Zusammenfassung
The surface electronic state of a strong topological insulator of spherical
shape bears two distinct types of Berry phase; one stemming from the curvature
of the spherical surface and the other from what we call "spin-to-surface
locking". The electronic spectrum on the spherical surface of a topological
insulator, offers a peculiar example of finite-size quantization, as a
consequence of the interplay between these two types of Berry phase. We have
established an explicit correspondence between the bulk Hamiltonian and the
effective Dirac operator on the curved spherical surface. A detailed comparison
of the result of this bulk/edge correspondence in the specific case of
spherical geometry with a related analysis on the electronic spectrum of
fullerene highlights the characteristic features of the topological insulator
surface state. Our explicit construction of the surface spinor wave functions
reveals a rich spin texture possibly realized on the surface of topological
insulator nano-particles. The electronic spectrum inferred by the obtained
effective surface Dirac theory is shown to be consistent with the bulk
tight-binding calculation.
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