Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials

TL;DR

This study uses theoretical and computational methods to analyze the topological phases of phonons in 2D buckled honeycomb lattices, revealing many possible phases but few realized in actual materials.

Contribution

It identifies potential topological phonon phases in the 2D buckled honeycomb lattice and explains their rarity in real materials through force constants analysis.

Findings

Nine topological phases identified in the analytical model.

All studied real materials are in trivial phonon phases.

Monte Carlo analysis explains the difficulty in realizing topological phases.

Abstract

By means of group theory, topological quantum chemistry, first-principles and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that eleven distinct phases are possible, five of which necessarily have non-trivial topology according to topological quantum chemistry. Another four of them are also identified as topological using Wilson loops in an analytical model that includes all the symmetry allowed force constants up to third nearest neighbors, making a total of nine topological phases. We then compute the ab initio phonon spectra for the two-dimensional crystals of Si, Ge, P, As and Sb in this structure and construct its phase diagram. Despite the large proportion of topological phases found in the analytical model, all of the crystals lie in a trivial phase. By analyzing the force constants space using Monte Carlo calculations, we elucidate why topological phonon phases are physically difficult to realize in real materials with this crystal structure.