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To tunnel, or not to tunnel, that is the question for a Josephson junction constructed by superconductors with unidentified pairing symmetry. Theoretically, Josephson tunneling is forbidden between two d-wave superconductors twisted by 45°. This is in sharp contrast to persistent tunneling between two s-wave superconductors. Experimentally, however, Josephson tunneling is observed in twisted bicrystalline cuprates at around 45°, against the expectation that cuprate superconductors possess d-wave pairing. Due to technical uncertainties, the early studies on twisted bulk cuprates were not widely recognized. The recent advent of van der Waals stacking has allowed a fresh look at this problem. Indeed, twisted thin flakes of cuprates have been realized and the corresponding pairing symmetry has been revisited both experimentally and theoretically. In this work, we overview the recent development on twisted cuprates. After summarizing the theoretical treatment and recent proposals, we introduce the technical progress of making the twisted cuprate junctions in van der Waal stacking, and discuss the recent experimental results of s-, d-, or d + id-wave pairing. In the end, we propose possible directions for future exploration in this field. This paper has three major sections: theories on twisted cuprates in Section 1, techniques of realizing twisted cuprates in Section 2, and experimental results on twisted cuprates in Section 3. Specifically, in Section 1, both the early theory and the latest theoretical proposals are introduced. After discussing the calculated angular dependence of Josephson tunneling between two d-wave or s-wave superconductors, we summarize the predicted features from the emergent d+id-wave pairing. They include unconventional temperature dependence of the critical Josephson current, doubling in frequency of the Fraunhofer pattern or Shapiro steps, and spontaneous Kerr rotation or emergence of Josephson diode effect. In Section 2, the technological progress of van der Waals stacking of cuprate superconductors is presented. Ultrathin twisted Josephson junctions of cuprates can be realized by either dry stacking together with oxygen post-annealing or cryogenic stacking at tens of degrees below 0 °C. In Section 3, the recent experimental results on van der Waals stacked twisted cuprates are reviewed. Tunneling in twisted underdoped cuprates realized by post-annealing indicates the existence of s-wave pairing and strong deviation from pure d-wave pairing. This result is contrasted with another study on cryogenically stacked junctions. There, signatures of d+id-wave pairing, such as fractional Shapiro steps, are reported. Still, our recent experiments on 45°-twisted junctions with ultraclean interfaces, which are also realized by cryogenic stacking, show standard Fraunhofer patterns and AC Josephson effect with only integer steps, indicating the absence of d + id-wave pairing. These results have far-reaching influence on understanding the pairing symmetry of twisted cuprates. Future efforts to study the twisted cuprates may include: extending to a wider pool of materials, pushing the thickness to the atomic limit, and adopting other characterization tools. The twisted cuprates may also find applications in high temperature superconducting quantum bit as well as Josephson diodes. -
Keywords:
- high-temperature cuprate superconductors /
- Josephson junction /
- phase-sensitive experiment /
- twisted bicrystalline junction
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图 1 (a)转角铜氧化物双晶以及s波、d波、d + id波约瑟夫森隧穿的示意图; (b)利用铋锶钙铜氧构建的45°转角的双晶的原子结构示意图, 转角界面上下各取半个原胞的厚度; (c) 转角铜氧化物结中典型电流-电压特性曲线
Figure 1. (a) Schematic drawing of a twisted cuprate bicrystal and the Josephson tunneling due to s-, d-, or d + id-wave pairing; (b) illustration of the atomic structure at the 45°-twisted interface for Bi2Sr2CaCu2O8, here the top or bottom layer has a thickness of half an unit cell; (c) typical current-voltage characteristic of a twisted cuprate junction.
图 2 (a) 低温下解理再堆叠方法的主要步骤示意图[10]; (b) 高分辨扫描透射电子显微镜所拍摄的铋锶钙铜氧双晶(上)[11]和铋锶镧铜氧双晶(下)[10]的原子结构图
Figure 2. (a) Schematic drawing of major steps in the cryogenic cleave-and-stack method[10]; (b) high resolution scanning tunneling electron microscopy images of twisted Bi-2212[11] and twisted Bi-2201[10] bicrystals.
图 3 两个研究团队利用室温堆叠后氧退火(I)和低温堆叠(II)两种方法制备出的样品在一系列转角下的约瑟夫森耦合强度 (a) 清华研究团队利用方法I得到的铋锶钙铜氧欠掺杂区间实验数据 [9]; (b) 哈佛研究团队利用方法II得到的铋锶钙铜氧最佳掺杂区间实验数据[12]; (c), (d) 清华研究团队利用方法II得到的铋锶钙铜氧最佳掺杂区间、过掺杂区间实验数据[11]和铋锶镧铜氧最佳掺杂区间的实验数据[10]
Figure 3. Josephson coupling strength as a function of twist angle from two research groups using two methods of room temperature stacking with oxygen post-annealing (I) and cryogenic stacking (II): (a) Data of underdoped Bi-2212 from the research group in Tsinghua University by using method I [9]; (b) data of optimally doped Bi-2212 from the research group in Harvard University by using method II [12]; (c), (d) data of optimally doped Bi-2212, overdoped Bi-2212[11], and optimally doped Bi-2201[10] from the research group in Tsinghua University by using method II.
图 5 (a) 实验观测到的铜氧化物转角结中的约瑟夫森二极管效应[11], 表现为一个方向(此处为正方向)约瑟夫森临界电流显著大于另一方向的值; (b) 利用约瑟夫森二极管所实现的半波整流, 共重复1000次 [11]
Figure 5. (a) Experimental observation of Josephson diode effect in twisted cuprates[11], the Josephson critical current in one direction (positive direction here) is larger than the one in the other direction; (b) demonstration of rectification effect of a square-wave with 1000 repetitions [11].
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[1] Yazdani A, da Silva Neto E H, Aynajian P 2016 Annu. Rev. Condens. Matter Phys. 7 11
Google Scholar
[2] Tsuei C C, Kirtley J R 2000 Rev. Mod. Phys. 72 969
Google Scholar
[3] Misra S, Oh S, Hornbaker D J, DiLuccio T, Eckstein J N, Yazdani A 2002 Phys. Rev. Lett. 89 087002
Google Scholar
[4] Zhong Y, Wang Y, Han S, Lü Y F, Wang W L, Zhang D, Ding H, Zhang Y M, Wang L, He K, Zhong R D, Schneeloch J A, Gen G D, Song C L, Ma X C, Xue Q K 2016 Sci. Bull. 61 1239
Google Scholar
[5] Fan J Q, Yu X Q, Cheng F J, Wang H, Wang R, Ma X, Hu X P, Zhang D, Ma X C, Xue Q K, Song C L 2022 Natl. Sci. Rev. 9 nwab225
Google Scholar
[6] Li Q, Tsay Y N, Suenaga M, Klemm R A, Gu G D, Koshizuka N 1999 Phys. Rev. Lett. 83 4160
Google Scholar
[7] Takano Y, Hatano T, Fukuyo A, Ishii A, Ohmori M, Arisawa S, Togano K, Tachiki M 2002 Phys. Rev. B 65 140513
Google Scholar
[8] Latyshev Y I, Orlov A P, Nikitina A M, Monceau P, Klemm R A 2004 Phys. Rev. B 70 094517
Google Scholar
[9] Zhu Y Y, Liao M H, Zhang Q H, Xie H Y, Meng F Q, Liu Y W, Bai Z H, Ji S H, Zhang J, Jiang K L, Zhong R D, Schneeloch J, Gu G D, Gu L, Ma X C, Zhang D, Xue Q K 2021 Phys. Rev. X 11 031011
Google Scholar
[10] Wang H, Zhu Y Y, Bai Z H, Wang Z C, Hu S X, Xie H Y, Hu X P, Cui J, Huang M L, Chen J H, Ding Y, Zhao L, Li X Y, Zhang Q H, Gu L, Zhou X J, Zhu J, Zhang D, Xue Q K 2023 Nat. Commun. 14 5201
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[11] Zhu Y Y, Wang H, Wang Z C, Hu S X, Gu G D, Zhu J, Zhang D, Xue Q K 2023 Phys. Rev. B 108 174508
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[12] Zhao S Y F, Poccia N, Cui X, Volkov P A, Yoo H, Engelke R, Ronen Y, Zhong R D, Gu G D, Plugge S, Tummuru T, Franz M, Pixley J H, Kim P 2021 arXiv: 2108.13455v1 [cond-mat. supr-con
[13] Lee J, Lee W, Kim G Y, Choi Y B, Park J, Jang S, Gu G D, Choi S Y, Cho G Y, Lee G H, Lee H J 2021 Nano Lett. 21 10469
Google Scholar
[14] Lee Y, Martini M, Confalone T, Shokri S, Saggau C N, Wolf D, Gu G D, Watanabe K, Taniguchi T, Montemurro D, Vinokur V M, Nielsch K, Poccia N 2023 Adv. Mater. 35 2209135
Google Scholar
[15] Klemm R A 2005 Philos. Mag. 85 801
Google Scholar
[16] Yokoyama T, Kawabata S, Kato T, Tanaka Y 2007 Phys. Rev. B 76 134501
Google Scholar
[17] Yang Z S, Qin S S, Zhang Q, Fang C, Hu J P 2018 Phys. Rev. B 98 104515
Google Scholar
[18] Can O, Tummuru T, Day R P, Elfimov I, Damascelli A, Franz M 2021 Nat. Phys. 17 519
Google Scholar
[19] Mercado A, Sahoo S, Franz M 2022 Phys. Rev. Lett. 128 137002
Google Scholar
[20] Tummuru T, Plugge S, Franz M 2022 Phys. Rev. B 105 064501
Google Scholar
[21] Song X Y, Zhang Y H, Vishwanath A 2022 Phys. Rev. B 105 L201102
Google Scholar
[22] Liu Y B, Zhou J, Zhang Y, Chen W Q, Yang F 2023 arXiv: 2301.07553v1 [cond-mat. supr-con
[23] Yuan A, Vituri Y, Berg E, Spivak B, Kivelson S 2023 arXiv: 2305.15472v1 [cond-mat. supr-con
[24] Irie A, Oya G 1997 Physica C Supercond 293 249
Google Scholar
[25] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. U.S.A. 102 10451
Google Scholar
[26] Jiang D, Hu T, You L X, Li Q, Li A, Wang H M, Mu G, Chen Z Y, Zhang H R, Yu G H, Zhu J, Sun Q J, Lin C T, Xiao H, Xie X M, Jiang M H 2014 Nat. Commun. 5 5708
Google Scholar
[27] Liao M H, Zhu Y Y, Zhang J, Zhong R D, Schneeloch J, Gu G D, Jiang K L, Zhang D, Ma X C, Xue Q K 2018 Nano Lett. 18 5660
Google Scholar
[28] Yu Y J, Ma L G, Cai P, Zhong R D, Ye C, Shen J, Gu G D, Chen X H, Zhang Y B 2019 Nature 575 156
Google Scholar
[29] Ghosh S, Patil V, Basu A, Kuldeep, Dutta A, Jangada D A, Kulkarni R, Thamizhavel A, Steiner J F, Oppen F, Deshmukh M M 2022 arXiv: 2210.11256v2 [cond-mat. supr-con
[30] Inomata K, Sato S, Nakajima K, Tanaka A, Wang H B, Nagao M, Hatano H, Kawabata S 2005 Phys. Rev. Lett. 95 107005
Google Scholar
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