Magic-angle semimetals
Source abstract
Abstract
Abstract Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Cold Atom Physics and Bose-Einstein Condensates · Topological Materials and Phenomena · Quantum many-body systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (67)
Show source-provided references
1. Xu, S.-Y. et al. Topological phase transition and texture inversion in a tunable topological insulator. Science 332, 560–564 (2011).10.1126/science.1201607 ↗
2. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).10.1038/nphys1926 ↗
3. Burkov, A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).10.1103/PhysRevLett.107.127205 ↗
4. Belopolski, I. et al. A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases. Sci. Adv. 3, e1501692 (2017).10.1126/sciadv.1501692 ↗
5. Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Colloquium: artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).10.1103/RevModPhys.83.1523 ↗
6. Aidelsburger, M., Nascimbene, S. & Goldman, N. Artificial gauge fields in materials and engineered systems. C. R. Phys. 19, 394–432 (2018).10.1016/j.crhy.2018.03.002 ↗
7. Lee, C. H. et al. Topolectrical circuits. Commun. Phys. 1, 39 (2018).10.1038/s42005-018-0035-2 ↗
8. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).10.1103/RevModPhys.91.015006 ↗
9. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).10.1038/nature26154 ↗
10. Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).10.1038/s41567-018-0387-2 ↗
11. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).10.1038/nature26160 ↗
12. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).10.1126/science.aav1910 ↗
13. Song, J. C. W., Shytov, A. V. & Levitov, L. S. Electron interactions and gap opening in graphene superlattices. Phys. Rev. Lett. 111, 266801 (2013).10.1103/PhysRevLett.111.266801 ↗
14. Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).10.1073/pnas.1620140114 ↗
15. Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).10.1103/PhysRevLett.121.026402 ↗
16. Trambly de Laissardiere, G., Mayou, D. & Magaud, L. Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804–808 (2010).10.1021/nl902948m ↗
17. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).10.1073/pnas.1108174108 ↗
18. dos Santos, J. L., Peres, N. & Neto, A. C. Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012).10.1103/PhysRevB.86.155449 ↗
19. San-Jose, P., González, J. & Guinea, F. Non-abelian gauge potentials in graphene bilayers. Phys. Rev. Lett. 108, 216802 (2012).10.1103/PhysRevLett.108.216802 ↗
20. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).10.1038/nphys1463 ↗
21. Brihuega, I. et al. Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis. Phys. Rev. Lett. 109, 196802 (2012).10.1103/PhysRevLett.109.196802 ↗
22. Kim, Y. et al. Charge inversion and topological phase transition at a twist angle induced van Hove singularity of bilayer graphene. Nano Lett. 16, 5053–5059 (2016).10.1021/acs.nanolett.6b01906 ↗
23. Padhi, B., Setty, C. & Phillips, P. W. Doped twisted bilayer graphene near magic angles: proximity to Wigner crystallization, not Mott insulation. Nano Lett. 18, 6175–6180 (2018).10.1021/acs.nanolett.8b02033 ↗
24. Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).
25. Yuan, N. F. Q. & Fu, L. Model for the metal-insulator transition in graphene superlattices and beyond. Phys. Rev. B 98, 045103 (2018).10.1103/PhysRevB.98.045103 ↗
26. Kang, J. & Vafek, O. Symmetry, maximally localized Wannier states, and a low-energy model for twisted bilayer graphene narrow bands. Phys. Rev. X 8, 031088 (2018).
27. Xu, C. & Balents, L. Topological superconductivity in twisted multilayer graphene. Phys. Rev. Lett. 121, 087001 (2018).10.1103/PhysRevLett.121.087001 ↗
28. Lian, B., Wang, Z. & Bernevig, B. A. Twisted bilayer graphene: a phonon-driven superconductor. Phys. Rev. Lett. 122, 257002 (2019).10.1103/PhysRevLett.122.257002 ↗
29. Dodaro, J. F., Kivelson, S. A., Schattner, Y., Sun, X. Q. & Wang, C. Phases of a phenomenological model of twisted bilayer graphene. Phys. Rev. B 98, 075154 (2018).10.1103/PhysRevB.98.075154 ↗
30. Tarnopolsky, G., Kruchkov, A. J. & Vishwanath, A. Origin of magic angles in twisted bilayer graphene. Phys. Rev. Lett. 122, 106405 (2019).10.1103/PhysRevLett.122.106405 ↗
31. Wolf, T. M. R., Zilberberg, O., Levkivskyi, I. & Blatter, G. Substrate-induced topological minibands in graphene. Phys. Rev. B 98, 125408 (2018).10.1103/PhysRevB.98.125408 ↗
32. Janot, C. Quasicrystals: A Primer. Monographs on the Physics and Chemistry of Materials (OUP Oxford, 2012).
33. Evers, F. & Mirlin, A. D. Anderson transitions. Rev. Mod. Phys. 80, 1355–1417 (2008).10.1103/RevModPhys.80.1355 ↗
34. Pixley, J. H., Wilson, J. H., Huse, D. A. & Gopalakrishnan, S. Weyl semimetal to metal phase transitions driven by quasiperiodic potentials. Phys. Rev. Lett. 120, 207604 (2018).10.1103/PhysRevLett.120.207604 ↗
35. Gärttner, M., Syzranov, S., Rey, A., Gurarie, V. & Radzihovsky, L. Disorder-driven transition in a chain with power-law hopping. Phys. Rev. B 92, 041406 (2015).10.1103/PhysRevB.92.041406 ↗
36. Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G. & Esslinger, T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012).10.1038/nature10871 ↗
37. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).10.1038/nature13915 ↗
38. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2015).10.1038/nphys3171 ↗
39. Huang, L. et al. Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases. Nat. Phys. 12, 540–544 (2016).10.1038/nphys3672 ↗
40. Wu, Z. et al. Realization of two-dimensional spin-orbit coupling for bose-einstein condensates. Science 354, 83–88 (2016).10.1126/science.aaf6689 ↗
41. Richerme, P. et al. Non-local propagation of correlations in quantum systems with long-range interactions. Nature 511, 198 (2014).10.1038/nature13450 ↗
42. Sun, K., Liu, W. V., Hemmerich, A. & Das Sarma, S. Topological semimetal in a fermionic optical lattice. Nat. Phys. 8, 67–70 (2012).10.1038/nphys2134 ↗
43. Jiang, J.-H. Tunable topological Weyl semimetal from simple-cubic lattices with staggered fluxes. Phys. Rev. A 85, 033640 (2012).10.1103/PhysRevA.85.033640 ↗
44. Dubček, T. et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett. 114, 225301 (2015).10.1103/PhysRevLett.114.225301 ↗
45. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).10.1126/science.aaa7432 ↗
46. Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016).10.1038/nphys3783 ↗
47. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).10.1038/nature09827 ↗
48. Peterson, C. W., Benalcazar, W. A., Hughes, T. L. & Bahl, G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555, 346–350 (2018).10.1038/nature25777 ↗
49. Abrahams, E., Anderson, P., Licciardello, D. & Ramakrishnan, T. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).10.1103/PhysRevLett.42.673 ↗
50. Devakul, T. & Huse, D. A. Anderson localization transitions with and without random potentials. Phys. Rev. B 96, 214201 (2017).10.1103/PhysRevB.96.214201 ↗
51. Hiramoto, H. & Kohmoto, M. Electronic spectral and wavefunction properties of one-dimensional quasiperiodic systems: a scaling approach. Int. J. Mod. Phys. B 6, 281–320 (1992).10.1142/S0217979292000153 ↗
52. Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012).10.1103/RevModPhys.84.1419 ↗
53. Brouder, C., Panati, G., Calandra, M., Mourougane, C. & Marzari, N. Exponential localization of Wannier functions in insulators. Phys. Rev. Lett. 98, 046402 (2007).10.1103/PhysRevLett.98.046402 ↗
54. Cano, J. et al. Topology of disconnected elementary band representations. Phys. Rev. Lett. 120, 266401 (2018).10.1103/PhysRevLett.120.266401 ↗
55. Po, H. C., Watanabe, H. & Vishwanath, A. Fragile topology and wannier obstructions. Phys. Rev. Lett. 121, 126402 (2018).10.1103/PhysRevLett.121.126402 ↗
56. Rechtsman, M. C., Jeong, H.-C., Chaikin, P. M., Torquato, S. & Steinhardt, P. J. Optimized structures for photonic quasicrystals. Phys. Rev. Lett. 101, 073902 (2008).10.1103/PhysRevLett.101.073902 ↗
57. Gaebler, J. et al. Observation of pseudogap behaviour in a strongly interacting Fermi gas. Nat. Phys. 6, 569–573 (2010).10.1038/nphys1709 ↗
58. Schneider, U. et al. Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms. Nat. Phys. 8, 213–218 (2012).10.1038/nphys2205 ↗
59. Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405 (2010).10.1103/PhysRevB.81.161405 ↗
60. Scardicchio, A. & Thiery, T. Perturbation theory approaches to Anderson and many-body localization: some lecture notes. Preprint at https://arxiv.org/abs/1710.01234 (2017).
61. Pal, H. K., Spitz, S. & Kindermann, M. Emergent geometric frustration and flat band in moiré bilayer graphene. Phys. Rev. Lett. 123, 186402 (2019).10.1103/PhysRevLett.123.186402 ↗
62. Yao, W. et al. Quasicrystalline 30∘ twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling. Proc. Natl Acad. Sci. USA 115, 6928–6933 (2018).10.1073/pnas.1720865115 ↗
63. Ahn, S. J. et al. Dirac electrons in a dodecagonal graphene quasicrystal. Science 361, 782–786 (2018).10.1126/science.aar8412 ↗
64. Salamon, T, et al. Simulating Twistronics without a Twist. Phys. Rev. Lett. 125, 030504 (2020).10.1103/PhysRevLett.125.030504 ↗
65. González-Tudela, A. & Cirac, J. I. Cold atoms in twisted-bilayer optical potentials. Phys. Rev. A. 100, 053604 (2019).10.1103/PhysRevA.100.053604 ↗
66. Weiße, A., Wellein, G., Alvermann, A. & Fehske, H. The kernel polynomial method. Rev. Mod. Phys. 78, 275–306 (2006).10.1103/RevModPhys.78.275 ↗
67. Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012).10.1103/RevModPhys.84.1419 ↗