Topological edge states of the hexagonal linear chain

TL;DR

This paper investigates the topological properties of a one-dimensional hexagonal molecular chain, revealing edge states and phase transitions driven by hopping parameter ratios.

Contribution

It introduces a model with alternating hopping parameters in a hexagonal chain and characterizes its topological phases and edge states.

Findings

Identification of two insulating phases separated by a gap-closing transition.

Emergence of localized edge states in the topological phase.

Rich energy spectrum with dispersive and flat bands.

Abstract

We study the eigenspectrum properties of a one-dimensional molecular chain composed of hexagonal unit cells. The system features two alternating hopping parameters, resulting in a rich energy spectrum with both dispersive and flat bands. By analyzing the model under periodic and open boundary conditions, we identify two insulating phases separated by a gap-closing transition controlled by the ratio of hopping amplitudes. In the topological phase, realized when the hopping ratio falls below a critical value, edge states emerge that are exponentially localized at the boundaries of finite chains.