Four-band non-Abelian topological insulator and its experimental realization

Jiang, Tianshu; Guo, Qinghua; Zhang, Ruo-Yang; Zhang, Zhao-Qing; Yang, Biao; Chan, Che Ting

doi:10.1038/s41467-021-26763-1

Cited by 24 publications

(12 citation statements)

References 37 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Non-abelian topological systems have been ingeniously realized by photonic [26][27][28] , transmission line network 27,29 and acoustic 30,31 means. And relevant phase transitions have also been clearly observed 30 .…”

Section: Full Textmentioning

confidence: 99%

Minimal non-abelian nodal braiding in ideal metamaterials

Qiu

Zhang

Liu

et al. 2022

Preprint

View full text Add to dashboard Cite

Exploring new topological phases and phenomena has become a vital topic in condensed matter physics and material sciences. Recent studies reveal that a braided colliding nodal pair can be stabilized in a multi-gap system with PT or C_2z T symmetry. Beyond the conventional single-gap abelian band topology, this intriguing phenomenon exemplifies non-abelian topological charges. Here, we construct ideal acoustic metamaterials to realize non-abelian braiding with the fewest band nodes. We experimentally observe an elegant but nontrivial nodal braiding process, including nodes creation, braiding, collision, and repulsion (i.e., failure to annihilate), and measure the mirror eigenvalues to elucidate the essential braiding consequence. The latter, at the level of wavefunctions, is of prime importance since the braiding physics essentially aims to entangle multi-band wavefunctions. Furthermore, we experimentally unveil the highly intricate correspondence between the edge responses and the bulk non-abelian charges. Our findings pave the way for developing non-abelian topological physics that is still in its infancy.

show abstract

Section: Full Textmentioning

confidence: 99%

Minimal non-abelian nodal braiding in ideal metamaterials

Qiu

Zhang

Liu

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…We also selected 25 materials with good hourglass phonon band structures and the number in the parentheses denotes the SG number. Selected Materials TlF (57) PtSi( 62) LaSi( 62) AsRh( 62) AuGa( 62) PdSi (62) HgO( 62) TiSi( 62)) HfSi( 62) SrZn( 62) SrSi (62) IrSi( 62) LuPt( 62) PtY( 62) ZrSi( 62) TiB (62) GeSe( 62) PW( 62) MoAs( 62) AgBa( 62) RhSi (62) ZrTe( 62) GePd( 62) AuI(138) AuBr(138) hourglass band structures in P 2 and S separately, which could restrict the configuration of nodal line as shown later. S, P 2 or P 3, as the role of X described above, can be related by some high-symmetry points or lines, in the form of R-X-B listed below:…”

Section: Hourglass Phonons In Sg 138mentioning

confidence: 99%

“…This is obvious much more easier than the method of making two nodal loops by tuning structure parameters [54]. Such strategy of designing nodal structures might be easily implemented in artificial structures [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups

Fan¹,

Wan²,

Tian³

2022

Preprint

View full text Add to dashboard Cite

The band connectivity as imposed by the compatibility relations between the irreducible representations of little groups can give rise to the exotic hourglass-like shape composed of four branches of bands and five band crossings (BCs). Such an hourglass band connectivity could enforce the emergence of nontrivial excitations like Weyl fermion, Dirac fermion or even beyond them. On the other hand, the bosons, like phonons, magnons, and photons, were also shown to possess nontrivial topology and a comprehensive symmetry classification of the hourglass bosonic excitations would be of great significance to both materials design and device applications.Here we firstly list all concrete positions and representations of little groups in the Brillouin zone (BZ) related with the hourglass bosonic excitations in all the 1651 magnetic space groups and 528 magnetic layer groups, applicable to three dimensional (3D) and two dimensional (2D) systems, respectively. 255 (42) MSGs (MLGs) are found to essentially host such hourglass BCs: Here "essentially" means that the bosonic hourglass BC exists definitely as long as the studied system is crystallized in the corresponding MSG/MLG. We also perform firstprinciples calculations on hundreds of 3D nonmagnetic materials essentially hosting hourglass phonons and propose that the 2D material AlI can host hourglass phonons. We choose AuX (X=Br and I) as illustrative examples to demonstrate that two essential hourglass band structures can coexist in the phonon spectra for both materials while for AuBr, an accidental band crossing sticking two hourglasses is found interestingly. Our results of symmetry conditions for hourglass bosonic excitations can provide a useful guide of designing artificial structures with hourglass bosonic excitations.

show abstract

“…Besides the quaternion charges, the nodal braiding can also be characterized by Euler classes 21 , 24 and Dirac strings 19 , 25 . Non-abelian topological systems have been ingeniously realized by photonic 26 – 28 , transmission line network 27 , 29 and acoustic 30 – 32 means. And relevant phase transitions have also been clearly observed 30 .…”

Section: Introductionmentioning

confidence: 99%

Minimal non-abelian nodal braiding in ideal metamaterials

et al. 2023

View full text Add to dashboard Cite

Exploring new topological phases and phenomena has become a vital topic in condensed matter physics and materials sciences. Recent studies reveal that a braided colliding nodal pair can be stabilized in a multi-gap system with $$PT$$ P T or $${C}_{2z}T$$ C 2 z T symmetry. This exemplifies non-abelian topological charges beyond the scope of conventional single-gap abelian band topology. Here, we construct ideal acoustic metamaterials to realize non-abelian braiding with the fewest band nodes. By emulating the time with a sequence of acoustic samples, we experimentally observe an elegant but nontrivial nodal braiding process, including nodes creation, braiding, collision, and repulsion (i.e., impossible to annihilate), and measure the mirror eigenvalues to elucidate the braiding consequence. The latter, at the level of wavefunctions, is of prime importance since essentially braiding physics aims to entangle multi-band wavefunctions. Furthermore, we experimentally unveil the highly intricate correlation between the multi-gap edge responses and the bulk non-abelian charges. Our findings pave the way for developing non-abelian topological physics that is still in its infancy.

show abstract

Four-band non-Abelian topological insulator and its experimental realization

Cited by 24 publications

References 37 publications

Minimal non-abelian nodal braiding in ideal metamaterials

Minimal non-abelian nodal braiding in ideal metamaterials

All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups

Minimal non-abelian nodal braiding in ideal metamaterials

Contact Info

Product

Resources

About