The Weyl side of ultracold matter

doi:10.1126/science.abg0892

GSTDTAP > 气候变化

DOI	10.1126/science.abg0892
	The Weyl side of ultracold matter
	Nathan Goldman; Tarik Yefsah
	2021-04-16
发表期刊	Science
出版年	2021
英文摘要	The discovery of Weyl semimetals in 2015 was a breakthrough in the modern history of quantum matter, connecting relativistic phenomena predicted in particle physics with unusual topological properties of the solid state ([ 1 ][1]). This connection originates from the peculiar band structure of Weyl materials. In general, the band structure of a solid governs which energies are accessible to an electron moving with a given momentum. In Weyl semimetals, energy bands touch at singular points (the Weyl nodes), around which energy has a linear dependence on momentum k , reminiscent of relativistic elementary particles. On page 271 of this issue, Wang et al. ([ 2 ][2]) realized Weyl-type band structures for ultracold atoms with a high degree of control and tunability. This work paves the way for the exploration of the properties of Weyl-type band structures with a bottom-up, tunable approach and incremental complexity. ![Figure][3] Tunable Weyl nodes for ultracold atoms The engineering of Weyl-type band structures in optical lattices relies on correlating the spin and momentum of the atoms along all three spatial directions. By realizing such a spin-orbit coupling (SOC), Wang et al. formed and tuned a Weyl-type band structure for ultracold rubidium atoms. GRAPHIC: C. BICEKL/ SCIENCE Whenever a concept of relativity finds an echo in the realm of quantum materials, it triggers a wave of astonishment and excitement. Indeed, relativistic phenomena are naturally linked to high-energy physics. The excitement comes from the possibility of bringing to reality predictions that otherwise may only be recognized for their mathematical esthetics. Herman Weyl's 1929 prediction of hypothetical massless fermions is a prime example because their existence was never confirmed in particle-physics experiments but was instead observed in solid-state quantum materials ([ 1 ][1]). Observing “pseudo-relativistic electrons” in materials is not completely surprising, given the formal equivalence between the Dirac or Weyl equations describing relativistic elementary particles and the effective Schrödinger equation describing electronic excitations in semimetals ([ 1 ][1]). Beyond this formal analogy, the pseudo-relativistic band structure of Weyl semimetals also hosts a robust mathematical property, a so-called topological defect that cannot be removed under small deformations of the crystal ([ 1 ][1]). To appreciate this notion, one should first realize that a fictitious “magnetic” field (also called Berry curvature) can be associated with the energy bands of crystalline structures ([ 3 ][4]). In the vicinity of a Weyl node, this fictitious magnetic field emanates radially. This structure implies the existence of a fictitious monopole (a point-like source of fictitious magnetic field) that is located exactly at the Weyl node. The key ingredient for the emergence of Weyl-type band structures is spin-orbit coupling (SOC) ([ 1 ][1]), which is an interplay between the intrinsic angular momentum of a particle (spin) and its trajectory. Spin-orbit coupling can create band structures with strong correlations between the momentum and spin of electrons and give rise to a variety of topological quantum states of matter ([ 3 ][4]). However, not all SOCs are equivalent: Emerging topological properties crucially depend on the d imensionality of both the SOC and the material ([ 3 ][4]). In the case of Weyl semimetals, three-dimensional (3D) SOC is required and, as is often the case in solid-state physics, the path to the 2015 discovery relied on the identification of the “right” materials. Since then, much effort has focused on finding materials displaying only a few Weyl nodes, and ideally only a single pair, the minimum number allowed by the so-called doubling theorem ([ 1 ][1]). Synthetic lattices for ultracold atomic gases allow Weyl-type band structures to be built by putting in the right ingredients ([ 4 ][5]), rather than search for new materials. Wang et al. not only created a band structure on-demand with either one or two pairs of Weyl nodes, but they also dynamically turned a trivial band structure into a Weyl-type one. They set ultracold atomic clouds of rubidium-87 in their designed laser landscape that both provides a 3D lattice potential that mimics the crystalline structure of solids and couples the motion of the atoms to their spin in all three spatial directions. Its Weyl-semimetal band structure was revealed by performing tomography of the 3D momentum distribution of the atoms while keeping track of their spin texture (see the figure). With the spin-momentum distribution at hand, they probed the topological nature of the band structure; namely, the monopole charge associated with each Weyl node. The tunability of the setup allowed the effects of a sudden change in the system's parameters to be studied. Starting from atoms initially placed in a regular lattice configuration without 3D-SOC, they suddenly activated the Weyl semimetal lattice and followed the spin-population dynamics in the band structure. This provided a complementary measure of the Weyl-nodes location. Further studies with ultracold gases could explore special surface modes, previously revealed in the solid state ([ 5 ][6]) and photonics ([ 6 ][7]), whose robustness directly follows from the topological nature of the Weyl nodes. The spectroscopic detection of these Fermi-arc states could be facilitated by confining the atoms in a box with sharp boundaries ([ 7 ][8], [ 8 ][9]). Cold-atom realizations of Weyl semimetals could offer an ideal platform to study their exceptional transport properties. Subjecting them to synthetic electric and magnetic fields should induce a so-called chiral anomaly, a quantized transport of particles from one Weyl node to the other ([ 1 ][1]). This anomaly is subtle in the context of particle physics, but it could be directly measured in optical lattices through momentum-distribution measurements ([ 9 ][10]). The chiral anomaly can also be induced by axial gauge fields generated by modulating the optical lattice in space and time ([ 10 ][11]). Weyl semimetals also exhibit anomalous Hall and circular photogalvanic effects ([ 1 ][1]) that could both be revealed in optical-lattice setups through circular shaking ([ 11 ][12]). The tunability of this setting could be exploited to engineer various types of semimetals displaying exotic nodal lines, rings, or spheres in the band structure ([ 12 ][13], [ 13 ][14]). Synthetic 3D SOCs also constitute a central ingredient for the engineering of 3D topological insulators with cold gases ([ 3 ][4]). Promoting a 3D optical lattice to a fictitious 4D lattice could also be envisaged through the concept of synthetic dimension ([ 14 ][15])—for example, by inducing motion along the space spanned by atomic internal states. Applying this strategy could produce a 4D Weyl semimetal that displays fictitious Kalb-Ramond monopole fields originally introduced in string theory ([ 15 ][16]). Another exciting possibility would be to engineer 4D topological insulators ([ 14 ][15]), which have the appealing property of displaying a single isolated Weyl node on their surfaces. 1. [↵][17]1. N. P. Armitage, 2. E. J. Mele, 3. A. Vishwanath , Rev. Mod. Phys. 90, 015001 (2018). [OpenUrl][18][CrossRef][19] 2. [↵][20]1. Z.-Y. Wang et al ., Science 372, 271 (2021). [OpenUrl][21][Abstract/FREE Full Text][22] 3. [↵][23]1. X.-L. Qi, 2. S.-C. Zhang , Rev. Mod. Phys. 83, 1057 (2011). [OpenUrl][24][CrossRef][25] 4. [↵][26]1. N. R. Cooper, 2. J. Dalibard, 3. B. Spielman , Rev. Mod. Phys. 91, 015005 (2019). [OpenUrl][27] 5. [↵][28]1. S.-Y. Xu et al ., Science 349, 613 (2015). [OpenUrl][29][Abstract/FREE Full Text][30] 6. [↵][31]1. B. Yang et al ., Nat. Commun. 8, 97 (2017). [OpenUrl][32][CrossRef][33][PubMed][34] 7. [↵][35]1. T. Dubček et al ., Phys. Rev. Lett. 114, 225301 (2015). [OpenUrl][36][CrossRef][37][PubMed][38] 8. [↵][39]1. J. Y. Choi et al ., Science 352, 1547 (2016). [OpenUrl][40][Abstract/FREE Full Text][41] 9. [↵][42]1. S. Roy et al ., Phys. Rev. B 94, 161107(R) (2016). [OpenUrl][43] 10. [↵][44]1. S. Roy et al ., 2D Mater. 5, 024001 (2018). [OpenUrl][45] 11. [↵][46]1. D. T. Tran, 2. A. Dauphin, 3. A. G. Grushin, 4. P. Zoller, 5. N. Goldman , Sci. Adv. 3, e1701207 (2017). [OpenUrl][47][FREE Full Text][48] 12. [↵][49]1. B. Song et al ., Nat. Phys. 15, 911 (2019). [OpenUrl][50] 13. [↵][51]1. G. Salerno, 2. N. Goldman, 3. G. Palumbo , Phys. Rev. Res. 2, 013224 (2020). [OpenUrl][52] 14. [↵][53]1. T. Ozawa, 2. H. M. Price , Nat. Rev. Phys. 1, 349 (2019). [OpenUrl][54] 15. [↵][55]1. G. Palumbo, 2. N. Goldman , Phys. Rev. Lett. 121, 170401 (2018). [OpenUrl][56] Acknowledgments: N.G. acknowledges A. Grushin for discussions on the chiral anomaly and the Fund for Scientific Research (FRS-FNRS) (Belgium) and the European Research Council (Starting Grant TopoCold) for financial support. [1]: #ref-1 [2]: #ref-2 [3]: pending:yes [4]: #ref-3 [5]: #ref-4 [6]: #ref-5 [7]: #ref-6 [8]: #ref-7 [9]: #ref-8 [10]: #ref-9 [11]: #ref-10 [12]: #ref-11 [13]: #ref-12 [14]: #ref-13 [15]: #ref-14 [16]: #ref-15 [17]: #xref-ref-1-1 "View reference 1 in text" [18]: {openurl}?query=rft.jtitle%253DRev.%2BMod.%2BPhys.%26rft.volume%253D90%26rft.spage%253D015001%26rft_id%253Dinfo%253Adoi%252F10.1103%252FRevModPhys.90.015001%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [19]: /lookup/external-ref?access_num=10.1103/RevModPhys.90.015001&link_type=DOI [20]: #xref-ref-2-1 "View reference 2 in text" [21]: {openurl}?query=rft.jtitle%253DScience%26rft.stitle%253DScience%26rft.aulast%253DWang%26rft.auinit1%253DZ.-Y.%26rft.volume%253D372%26rft.issue%253D6539%26rft.spage%253D271%26rft.epage%253D276%26rft.atitle%253DRealization%2Bof%2Ban%2Bideal%2BWeyl%2Bsemimetal%2Bband%2Bin%2Ba%2Bquantum%2Bgas%2Bwith%2B3D%2Bspin-orbit%2Bcoupling%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.abc0105%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [22]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEyOiIzNzIvNjUzOS8yNzEiO3M6NDoiYXRvbSI7czoyMjoiL3NjaS8zNzIvNjUzOS8yMzQuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9 [23]: #xref-ref-3-1 "View reference 3 in text" [24]: {openurl}?query=rft.jtitle%253DRev.%2BMod.%2BPhys.%26rft.volume%253D83%26rft.spage%253D1057%26rft_id%253Dinfo%253Adoi%252F10.1103%252FRevModPhys.83.1057%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [25]: /lookup/external-ref?access_num=10.1103/RevModPhys.83.1057&link_type=DOI [26]: #xref-ref-4-1 "View reference 4 in text" [27]: {openurl}?query=rft.jtitle%253DRev.%2BMod.%2BPhys.%26rft.volume%253D91%26rft.spage%253D015005%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [28]: #xref-ref-5-1 "View reference 5 in text" [29]: {openurl}?query=rft.jtitle%253DScience%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.aaa9297%26rft_id%253Dinfo%253Apmid%252F26184916%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [30]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEyOiIzNDkvNjI0OC82MTMiO3M6NDoiYXRvbSI7czoyMjoiL3NjaS8zNzIvNjUzOS8yMzQuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9 [31]: #xref-ref-6-1 "View reference 6 in text" [32]: {openurl}?query=rft.jtitle%253DNat.%2BCommun.%26rft.volume%253D8%26rft.spage%253D97%26rft_id%253Dinfo%253Adoi%252F10.1038%252Fs41467-017-00134-1%26rft_id%253Dinfo%253Apmid%252F28733654%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [33]: /lookup/external-ref?access_num=10.1038/s41467-017-00134-1&link_type=DOI [34]: /lookup/external-ref?access_num=28733654&link_type=MED&atom=%2Fsci%2F372%2F6539%2F234.atom [35]: #xref-ref-7-1 "View reference 7 in text" [36]: {openurl}?query=rft.jtitle%253DPhys.%2BRev.%2BLett.%26rft.volume%253D114%26rft.spage%253D225301%26rft_id%253Dinfo%253Adoi%252F10.1103%252FPhysRevLett.114.225301%26rft_id%253Dinfo%253Apmid%252F26196624%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [37]: /lookup/external-ref?access_num=10.1103/PhysRevLett.114.225301&link_type=DOI [38]: /lookup/external-ref?access_num=26196624&link_type=MED&atom=%2Fsci%2F372%2F6539%2F234.atom [39]: #xref-ref-8-1 "View reference 8 in text" [40]: {openurl}?query=rft.jtitle%253DScience%26rft.stitle%253DScience%26rft.aulast%253DChoi%26rft.auinit1%253DJ.-y.%26rft.volume%253D352%26rft.issue%253D6293%26rft.spage%253D1547%26rft.epage%253D1552%26rft.atitle%253DExploring%2Bthe%2Bmany-body%2Blocalization%2Btransition%2Bin%2Btwo%2Bdimensions%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.aaf8834%26rft_id%253Dinfo%253Apmid%252F27339981%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [41]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEzOiIzNTIvNjI5My8xNTQ3IjtzOjQ6ImF0b20iO3M6MjI6Ii9zY2kvMzcyLzY1MzkvMjM0LmF0b20iO31zOjg6ImZyYWdtZW50IjtzOjA6IiI7fQ== [42]: #xref-ref-9-1 "View reference 9 in text" [43]: {openurl}?query=rft.jtitle%253DPhys.%2BRev.%2BB%26rft.volume%253D94%26rft.spage%253DR161107%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [44]: #xref-ref-10-1 "View reference 10 in text" [45]: {openurl}?query=rft.jtitle%253D2D%2BMater.%26rft.volume%253D5%26rft.spage%253D024001%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [46]: #xref-ref-11-1 "View reference 11 in text" [47]: {openurl}?query=rft.jtitle%253DScience%2BAdvances%26rft.stitle%253DSci%2BAdv%26rft.aulast%253DTran%26rft.auinit1%253DD.%2BT.%26rft.volume%253D3%26rft.issue%253D8%26rft.spage%253De1701207%26rft.epage%253De1701207%26rft.atitle%253DProbing%2Btopology%2Bby%2B%2522heating%2522%253A%2BQuantized%2Bcircular%2Bdichroism%2Bin%2Bultracold%2Batoms%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fsciadv.1701207%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [48]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6MzoiUERGIjtzOjExOiJqb3VybmFsQ29kZSI7czo4OiJhZHZhbmNlcyI7czo1OiJyZXNpZCI7czoxMjoiMy84L2UxNzAxMjA3IjtzOjQ6ImF0b20iO3M6MjI6Ii9zY2kvMzcyLzY1MzkvMjM0LmF0b20iO31zOjg6ImZyYWdtZW50IjtzOjA6IiI7fQ== [49]: #xref-ref-12-1 "View reference 12 in text" [50]: {openurl}?query=rft.jtitle%253DNat.%2BPhys.%26rft.volume%253D15%26rft.spage%253D911%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [51]: #xref-ref-13-1 "View reference 13 in text" [52]: {openurl}?query=rft.jtitle%253DPhys.%2BRev.%2BRes.%26rft.volume%253D2%26rft.spage%253D013224%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [53]: #xref-ref-14-1 "View reference 14 in text" [54]: {openurl}?query=rft.jtitle%253DNat.%2BRev.%2BPhys.%26rft.volume%253D1%26rft.spage%253D349%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [55]: #xref-ref-15-1 "View reference 15 in text" [56]: {openurl}?query=rft.jtitle%253DPhys.%2BRev.%2BLett.%26rft.volume%253D121%26rft.spage%253D170401%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx
领域	气候变化 ; 资源环境
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文献类型	期刊论文
条目标识符	http://119.78.100.173/C666/handle/2XK7JSWQ/322882
专题	气候变化资源环境科学
推荐引用方式 GB/T 7714	Nathan Goldman,Tarik Yefsah. The Weyl side of ultracold matter[J]. Science,2021.
APA	Nathan Goldman,&Tarik Yefsah.(2021).The Weyl side of ultracold matter.Science.
MLA	Nathan Goldman,et al."The Weyl side of ultracold matter".Science (2021).