Triple nodal points characterized by their nodal-line structure in all magnetic space groups

Lenggenhager, Patrick M.; Liu, Xiaoxiong; Neupert, Titus; Bzdušek, Tomáš

doi:10.1103/physrevb.106.085128

Cited by 10 publications

(1 citation statement)

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“…Notably, the linear triply-degenerate points are the unavoidable nodes for the braiding of two charges in adjacent gaps. Such triply-degenerate points are widely studied before and after the birth of the non-Abelian band topology [442][443][444][445][446][447][448][449]. The non-Abelian node dispersions are illustrated in figure 30(d).…”

Section: Non-abelian Topological Statesmentioning

confidence: 99%

Topological phononic metamaterials

Zhu,

Deng,

Liu

et al. 2023

Rep. Prog. Phys.

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The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological `sasers' (i.e., the phononic analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science.

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Section: Non-abelian Topological Statesmentioning

confidence: 99%

Topological phononic metamaterials

Zhu,

Deng,

Liu

et al. 2023

Rep. Prog. Phys.

View full text Add to dashboard Cite

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Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling

Yang,

Liu,

Fang

2024

Nat Commun

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Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full rotation group O(3), leading to new quasiparticles restricted to lattices that do not have any counterpart in a vacuum. We focus on the fermionic quasiparticle excitations under “spin-space group” symmetries, applicable to materials where long-range magnetic order and itinerant electrons coexist. We provide a list of 218 classes of new quasiparticles that can only be realized in the spin-space groups. These quasiparticles have at least one of the following properties that are qualitatively distinct from those discovered in magnetic space group(MSG)s, and distinct from each other:(i) degree of degeneracy,(ii) dispersion as function of momentum, and(iii) rules of coupling to external probe fields. We rigorously prove this result as a theorem that directly relates these properties to the symmetry invariants, and then illustrate this theorem with a concrete example, by comparing three 12-fold fermions having different sets of symmetry invariants including one discovered in MSG. Our approach can be generalized to realize more quasiparticles whose little co-groups are beyond those considered in our work.

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