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We consider the energy spectrum and the spin-parity structure of theeigenstates for a quantum dot made of a strong topological insulator. Using theeffective low-energy theory in a finite-length cylinder geometry, numericalcalculations show that even at the lowest energy scales, the spin direction ina 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 basicallyreproduced from an analytical surface Dirac fermion description. Our resultsare compared to microscopic calculations using a tight-binding model for astrong topological insulator in a finite-length nanowire geometry.

Energy spectrum and broken spin-surface locking in topological insulator quantum dots