(a) Band structure of (2 × 1)-reconstructed (111) surface, where the surface states are denoted by red lines. Inset: surface atomic configuration, where only one of original three {110} mirror symmetries (indicated by yellow line) remains after reconstruction. (b) The surface Brillouin zones (SBZs): SBZ1 (blue hexagon) for original unreconstructed (111) surface and SBZ2 (red rectangle) for (2 × 1)-reconstructed surface structure. The iso-energetic contour with energies at 5 meV (30 meV) above the Fermi energy is represented by red circle (green dotted circle and shaded area). (c) Band structure of -reconstructed surface. Three mirror symmetry planes still exist (yellow lines in the inset). (d) SBZ3 and schematic iso-energetic contour with energy between the two Dirac points of and M̄.^[60]