Phononic Helical Nodal Lines with $\mathcal{P}\mathcal{T}$ Protection in MoB${}_2$

Abstract

While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal ($\mathcal{P}\mathcal{T}$) symmetry protected helical nodal lines in the phonon spectrum of MoB${}_2$. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

References in corpus (4)

• Topological nodal line semimetals
• Double-Weyl phonons in transition-metal monosilicides
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Incommensurate phonon anomaly and the nature of charge density waves in cuprates