Spontaneous parity symmetry breaking of pi-bonds in 2D: describing topological insulators in real space

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.