Single-pair Weyl points with the maximum charge number in acoustic crystals

Wang, Zhe-Qi; Liu, Qingbo; Yang, Xiang‐Feng; Fu, Hua‐Hua

doi:10.1103/physrevb.106.l161302

Cited by 16 publications

(2 citation statements)

References 36 publications

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“…[53,54] Nevertheless, in comparison with surface arc state and quadruple-helix surface state, the fan-shape phononic surface state may exhibit weaker transport signatures due to their divergence behavior or burying in trivial bulk states. However, if we obtain high-quality material samples or design ideal acoustic crystals, [55] we believe that this new kind of topological surface states may be observed easily in experiments. Additionally, to confirm our findings, IWPs and the related fan-shape surface state in other SGs listed in Table 1 are also provided in Supporting Information, Section C-G.…”

Section: Discussionmentioning

confidence: 99%

Multi‐Fold Fan‐Shape Surface State Induced by an Isolated Weyl Phonon Beyond No‐Go Theorem

Liu

Wang

et al. 2023

Advanced Science

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Absence of any surface arc state has been regarded as the fundamental property of singular Weyl points, because they are circumvented from the Nielsen‐Ninomiya no‐go theorem. In this work, through systematic investigations on topological properties of isolated Weyl phonons (IWPs) surrounded by closed Weyl nodal walls (WNWs), which are located at the Brillouin zone (BZ) boundaries of bosonic systems, it uncovers that a new kind of phononic surface state, that is, the multi‐fold fan‐shape surface state named by us, is exhibited to connect the projections of IWP and WNWs. Importantly, the number of fan leaves in this surface state is associated with the Chern number of IWP. Moreover, the topological features of charge‐two IWP in K2Mg2O3 (SG No. 96) and charge‐four IWP in Nb3Al2N (SG No. 213) confirm further the above fundamental properties of this kind of surface state. The theoretical work not only provides an effective way to seek for IWPs as well as to determine their Chern number in real materials, but also uncovers a new class of surface states in the topological Weyl complex composed of IWPs and WNWs.

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Section: Discussionmentioning

confidence: 99%

Multi‐Fold Fan‐Shape Surface State Induced by an Isolated Weyl Phonon Beyond No‐Go Theorem

Liu

Wang

et al. 2023

Advanced Science

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“…Moreover, highly-degenerated band crossings characterized by multifold rotation symmetries tend to also appear at HSPs, which provide the possibilities to realize intriguing Weyl-type excitations such as quadratic-double, cubic-triple and high-order Weyl points with higher Chern number . [44] Comparatively speaking, at high-symmetry lines (HSLs, not including HSPs), the highlydegenerated band crossings and the required screw rotation symmetries for Weyl point are much more difficult to ensure simultaneously. As a result, topological characters of Weyl point at HSLs are still rarely studied, making that some shortcomings still remain in the topic of Weyl-type excitations both in electronic and bosonic systems.…”

Section: Introductionmentioning

confidence: 99%

Unconventional Charge‐Two Weyl Phonons in High‐Symmetry Lines

Yang

Liu

Wang

et al. 2023

Advanced Physics Research

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Weyl phonons have long been regarded as an important kind of topological bosonic quasiparticle states. Previous investigations in this field mainly focus on Weyl phonons located at high‐symmetry points (HSPs) in Brillouin zone (BZ), while those located at high‐symmetry lines (HSLs, not including HSPs) are still rarely studied. Considering that their symmetry‐protected conditions are much different, we name them conventional and unconventional Weyl phonons, respectively. In this work, taking charge‐two Weyl phonons (CTWPs) as examples, the complete classifications of all unconventional CTWPs is summarized by performing symmetry analysis in all 230 space groups (SGs). Moreover, due to their different phononic dispersions, the unconventional CTWPs can be classified as Type‐I, Type‐II, and Type‐III ones. Particularly, the k · p model of unconventional CTWPs shows a k‐type feature along the invariant lines while a k2‐type feature along other directions. Additionally, we uncover that a real chiral crystal material, that is, CsBe2F5 in SG 213, can exhibit well‐defined Type‐I and Type‐II unconventional CTWPs characterized by multiple double‐helicoid surface states. Our theoretical work not only puts forward an effective way for seeking for unconventional CTWPs, but also uncover the unique advantages of this kind of CTWPs toward realistic device applications.

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Group-theoretical study of band nodes and the emanating nodal structures in crystalline materials

Tang,

Wan

2024

Quantum Front

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Topological materials usually possess protected gapless states in either the boundary or bulk, exhibiting various properties such as spin-momentum locking, Klein tunneling, Fermi arcs and so on. Database searches using symmetry data at high-symmetry points have catalogued thousands of topological materials revealing a magnitude of band nodes (BNs) at high-symmetry points or lying within high-symmetry lines/planes. A complete mapping from symmetry data (namely, representation of little group) in any BN to the $k\cdot p$ k ⋅ p model characterizing low-energy Hamiltonian around the BN (and from the $k\cdot p$ k ⋅ p model to concrete BN, inversely), is expected to complete the characterization of all BNs and gapless states. Here we first review recent progress on classifying BNs by systematically and automatically constructing $k\cdot p$ k ⋅ p models based on recently completed tabulation of all irreducible (co-)representation matrices of little groups of the 1651 magnetic space groups. As one indispensable input in constructing a symmetry-allowed and generic $k\cdot p$ k ⋅ p model, the expansion order, has been carefully and systematically truncated for any BN to a reasonable nonzero integer, by comparing the emanating nodal structure (ENS, including nodal point, nodal line and nodal surface) near the BN obtained by the explicitly constructed $k\cdot p$ k ⋅ p model and that by pure symmetry analysis using compatibility relations (CRs). Owing to the progress, we are able to summarize all 25 different configurations of ENS near BN required by CRs, provide a complete mapping from $k\cdot p$ k ⋅ p model to its realization around BN, and the corresponding ENS by CRs in an accessible file, and also reveal the protection mechanism of additional nodal lines that escape conventional analysis by CRs and is only predictable by constructing $k\cdot p$ k ⋅ p model. The symmetry-based classification results on all BNs could facilitate large-scale materials prediction and hold promise for realizing topological semimetals suitable for device applications.

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Single-pair Weyl points with the maximum charge number in acoustic crystals

Cited by 16 publications

References 36 publications

Multi‐Fold Fan‐Shape Surface State Induced by an Isolated Weyl Phonon Beyond No‐Go Theorem

Multi‐Fold Fan‐Shape Surface State Induced by an Isolated Weyl Phonon Beyond No‐Go Theorem

Unconventional Charge‐Two Weyl Phonons in High‐Symmetry Lines

Group-theoretical study of band nodes and the emanating nodal structures in crystalline materials

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