, the
spin-preserving symmetries become manifest in the vanishing of certain spin
current tensor components. Our analytic description relates the distinctive
features of the optical conductivity and persistent currents to bandstructure
characteristics which allows to deduce spin-orbit coefficients and other band
parameters from measurements.
