Phononic Helical Nodal Lines with $\mathcal{PT}$ Protection in MoB$_{2}$

TL;DR

This paper reports the first experimental observation of $ ext{PT}$-protected helical nodal lines in the phonon spectrum of MoB$_{2}$, combining first-principles calculations with inelastic x-ray scattering to identify topological Bosonic excitations.

Contribution

It introduces a novel method to identify topological Bosonic excitations, demonstrating $ ext{PT}$ symmetry protected nodal lines in phonons of MoB$_{2}$, distinct from electronic systems.

Findings

First realization of $ ext{PT}$-protected helical nodal lines in phonons.

Combines first-principles calculations with inelastic x-ray scattering.

Establishes a protocol for identifying topological Bosonic states.

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 ($\mathcal{PT}$) 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.