  The existence of pi-bonds on topological insulator surfaces is found to be
closely related to the phenomena of surface conduction and surface band spin
polarization. A pi-bond trimer or pi-bond dimer on the surface can form open
conjugated systems that are responsible for the unique surface conduction
mechanism of a topological insulator. Parity operation in 2D is identified for
a pi-bond trimer within a six-fold symmetry coordination and a pi-bond dimer
within a four-fold symmetry coordination. Spontaneous 2D parity symmetry
breaking is found to be closely related to the theoretically predicted pi
Berry's phase and the observed surface band spin polarization. The role of
pi-bonds on a cleaved Bi2Se3 surface is compared to that for graphene with a 2D
band structure containing Dirac cones. Similar pi-bond dimers within a
four-fold 2D symmetry coordination can also be identified in strained alpha-Sn
of diamond structure as a theoretically predicted topological insulator.
