  We consider the energy spectrum and the spin-parity structure of the
eigenstates for a quantum dot made of a strong topological insulator. Using the
effective low-energy theory in a finite-length cylinder geometry, numerical
calculations show that even at the lowest energy scales, the spin direction in
a topologically protected surface mode is not locked to the surface. We find
"zero-momentum" modes, and subgap states localized near the "caps" of the dot.
Both the energy spectrum and the spin texture of the eigenstates are basically
reproduced from an analytical surface Dirac fermion description. Our results
are compared to microscopic calculations using a tight-binding model for a
strong topological insulator in a finite-length nanowire geometry.
