Dual energy-differentiated topological transition in artificial red phosphorus chains

TL;DR

This paper explores the topological phase transitions in red phosphorus atomic chains, revealing dual energy-dependent transitions and edge states through analytical, numerical, and experimental methods.

Contribution

It introduces a novel analysis of topological phases in red phosphorus chains, including analytical band calculations and experimental validation via phononic lattice simulations.

Findings

Identification of flat-band state separation

Discovery of dual topological phase transitions

Confirmation of edge states in finite lattices

Abstract

We investigate the spectral and transport properties of an atomic chain of red phosphorus. We reveal the separation of flat-band states from the rest of the system and calculate its energy bands analytically. The topological properties of the system are established through the evaluation of the Berry (Zak) phase of the energy bands, revealing nontrivial topology. The Berry phase depends on the relative strength of the hopping parameters and exhibits dual energy-dependent topological phase transitions. Remarkably, the emergence of inert band edges provides a direct spectral signature of these transitions, acting as energy-resolved indicators of the redistribution of topological charge between bands. The existence of the associated edge states is proved numerically for finite lattices. The theoretical predictions, particularly the band structure and the existence of edge states, are further confirmed by numerical simulations of red phosphorus through a phononic lattice in the form of a highly structured aluminum plate.