Observation of a linked-loop quantum state in a topological magnet

Belopolski, Ilya; Chang, Guoqing; Cochran, Tyler A.; Cheng, Zi-Jia; Yáng, Xiàn; Hugelmeyer, Cole; Manna, Kaustuv; Yin, Jia-Xin; Cheng, Guangming; Multer, Daniel; Litskevich, Maksim; Shumiya, Nana; Zhang, Songtian S.; Shekhar, Chandra; Schröter, Niels B. M.; Chikina, Alla; Polley, Craig; Balasubramanian, T.; Leandersson, M.; Adell, Johan; Huang, Shin-Ming; Yao, Nan; Strocov, Vladimir N.; Felser, Claudia; Hasan, M. Zahid

doi:10.1038/s41586-022-04512-8

Cited by 22 publications

(12 citation statements)

References 58 publications

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“…Furthermore, given the twofold degeneracy of the band crossings, the nodal lines are Weyl lines and thus are sources of strong Berry curvature. [5,7] Having provided evidence for kagome Weyl lines in GdMn 6 Sn 6 , we next explore magnetically tuning this topo logical electronic structure. We investigate Tb 0.2 Gd 0.8 Mn 6 Sn 6 , with outof-plane magnetic order, by ARPES near H u .…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, given the twofold degeneracy of the band crossings, the nodal lines are Weyl lines and thus are sources of strong Berry curvature. [ 5,7 ]…”

Section: Resultsmentioning

confidence: 99%

“…Topological quantum magnets can host electronic structures with Dirac and Weyl points and lines near the Fermi level, which are effective in concentrating Berry curvature in bulk momentum space. [1][2][3][4][5][6][7] This large Berry curvature, in turn, has been observed to drive giant anomalous Hall effect (AHE) and Nernst effect, [8][9][10][11][12][13][14] even up to room temperature, [15][16][17] making these exotic magnets promising candidates for magnetic field sensors, [11,18] thermoelectric converters, [15,19] and Berry curvature memories. [20,21] Manipulation of the global topology and Berry curvature Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states.…”

Section: Introductionmentioning

confidence: 99%

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Visualization of Tunable Weyl Line in A–A Stacking Kagome Magnets

et al. 2022

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Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin–orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle‐resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out‐of‐plane dispersion in the A–A stacked kagome magnet GdMn6Sn6. Remarkably, the Weyl lines exhibit a strong magnetization‐direction‐tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

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Section: Resultsmentioning

confidence: 99%

“…Furthermore, given the twofold degeneracy of the band crossings, the nodal lines are Weyl lines and thus are sources of strong Berry curvature. [ 5,7 ]…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Visualization of Tunable Weyl Line in A–A Stacking Kagome Magnets

et al. 2022

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“…Our general scheme brings the experimental study of Hopf insulators to reality and paves the way for exploring other exotic topological phases associated with peculiar SOC. With our established platforms, the experimental exploration of links and knots with very rich topological structures becomes accessible [36][37][38] . Moreover, the idea behind our scheme can be applied to the future design of systems with more but fixed bands to implement the novel topological phases beyond the known topological classifications, such as Hopf insula-tors in three-band systems 39 and models constructed by higher-dimensional generalizations of the Hopf map 40 .…”

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confidence: 99%

Realization of a Hopf insulator in circuit systems

Wang,

Zeng,

Biao

et al. 2023

Preprint

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Three-dimensional (3D) two-band Hopf insulators are a paradigmatic example of topological phases beyond the topological classifications based on powerful methods like K-theory and symmetry indicators. Since this class of topological insulating phases was theoretically proposed in 2008, they have attracted significant interest owing to their conceptual novelty, connection to knot theory, and many fascinating physical properties. However, because their realization requires special forms of long-range spin-orbit coupling (SOC), they have not been achieved in any 3D system yet. Here we report the first experimental realization of the long-sought-after Hopf insulator in a 3D circuit system. To implement the Hopf insulator, we construct basic pseudo-spin modules and connection modules that can realize 2 × 2-matrix elements and then design the circuit network according to a tight-binding Hopf insulator Hamiltonian constructed by the Hopf map. By simulating the band structure of the designed circuit network and calculating the Hopf invariant, we find that the circuit realizes a Hopf insulator with Hopf invariant equaling 4. Experimentally, we measure the band structure of a printed circuit board and find the observed properties of the bulk bands and topological surface states (TSS) are in good agreement with the theoretical predictions, verifying the bulk-boundary correspondence of the Hopf insulator. Our scheme brings the experimental study of Hopf insulators to reality and opens the door to the implementation of more unexplored topological phases beyond the known topological classifications.

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“…A Hopf link is a trace of points where the spin points to the same direction. It has been used to investigate topological solitons [22,32,33] and the topological properties in the Brillouin zone (a three-torus T 3 ) [3,34]. The link space here is an ordinary infinite space R 3 .…”

mentioning

confidence: 99%

Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates

Cong-Jun

et al. 2022

Phys. Rev. Lett.

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Topological vacua are a family of degenerate ground states of Yang-Mills fields with zero field strength but nontrivial topological structures. They play a fundamental role in particle physics and quantum field theory, but have not yet been experimentally observed. Here we report the first theoretical proposal and experimental realization of synthetic topological vacua with a cloud of atomic Bose-Einstein condensates. Our setup provides a promising platform to demonstrate the fundamental concept that a vacuum, rather than being empty, has rich spatial structures. The Hamiltonian for the vacuum of topological number n = 1 is synthesized and the related Hopf index is measured. The vacuum of topological number n = 2 is also realized, and we find that vacua with different topological numbers have distinctive spin textures and Hopf links. Our work opens up opportunities for exploring topological vacua and related long-sought-after instantons in tabletop experiments.

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Observation of a linked-loop quantum state in a topological magnet

Cited by 22 publications

References 58 publications

Visualization of Tunable Weyl Line in A–A Stacking Kagome Magnets

Visualization of Tunable Weyl Line in A–A Stacking Kagome Magnets

Realization of a Hopf insulator in circuit systems

Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates

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