  We investigate the low-energy properties of (quasi) helical and fractional
helical Luttinger liquids. In particular, we calculate the Drude peak of the
optical conductivity, the density of states, as well as charge transport
properties of the interacting system with and without attached Fermi liquid
leads at small and large (compared to the gap) frequencies. For fractional
wires, we find that the low energy tunneling density of states vanishes. The
conductance of a fractional helical Luttinger liquid is non-integer. It is
independent of the Luttinger parameters in the wire, despite the intricate
mixing of charge and spin degrees of freedom, and only depends on the relative
locking of charge and spin degrees of freedom.
