Topological edge states in bowtie ladders with different cutting edges

We have studied topological edge states in bowtie ladders with various edge truncations. The symmetric bowtie ladder, which comprises two trivial Su–Schrieffer–Heeger (SSH) lattices, exhibits an insulator–metal transition with trivial insulating states. On the other hand, the lattice can be transformed into an extended SSH lattice depending on the edge shapes with non-trivial insulating states in that the winding number is non-zero. The winding numbers are permutationally designated in the phase diagram depending on the choice of unit cell. The topological edge states are affected by the shape of the edge and the corresponding winding number. We also studied general bowtie ladder models with richer phase diagrams using the characteristics of the localization length of the edge states showing state bifurcation.