Topological Quantum Chemistry on Phonon Spectra: An Application to the Buckled Honeycomb Lattice

Recently the systematic application of the methods of Topological Quantum Chemistry (TQC) [1] has enormously enlarged the number of known topological materials [2] and led to new and more refined methods of classifying their topology.

We use the methods of TQC to analyse the topology of phonon spectra. Using only the structure as input, a general recipe to find whether a material can host topological phonons is described. Applying these methods to the buckled honeycomb lattice we show how eleven phases arise, nine of which have non trivial topology. Using an analytical model consistent with the system symmetries we are able to compute Wilson loop spectrum fully characterizing all the possible topological phases. We compute the phonon spectra with DFT for Si, Ge, P, As and Sb placing them in the phase diagram, these results are justified with a Monte Carlo analysis of the phase space that shows why topological phases are physically difficult to realize.

[1] B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory,Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature547, 298 ( 2017).
[2] M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, Z. Wang, Science 582 (2020).