Symmorphic and nonsymmorphic symmetries jointly-protected hourglass phonons

TL;DR

This paper demonstrates that hourglass phonon dispersions can be protected by both symmorphic and nonsymmorphic symmetries, supported by first-principles calculations revealing unique topological features in realistic materials.

Contribution

It introduces a novel symmetry protection mechanism for hourglass dispersions involving symmorphic symmetries, expanding understanding of topological phonons.

Findings

Hourglass dispersions can be jointly protected by symmorphic and nonsymmorphic symmetries.

Realistic materials exhibit hourglass phonon spectra with nodal rings and lines.

Nontrivial topological surface states and arcs are observed.

Abstract

Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the only conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in phonon spectra of realistic materials that share an antiperovskite structure with space group \emph{P}4/\emph{nmm}. Importantly, the neck points of these hourglass dispersions trace out two nodal rings tangent to four nodal lines, forming a unique hourglass nodal cage in the bulk Brillouin zone. The Berry phase analysis reveal the nontrivial topology of these nodal rings and nodal lines. Furthermore, the nontrivial surface states and isofrequency surface arcs are visible, facilitating their experimental confirmation of such exotic quasiparticles. Our work not only offers a new insight into the hourglass dispersion, but also expands aspects for studying promising topological quasiparticles in condensed-matter systems.