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当前常压下超导转变温度最高的材料仍然来自铜氧化物家族. 然而, 铜氧化物超导的微观机理仍未被完全建立起来, 成为了凝聚态物理领域最具挑战性的问题之一. 测定配对波函数的相位部分是全面理解高温超导机理不可或缺的一环. 该实验往往需要将不同晶向的铜氧化物拼接成高质量的约瑟夫森结, 十分考验样品的合成制备技术. 近年来, 利用二维材料中发展起来的范德瓦耳斯堆垛技术, 研究者们构建了具有原子级平整界面的转角铜氧化物双晶结, 研究了不同掺杂浓度、不同转角下的约瑟夫森隧穿, 探索了其中出现s波、d波、以及由于界面耦合演生出的d + id波配对的可能性. 本文将回顾转角铜氧化物约瑟夫森结的研究进展, 介绍近年来发展起来的转角结制备技术, 讨论当前实验测量的结果及其意义, 提出尚待解决的关键性问题.
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
Fig. 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
Fig. 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]
Fig. 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]
Fig. 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
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[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
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[15] Klemm R A 2005 Philos. Mag. 85 801
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[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
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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
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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
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Google Scholar
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Google Scholar
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