轉角電子學（twistronics），一項藉由旋轉堆疊凡得瓦材料這項全新的技術，成為了操控材料能帶結構及相關物理性質的強大方法之一。其中，通過扭轉堆疊石墨烯可以製造高態密度（density of state）的平帶（flat band）。並且在平帶內被發現了各種不同的性質，如：莫特絕緣態、超導態、鐵磁性等，讓扭轉石墨烯成為了多種不同物理研究的選擇。在這裡，我們利用AFM探針切割並製成由扭轉雙‧雙層石墨烯（twisted double bilayer graphene（TDBG））組成的環形結構，並且精準定義電閘位置，使其成為空間對稱的超導量子干涉儀（SQUID），並由電閘控制其超導電流對稱性，達成對磁場量測靈敏度可調元件。最後期望此元件可以在超導電子學與量子訊息技術中扮演重要的角色。在我們的量測中，藉由位移場的分析，我們可以精準計算出樣品實際扭轉角，並且看到了平帶特有的強關聯絕緣現象，也證實了此設計下的所有電閘都可以如期運作。此結果顯示藉由TDBG製造可調對稱性的SQUID已是指日可待。

Twistronics, a new technique of twisting and stacking van der Waals materials, has become a powerful method for manipulating the band structure and correlated physical properties of materials. Furthermore, flat band, with high density of states, can be discovered in twisted graphene family. And various properties combined in the flat band, such as Mott insulating, superconducting and ferromagnetism, make twisted graphene as a versatile platform for multifunctional research. Here, we use twisted double bilayer graphene (TDBG) to fabricate a ring-shaped with spatial symmetry and define the position of the electrical gate by cut-and-stack technique, making it as a symmetry-tunable superconducting quantum interference device (SQUID) by controlling critical current of Josephson junctions to achieve adjustable sensitivity to magnetic field measurement components. This design is anticipated optimistically for future applications in superconducting electronics and quantum information technology. As result, we can make sure the real twist angle by displacement field, and the strongly correlated insulation phenomenon is observed in the measurements. Also, all gates have confirmed to be work with this complex design. This result shows that symmetry-tunable SQUID with TDBG-based are just around the corner.

1. Andre. K. G., et al., Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
2. Andre. K. G., Irina G., Van der Waals heterostructures. Nature 499, 419–425 (2013).
3. Ho, SC., Chang, CH., Hsieh, YC. et al., Hall effects in artificially corrugated bilayer graphene without breaking time-reversal symmetry. Nat Electron 4, 116–125 (2021).
4. Forsythe, C., Zhou, X., Watanabe, K. et al., Band structure engineering of 2D materials using patterned dielectric superlattices. Nature Nanotech 13, 566–571 (2018).
5. Rafi B. & Allan H. M., Moiré bands in twisted double-layer graphene. PNAS 108 (30), 12233-12237 (2011).
6. Cao, Y., Fatemi, V., Fang, S. et al., Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
7. Cao, Y., Fatemi, V., Demir, A. et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
8. Shen, C., Chu, Y., Wu, Q. et al., Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
9. Aaron L. S., et al., Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
10. Park, J.M., Cao, Y., Xia, LQ. et al., Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater: 21, 877–883 (2022).
11. Prance, J.R., Ben Shalom, M., Building devices in magic-angle graphene. Nat. Nanotechnol. 16, 745–746 (2021).
12. Rodan-Legrain, D., Cao, Y., Park, J.M. et al., Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices. Nat. Nanotechnol. 16, 769–775 (2021).
13. de Vries, F.K., Portolés, E., Zheng, G. et al., Gate-defined Josephson junctions in magic-angle twisted bilayer graphene. Nat. Nanotechnol. 16, 760–763 (2021).
14. Thompson, M. D. et al., Graphene-based tunable squids. Appl. Phys. Lett. 110, 162602 (2017).
15. Liam S. F., et al., Superconducting Quantum Interference in Twisted van der Waals Heterostructures. Nano Letters 21 (16), 6725-6731 (2021).
16. Chesca, B., Kleiner, R. & Koelle, D., SQUID theory. In The SQUID Handbook (eds. Clarke, J. & Braginski, A. I.) 29–92 (Wiley-VCH, Weinheim, 2004).
17. Tinkham, M., Introduction to Superconductivity. Vol. 2 : Dover Publications, (2004).
18. Wendin, G., Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017).
19. Charles, K., P. McEuen, Introduction to solid state physics. Vol. 8. (Wiley New York, 1976).
20. Hong-Quan, S., Zhao, L., Dong-Bo, Z., Interlayer vibration of twisted bilayer graphene: A first-principles study, Physics Letters A 383, 2628–2632 (2019).
21. Edward, M., Mikito, K., E. McCann, M. Koshino, The electronic properties of bilayer graphene. Rep. Prog. Phys. 76, 056503 (2013).
22. Fatemeh, H., et al., Moiré Flat Bands in Twisted Double Bilayer Graphene. Nano Letters 20 (4), 2410–2415 (2020).
23. Guorui, C., et al., Emergence of Tertiary Dirac Points in Graphene Moiré Superlattices. Nano Letters 17 (6), 3576–3581 (2017).
24. Novoselov, K., Geim, A., Morozov, S. et al., Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
25. Luke, S., et al., The Nature of the Interlayer Interaction in Bulk and Few-Layer Phosphorus. Nano Letters 15 (12), 8170–8175 (2015).
26. Shen, C., Chu, Y., Wu, Q. et al., Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
27. Liu, X., Hao, Z., Khalaf, E. et al., Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).
28. Patrick, A. Lee, Naoto, Nagaosa, & Xiao-Gang, Wen, Doping a Mott insulator: Physics of high-temperature superconductivity. Rev. Mod. Phys. 78 , 17 (2006).
29. Lu, X., Stepanov, P., Yang, W. et al., Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
30. Saito, Y., Ge, J., Watanabe, K. et al., Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020).
31. Castro, E. V. et al., Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007).
32. Bardeen, J. & Cooper, L. N. & Schrieffer, J. R., Microscopic Theory of Superconductivity. Phys. Rev. 106, 162–164 (1957).
33. Wu, F., MacDonald, A. H. & Martin, I., Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018).
34. Arora, H.S., Polski, R., Zhang, Y. et al., Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).
35. Lieb, Elliott H., Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989).
36. Robert, P., & Thomas P., Orbital and magnetic order in the two-orbital Hubbard model. Phys. Rev. B 81, 035112 (2010).
37. Yamada, S., Imamura, T., Machida, M. (2018). High Performance LOBPCG Method for Solving Multiple Eigenvalues of Hubbard Model: Efficiency of Communication Avoiding Neumann Expansion Preconditioner. In: Yokota, R., Wu, W. (eds) Supercomputing Frontiers. SCFA 2018. Lecture Notes in Computer Science, vol 10776. Springer, Cham.
38. C. B. Christopher Ford, Tse Ming Chen, Mesoscopic Physics.
39. Weis, J. & von Klitzing K., Metrology and microscopic picture of the integer quantum Hall effect. Phil. Trans. R. Soc. A. 369, 3954–3974 (2011).
40. Crosse, J. A. et al., Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphene. Phys. Rev. B 102, 035421 (2020).
41. Heiselberg, P. Shapiro steps in Josephson Junctions. (2013).
42. Bardeen, J., Theory of the Meissner Effect in Superconductors. Physical Review. 97 (6) 1724–1725 (1955).
43. Little, W. A. & Parks, R. D., Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder. Phys. Rev. Lett. 9, 9–12 (1962).
44. Isingizwe, F. & Perold, W., Superconducting Quantum Interference Device (SQUID) Magnetometers: Principles, Fabrication and Applications. (2010).
45. Victor, J. K., The History of Stokes' Theorem, Mathematics Magazine 52:3, 146–156 (1979).
46. Hai, L., et al., Rapid and reliable thickness identification of two-dimensional nanosheets using optical microscopy. ACS nano 7, 10344-10353 (2013).
47. Rickhaus, P., et al., Correlated electron-hole state in twisted double-bilayer graphene. Science 373, 1257–1260 (2021).
48. Riccardo, F., et al., Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials. Chem. Soc. Rev. 47, 53–68 (2018).
49. Takuya, I., et al., Bubble-Free Transfer Technique for High-Quality Graphene/Hexagonal Boron Nitride van der Waals Heterostructures. ACS Applied Materials & Interfaces 12 (7), 8533–8538 (2020).
50. Island, Joshua O., et al., Mechanical manipulation and exfoliation of boron nitride flakes by micro-plowing with an AFM tip. Science Letters Journal 4(163), 1-13 (2015).
51. Lee, J.Y., Khalaf, E., Liu, S. et al., Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene. Nat Commun 10, 5333 (2019).
52. Liu, L., Zhang, S., Chu, Y. et al., Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene. Nat Commun 13, 3292 (2022).
53. Paul, A.K., Ghosh, A., Chakraborty, S. et al., Interaction-driven giant thermopower in magic-angle twisted bilayer graphene. Nat. Phys. 18, 691–698 (2022).
54. Elías, P., et al., A Tunable Monolithic SQUID in Twisted Bilayer Graphene. arXiv:2201.13276v1 (2022).
55. Fengcheng, W. & Sankar, D. S., Ferromagnetism and superconductivity in twisted double bilayer graphene. Phys. Rev. B 101, 155149 (2020).
56. Yamashita, T., Kim, S., Kato, H. et al., π phase shifter based on NbN-based ferromagnetic Josephson junction on a silicon substrate. Sci Rep 10, 13687 (2020).
57. Ai, L., Zhang, E., Yang, J. et al., Van der Waals ferromagnetic Josephson junctions. Nat Commun 12, 6580 (2021).