Symmetry-Enforced Nodal Chain Phonons

TL;DR

This paper introduces a new class of topological phonons called symmetry-enforced nodal-chain phonons, which are guaranteed by crystal symmetries and exhibit unique features in phononic systems, with potential realization in K2O.

Contribution

The study reveals a novel class of symmetry-enforced nodal-chain phonons, identifies candidate space groups, and demonstrates a realistic material realization in K2O with observable surface modes.

Findings

Nodal chains are guaranteed by $D_{2d}$ symmetry at specific points.

Five candidate space groups host these nodal chains with distinct patterns.

K$_{2}$O is identified as a realistic material hosting ideal nodal-chain phonons.

Abstract

Topological phonons in crystalline materials have been attracting great interest. However, most cases studied so far are direct generalizations of the topological states from electronic systems. Here, we reveal a novel class of topological phonons -- the symmetry-enforced nodal-chain phonons, which manifest features unique for phononic systems. We show that with $D_{2d}$ little co-group at a non-time-reversal-invariant-momentum point, the phononic nodal chain is guaranteed to exist owing to the vector basis symmetry of phonons, which is a unique character distinct from electronic and other systems. Combined with the spinless character, this makes the proposed nodal-chain phonons enforced by symmorphic crystal symmetries. We further screen all 230 space groups, and find five candidate groups. Interestingly, the nodal chains in these five groups exhibit two different patterns: for tetragonal systems, they are one-dimensional along the fourfold axis; for cubic systems, they form a three-dimensional network structure. Based on first-principles calculations, we identify K$_{2}$O as a realistic material hosting almost ideal nodal-chain phonons. We show that the effect of LO-TO splitting, another unique feature for phonons, helps to expose the nodal-chain phonons in K$_{2}$O in a large energy window. In addition, all the five candidate groups have spacetime inversion symmetry, so the nodal chains also feature a quantized $\pi$ Berry phase. This leads to drumhead surface phonon modes that must exist on multiple surfaces of a sample.