  Topological insulators are novel macroscopic quantum-mechanical phase of
matter, which hold promise for realizing some of the most exotic particles in
physics as well as application towards spintronics and quantum computation. In
all the known topological insulators, strong spin-orbit coupling is critical
for the generation of the protected massless surface states. Consequently, a
complete description of the Dirac state should include both the spin and
orbital (spatial) parts of the wavefunction. For the family of materials with a
single Dirac cone, theories and experiments agree qualitatively, showing the
topological state has a chiral spin texture that changes handedness across the
Dirac point (DP), but they differ quantitatively on how the spin is polarized.
Limited existing theoretical ideas predict chiral local orbital angular
momentum on the two sides of the DP. However, there have been neither direct
measurements nor calculations identifying the global symmetry of the spatial
wavefunction. Here we present the first results from angle-resolved
photoemission experiment and first-principles calculation that both show,
counter to current predictions, the in-plane orbital wavefunctions for the
surface states of Bi2Se3 are asymmetric relative to the DP, switching from
being tangential to the k-space constant energy surfaces above DP, to being
radial to them below the DP. Because the orbital texture switch occurs exactly
at the DP this effect should be intrinsic to the topological physics,
constituting an essential yet missing aspect in the description of the
topological Dirac state. Our results also indicate that the spin texture may be
more complex than previously reported, helping to reconcile earlier conflicting
spin resolved measurements.
