Catalog of phonon emergent particles and chiral phonons: Symmetry-based classification and materials database investigation

TL;DR

Addresses the lack of a systematic catalog of phonon emergent particles (EMPs) and chiral phonons by introducing a symmetry-based framework and an accompanying materials database. It provides a complete classification that determines the multiplicities of all (co-)irreps and the phonon angular momentum for each mode from space-group data and Wyckoff positions, enabling qualitative EMP counting prior to expensive calculations. The large-scale survey identifies millions of EMPs at high-symmetry points and along high-symmetry lines, with angular-momentum data compiled for tens of thousands of materials into a public portal. Two case studies demonstrate practical applications: chirality momentum locking of phonon surface states and materials with giant phonon magnetic moments, illustrating how symmetry and topology can be leveraged to engineer phonon-based functionality.

Abstract

Chirality and topology are fundamental and ubiquitous in nature. Symmetry has proven to be a powerful tool for predicting topological phonons. However, to date, topological phonon emergent particles (EMPs) have not been systematically cataloged in material databases. Moreover, traditional symmetry methods are often inadequate for predicting chiral phonons, because realistic calculations can yield negative results even when symmetry analysis permits phonon chirality. Here, we first establish a complete symmetry-based classification: given any space group and Wyckoff positions (WYPOs) occupied by atoms, the number of occurrences of all (co-)irreducible representations ((co-)irreps) (that can host EMPs) can be unambiguously known without omission prior to expensive and parameter-dependent calculation. Moreover, whether a phonon mode (belonging to one (co-)irrep) is chiral can also be determined from the occupied WYPOs. We then perform a materials database investigation identifying over 25 million EMPs at high-symmetry points and along high-symmetry lines and computing the concrete value of phonon angular momentum for each mode. We demonstrate two main applications: identifying ideal materials with surface chirality momentum locking and identifying materials with giant phonon magnetic moment. All computational data are compiled into a website: http://phonon.nju.edu.cn, which is expected to stimulate future studies on topological and chiral phonons.

Figures (3)

• Figure 1: Schematic workflow of this work (a) and an illustrative material example (b). (a) Symmetry-based classification: Given any SG and the occupied WYPOs, the multiplicities of (co-)irreps and expressions for the phonon AM can be determined. Materials database investigation: Using the symmetry results, we qualitatively identify EMPs at HSPs for each material in ICSD and PhononDB@Kyoto-u. For PhononDB@Kyoto-u, we further quantify the EMP frequencies at HSPs and along HSLs, and calculate the phonon AM for each mode. (b) Prototypical material example (BaLiP, MPID 10615, SG 187): There are three atoms per unit cell, with Li, P, and Ba occupying WYPOs 1b, 1d, and 1e, respectively. Based on the symmetry results in Table \ref{['tab']}, the co-irreps $\{1\}$, $\{3\}$, and $\{5\}$ appear twice at the K point, whereas co-irreps $\{2\}$, $\{4\}$, and $\{6\}$ appear once. Phonon modes belonging to co-irreps $\{1\}$, $\{3\}$, and $\{5\}$ carry phonon AM along the $z$ direction, while those belonging to co-irreps $\{2\}$, $\{4\}$, and $\{6\}$ carry zero phonon AM. For instance, co-irrep $\{3\}$ corresponds to a chiral mode with Li and Ba rotating oppositely in the $xy$ plane, whereas co-irrep $\{2\}$ corresponds to a linearly polarized mode (Ba vibrating along $z$). Moreover, symmetry results indicate that all phonon modes along the K$-$H path can carry nonzero phonon AM along the $z$ direction. $J_z$ represents the $z$ component of the phonon AM along K$-$H. Note that two accidental C-1 WPs with $J_z$ values of $-0.057\hbar$ and $0.165\hbar$ arise from crossings between bands with opposite signs of phonon AM along K$-$H. Paths GM$-$A and A$-$L host P-WNL and TP, respectively.
• Figure 2: Statistical overview of the materials database investigation. (a-c) Statistics of EMPs identified in materials from PhononDB@Kyoto-u and ICSD, and the number of materials hosting each EMP type. The blue bars represent the number of EMPs. The orange bars represent the number of materials. The numbers on the bars indicate the exact counts. Panels (a) and (b) summarize all 19 symmetry-allowed EMP types at HSPs based on PhononDB@Kyoto-u and ICSD. Panel (c) summarizes all 10 accidental EMP types along HSLs based on PhononDB@Kyoto-u. The full names of EMPs are from Ref. SciBul-yao. (d) Distribution of the maximum absolute value of phonon AM for 10,034 materials in PhononDB@Kyoto-u.
• Figure 3: (a) Workflow for material screening of chirality momentum locking (left) and giant phonon MM in phonon modes (right). The numbers in the workflows represent the number of materials at each stage of the screening process. (b-f) Material example (SiFeN$_2$O, MPID 972831, SG 4) with chirality momentum locking. (b) Phonon spectrum, WPs, and phonon AM. Phonon modes along paths A$-$E and C$-$Y can carry nonzero phonon AM along the $y$ direction ($J_y$ represents the $y$ component of the phonon AM) based on symmetry results. Note that there is one WP with charge $-1$ ($J_y=-0.07\hbar$) at 16.98 THz along A$-$E, and one with charge $+1$ ($J_y=-0.06\hbar$) at 16.80 THz along C$-$Y, formed by the 18th and 19th bands, respectively. (c) Crystal structure, bulk BZ, and (100) surface BZ. The bulk WPs and the projected four WPs formed by the 18th and 19th bands are denoted. (d) Isofrequency surface contours on the (100) surface at 16.98 THz and 16.80 THz, respectively. The clear Fermi arcs originating from the WPs in (c) are denoted. (e) Slab bands along a closed blue contour around one of the WPs in (c), revealing two unidirectional surface states. (f) $x, y, z$ component of the phonon AM of Slab bands in (e). The $y$ component relative to the $x$ and $z$ components of Phonon AM can be neglected. Chirality momentum locking: Left-moving and right-moving surface states have opposite phonon AM along the $x$ and $z$ directions.