Foray into the topology of poly‐bi‐[8]‐annulenylene

Analyzing phase transitions using the inherent geometrical attributes of a system has garnered enormous interest over the past few decades. The usual candidate often used for investigation is graphene—the most celebrated material among the family of tri‐coordinated graphed lattices. We show in this report that other inhabitants of the family demonstrate equally admirable structural and functional properties that at its core are controlled by their topology. Two interesting members of the family are cyclooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene, both in one and two dimensions that have been investigated by polymer chemists over a period of 50 years for its possible application in batteries exploiting its conducting properties. A single COT unit is demonstrated herein to exhibit topological solitons at sites of a broken bond similar to an open one‐dimensional Su–Schrieffer–Heeger (SSH) chain. We observe that poly‐bi‐[8]‐annulenylene in one dimension mimics two coupled SSH chains in the weak coupling limit, thereby showing the presence of topological edge modes. In the strong coupling limit, we investigate the different parameter values of our system for which we observe zero‐energy modes. Further, the application of an external magnetic field and its effects on the band flattening of the energy bands has also been studied. In two dimensions, poly‐bi‐[8]‐annulenylene forms a square‐octagon lattice which upon breaking time‐reversal symmetry goes into a topological phase forming noise‐resilient edge modes. We hope our analysis would pave the way for synthesizing such topological materials and exploiting their properties for promising applications in optoelectronics, photovoltaics, and renewable energy sources. We show in this paper tri‐coordinated lattice systems: cylooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene exhibit exotic topological properties. Flat bands are generated upon application of tailored magnetic flux for poly‐bi‐[8]‐annulenylene in one dimension. Insights from this paper open the possibility of using these polymers as an experimental ground to observe many flat‐band and topology‐related phenomena.