(a) The crystal structure of PbX with space group (b) First Brillouin zone (BZ) of bulk and the projected surface BZ on (001) and (111) planes. There are four L points (L₁, L₂, L₃, L₄) in the bulk first BZ. For the (001) face, L₁ and L₂ are projected to the , while L₃ and L₄ are projected to another . For the (111) face, L₃ is projected to , while L₁, L₂ and L₄ are projected to The light yellow region is invariant under the mirror symmetry .