Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
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Abstract
Abstract We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us to combine different kinds of unconventional Weyl semimetallic and higher-order topological phases to generate distinct phases. Remarkably, on 2D surfaces, the intertwining causes the Fermi-arc topology to change in a periodic pattern against surface orientation. This feature provides a characteristic and feasible signature to probe the intertwining Weyl phases. Moreover, we provide guidelines for searching candidate materials, and elaborate on emulating the intertwined double-Weyl phase in cold-atom experiments.
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Research context
OpenAlex topics: Topological Materials and Phenomena · Graphene research and applications · 2D Materials and Applications
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References (72)
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1. Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P. & Ryu, S. Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016).10.1103/RevModPhys.88.035005 ↗
2. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).10.1103/RevModPhys.90.015001 ↗
3. Yang, S. A., Pan, H. & Zhang, F. Dirac and Weyl superconductors in three dimensions. Phys. Rev. Lett. 113, 046401 (2014).10.1103/PhysRevLett.113.046401 ↗
4. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).10.1103/PhysRevB.83.205101 ↗
5. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).10.1126/science.aaa9297 ↗
6. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
7. Meng, T. & Balents, L. Weyl superconductors. Phys. Rev. B 86, 054504 (2012).10.1103/PhysRevB.86.054504 ↗
8. Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).10.1126/science.aav2334 ↗
9. Liu, D. F. et al. Magnetic Weyl semimetal phase in a kagomé crystal. Science 365, 1282–1285 (2019).10.1126/science.aav2873 ↗
10. Bradlyn, B. et al. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).10.1126/science.aaf5037 ↗
11. Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).10.1038/s41586-019-1037-2 ↗
12. Yang, Y. et al. Topological triply degenerate point with double Fermi arcs. Nat. Phys. 15, 645–649 (2019).10.1038/s41567-019-0502-z ↗
13. He, H. et al. Observation of quadratic Weyl points and double-helicoid arcs. Nat. Commun. 11, 1820 (2020).10.1038/s41467-020-15825-5 ↗
14. Fang, C., Gilbert, M. J., Dai, X. & Bernevig, B. A. Multi-Weyl topological semimetals stabilized by point group symmetry. Phys. Rev. Lett. 108, 266802 (2012).10.1103/PhysRevLett.108.266802 ↗
15. Chen, W.-J., Xiao, M. & Chan, C. T. Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states. Nat. Commun. 7, 13038 (2016).10.1038/ncomms13038 ↗
16. Huang, S.-M. et al. New type of Weyl semimetal with quadratic double Weyl fermions. Proc. Natl Acad. Sci. USA 113, 1180–1185 (2016).10.1073/pnas.1514581113 ↗
17. Vaidya, S. et al. Observation of a charge-2 photonic Weyl point in the infrared. Phys. Rev. Lett. 125, 253902 (2020).10.1103/PhysRevLett.125.253902 ↗
18. Yang, Y. et al. Ideal unconventional Weyl point in a chiral photonic metamaterial. Phys. Rev. Lett. 125, 143001 (2020).10.1103/PhysRevLett.125.143001 ↗
19. Dantas, R. M. A., Peña Benitez, F., Roy, B. & Surówka, P. Non-abelian anomalies in multi-Weyl semimetals. Phys. Rev. Res. 2, 013007 (2020).10.1103/PhysRevResearch.2.013007 ↗
20. Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).10.1103/PhysRevLett.106.106802 ↗
21. Hsieh, T. H. et al. Topological crystalline insulators in the SnTe material class. Nat. Commun. 3, 982 (2012).10.1038/ncomms1969 ↗
22. Tanaka, Y. et al. Experimental realization of a topological crystalline insulator in SnTe. Nat. Phys. 8, 800–803 (2012).10.1038/nphys2442 ↗
23. Dziawa, P. et al. Topological crystalline insulator states in PbSnSe. Nat. Mater. 11, 1023–1027 (2012).10.1038/nmat3449 ↗
24. Ando, Y. & Fu, L. Topological crystalline insulators and topological superconductors: from concepts to materials. Annu. Rev. Condens. Matter Phys. 6, 361–381 (2015).10.1146/annurev-conmatphys-031214-014501 ↗
25. Fang, C. & Fu, L. New classes of three-dimensional topological crystalline insulators: nonsymmorphic and magnetic. Phys. Rev. B 91, 161105 (2015).10.1103/PhysRevB.91.161105 ↗
26. Kruthoff, J. et al. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7, 041069 (2017).
27. Khalaf, E., Po, H. C., Vishwanath, A. & Watanabe, H. Symmetry indicators and anomalous surface states of topological crystalline insulators. Phys. Rev. X 8, 031070 (2018).
28. Po, H. C., Vishwanath, A. & Watanabe, H. Symmetry-based indicators of band topology in the 230 space groups. Nat. Commun. 8, 50 (2017).10.1038/s41467-017-00133-2 ↗
29. Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Comprehensive search for topological materials using symmetry indicators. Nature 566, 486–489 (2019).10.1038/s41586-019-0937-5 ↗
30. Zhang, T. et al. Catalogue of topological electronic materials. Nature 566, 475–479 (2019).10.1038/s41586-019-0944-6 ↗
31. Vergniory, M. G. et al. A complete catalogue of high-quality topological materials. Nature 566, 480–485 (2019).10.1038/s41586-019-0954-4 ↗
32. Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017).10.1126/science.aah6442 ↗
33. Song, Z., Fang, Z. & Fang, C. (d − 2)-dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett. 119, 246402 (2017).10.1103/PhysRevLett.119.246402 ↗
34. Langbehn, J. et al. Reflection-symmetric second-order topological insulators and superconductors. Phys. Rev. Lett. 119, 246401 (2017).10.1103/PhysRevLett.119.246401 ↗
35. Peterson, C. W. et al. A fractional corner anomaly reveals higher-order topology. Science 368, 1114–1118 (2020).10.1126/science.aba7604 ↗
36. Schindler, F. et al. Higher-order topological insulators. Sci. Adv. 4, eaat0346 (2018).10.1126/sciadv.aat0346 ↗
37. Schindler, F. et al. Higher-order topology in bismuth. Nat. Phys. 14, 918–924 (2018).10.1038/s41567-018-0224-7 ↗
38. Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator. Nature 555, 342–345 (2018).10.1038/nature25156 ↗
39. Ezawa, M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120, 026801 (2018).10.1103/PhysRevLett.120.026801 ↗
40. Wang, Z. et al. Higher-order topology, monopole nodal lines, and the origin of large fermi arcs in transition metal dichalcogenides XTe2 (X = Mo, W). Phys. Rev. Lett. 123, 186401 (2019).10.1103/PhysRevLett.123.186401 ↗
41. Chen, R. et al. Higher-order topological insulators in quasicrystals. Phys. Rev. Lett. 124, 036803 (2020).10.1103/PhysRevLett.124.036803 ↗
42. Zhang, S.-B., Calzona, A. & Trauzettel, B. All-electrically tunable networks of Majorana bound states. Phys. Rev. B 102, 100503 (2020).10.1103/PhysRevB.102.100503 ↗
43. Trifunovic, L. & Brouwer, P. W. Higher-order bulk-boundary correspondence for topological crystalline phases. Phys. Rev. X 9, 011012 (2019).
44. Khalaf, E. Higher-order topological insulators and superconductors protected by inversion symmetry. Phys. Rev. B 97, 205136 (2018).10.1103/PhysRevB.97.205136 ↗
45. Zhang, S.-B. et al. Topological and holonomic quantum computation based on second-order topological superconductors. Phys. Rev. Res. 2, 043025 (2020).10.1103/PhysRevResearch.2.043025 ↗
46. Lin, M. & Hughes, T. L. Topological quadrupolar semimetals. Phys. Rev. B 98, 241103 (2018).10.1103/PhysRevB.98.241103 ↗
47. Wang, K. et al. Boundary criticality of $${{{\mathcal{PT}}}}$$-invariant topology and second-order nodal-line semimetals. Phys. Rev. Lett. 125, 126403 (2020).10.1103/PhysRevLett.125.126403 ↗
48. Ghorashi, S. A. A., Hu, X., Hughes, T. L. & Rossi, E. Second-order Dirac superconductors and magnetic field induced Majorana hinge modes. Phys. Rev. B 100, 020509 (2019).10.1103/PhysRevB.100.020509 ↗
49. Tiwari, A., Jahin, A. & Wang, Y. Chiral Dirac superconductors: Second-order and boundary-obstructed topology. Phys. Rev. Res. 2, 043300 (2020).10.1103/PhysRevResearch.2.043300 ↗
50. Roy, B. Antiunitary symmetry protected higher-order topological phases. Phys. Rev. Res. 1, 032048 (2019).10.1103/PhysRevResearch.1.032048 ↗
51. Wang, H.-X. et al. Higher-order Weyl semimetals. Phys. Rev. Lett. 125, 146401 (2020).10.1103/PhysRevLett.125.146401 ↗
52. Ghorashi, S. A. A., Li, T. & Hughes, T. L. Higher-order Weyl semimetals. Phys. Rev. Lett. 125, 266804 (2020).10.1103/PhysRevLett.125.266804 ↗
53. Rui, W. B. et al. Higher-order Weyl superconductors with anisotropic Weyl-point connectivity. Phys. Rev. B 103, 184510 (2021).10.1103/PhysRevB.103.184510 ↗
54. Wei, Q. et al. Higher-order topological semimetal in acoustic crystals. Nat. Mater. 20, 812–817 (2021).10.1038/s41563-021-00933-4 ↗
55. Luo, L. et al. Observation of a phononic higher-order Weyl semimetal. Nat. Mater. 20, 794–799 (2021).10.1038/s41563-021-00985-6 ↗
56. Zhang, R.-X., Hsu, Y.-T. & Das Sarma, S. Higher-order topological Dirac superconductors. Phys. Rev. B 102, 094503 (2020).10.1103/PhysRevB.102.094503 ↗
57. Călugăru, D., Juričić, V. & Roy, B. Higher-order topological phases: a general principle of construction. Phys. Rev. B 99, 041301 (2019).10.1103/PhysRevB.99.041301 ↗
58. Szabó, A. L. & Roy, B. Dirty higher-order Dirac semimetal: quantum criticality and bulk-boundary correspondence. Phys. Rev. Res. 2, 043197 (2020).10.1103/PhysRevResearch.2.043197 ↗
59. Zhang, X. et al. Second-order topology and multidimensional topological transitions in sonic crystals. Nat. Phys. 15, 582–588 (2019).10.1038/s41567-019-0472-1 ↗
60. Bera, S., Sau, J. D. & Roy, B. Dirty Weyl semimetals: stability, phase transition, and quantum criticality. Phys. Rev. B 93, 201302 (2016).10.1103/PhysRevB.93.201302 ↗
61. Dantas, R. M. A., Peña Benitez, F., Roy, B. & Surówka, P. Non-abelian anomalies in multi-Weyl semimetals. Phys. Rev. Res. 2, 013007 (2020).10.1103/PhysRevResearch.2.013007 ↗
62. Tsirkin, S. S., Souza, I. & Vanderbilt, D. Composite Weyl nodes stabilized by screw symmetry with and without time-reversal invariance. Phys. Rev. B 96, 045102 (2017).10.1103/PhysRevB.96.045102 ↗
63. Hirschmann, M. M. et al. Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes. Phys. Rev. Mater. 5, 054202 (2021).10.1103/PhysRevMaterials.5.054202 ↗
64. Zhang, D.-W. et al. Topological quantum matter with cold atoms. Adv. Phys. 67, 253–402 (2018).10.1080/00018732.2019.1594094 ↗
65. Wu, Z. et al. Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates. Science 354, 83–88 (2016).10.1126/science.aaf6689 ↗
66. Song, B. et al. Observation of nodal-line semimetal with ultracold fermions in an optical lattice. Nat. Phys. 15, 911–916 (2019).10.1038/s41567-019-0564-y ↗
67. Wang, Z.-Y. et al. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling. Science 372, 271–276 (2021).10.1126/science.abc0105 ↗
68. Zhang, D.-W., Zhu, S.-L. & Wang, Z. D. Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice. Phys. Rev. A 92, 013632 (2015).10.1103/PhysRevA.92.013632 ↗
69. Zheng, Z. et al. Chiral magnetic effect in three-dimensional optical lattices. Phys. Rev. Res. 1, 033102 (2019).10.1103/PhysRevResearch.1.033102 ↗
70. Hasan, M. Z. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nat. Rev. Mater. 6, 784–803 (2021).10.1038/s41578-021-00301-3 ↗
71. Yu, Z.-M. et al. Encyclopedia of emergent particles in three-dimensional crystals. Sci. Bull. https://doi.org/10.1016/j.scib.2021.10.023 (2021).10.1016/j.scib.2021.10.023 ↗
72. Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).10.1038/ncomms6161 ↗