Effect of coordination on topological phases on self-similar structures

TL;DR

This study explores how local coordination differences in self-similar structures influence topological phases, revealing that coordination affects phase diagrams and emphasizing the need to incorporate site coordination in topological classifications.

Contribution

It demonstrates the impact of local coordination on topological phases in self-similar structures, highlighting the importance of site coordination in phase classification.

Findings

Both structures host topologically non-trivial phases.

Phase diagrams differ between the two structures.

Coordination number influences topological phase stability.

Abstract

Topologically non-trivial phases have recently been reported on self-similar structures. Here, we investigate the effect of local structure, specifically the role of the coordination number, on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski Gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both the structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both the structures host topologically non-trivial phases and the phase diagrams are different on the two structures. This suggests that, in order to extend the present classification scheme of topological phases to non-periodic structures, one should use a framework which explicitly takes the coordination of sites into account.