Topological edge states in bowtie ladders with different cutting edges

TL;DR

This paper investigates topological edge states in bowtie ladder structures with various edge truncations, revealing how edge shape influences topological properties and phase diagrams, including insulator-metal transitions and state bifurcations.

Contribution

It introduces a detailed analysis of how different edge shapes affect topological phases and edge states in bowtie ladders, expanding understanding of edge-dependent topological phenomena.

Findings

Symmetric bowtie ladder exhibits insulator-metal transition.

Edge shape determines the topological winding number.

Rich phase diagrams with state bifurcation observed.

Abstract

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.