  In this work we derive an effective Hamiltonian for the surface states of a
hollow topological insulator (TI) nanotube with finite width walls. Unlike a
solid TI cylinder, a TI nanotube possesses both an inner as well as outer
surface on which the states localized at each surface are coupled together. The
curvature along the circumference of the nanotube leads to a spatial variation
of the spin orbit interaction field experienced by the charge carriers as well
as an asymmetry between the inner and outer surfaces of the nanotube. Both of
these features result in terms in the effective Hamiltonian for a TI nanotube
absent in that of a flat TI thin film of the same thickness. We calculate the
numerical values of the parameters for a \ce{Bi2Se3} nanotube as a function of
the inner and outer radius, and show that the differing relative magnitudes
between the parameters result in qualitatively differing behaviour for the
eigenstates of tubes of different dimensions.
