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Superconducting gap modulations: Are they from pair density waves or pair-breaking scattering?

Yin Jia-Xin Wang Qiang-Hua

Yin Jia-Xin, Wang Qiang-Hua. Superconducting gap modulations: Are they from pair density waves or pair-breaking scattering?. Acta Phys. Sin., 2024, 73(15): 157401. doi: 10.7498/aps.73.20240807
Citation: Yin Jia-Xin, Wang Qiang-Hua. Superconducting gap modulations: Are they from pair density waves or pair-breaking scattering?. Acta Phys. Sin., 2024, 73(15): 157401. doi: 10.7498/aps.73.20240807

Superconducting gap modulations: Are they from pair density waves or pair-breaking scattering?

Yin Jia-Xin, Wang Qiang-Hua
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  • In his seminal work published in Acta Physica Sinica in 1965, Yu Lu pointed out that the superconducting gap exhibits weak modulations near the pair-breaking magnetic impurity in a superconductor. In the past ten year, a series high-resolution scanning tunneling microscopy works reported weak superconducting gap modulations in certain superconductors and explained these phenomena as pair density waves. In line with Yu Lu’s discovery, Lee D H et al. pointed out that in many cases, the interference effect of pair-breaking scattering can also lead to superconducting gap modulations in space. We will discuss the distinction and unification of these two kinds of mechanisms, as well as their relevance to recent experimental observations.
      PACS:
      74.25.Jb(Electronic structure (photoemission, etc.))
      74.55.+v(Tunneling phenomena: single particle tunneling and STM)
      74.62.En(Effects of disorder)
      Corresponding author: Yin Jia-Xin, yinjx@sustech.edu.cn

    超导是一种神奇的宏观量子态, 超导材料表现有零电阻和完全抗磁性. 一般认为形成这种量子态, 首要的微观机理是要使得材料费米能处的电子形成两两配对, 配对电子的动量相反, 即配对电子的波矢为零[1]. 这种情况下, 配对序参量不会呈现出波动特性, 衡量配对电子束缚能的超导能隙在空间中呈现均匀分布. 20世纪60年代初, 理论学家Fulde P, Ferrell R A和Larkin A I, Ovchinnikov Y N预言在磁场作用下, 配对电子的总动量不为零, 呈现出有限波矢[2,3]. 这种超导态就会呈现出波动的特性, 称为配对密度波态或者 “FFLO”态. 在“FFLO”态中, 超导能隙在空间中会呈现出周期为2π/Q的振荡(图1(a)), 其中, FF态是平面波形式的配对密度波, Δ(r)=Δ0eiQr, 而LO是驻波形式的配对密度波, Δ(r)=Δ0cos(Qr). 近十几年间, 随着扫描隧道显微技术的发展与测量精度的提高, 学者们逐渐在多种超导量子材料中观测到了超导能隙在空间中的微弱振荡行为(振荡幅度占能隙平均值的5%左右)[412], 并指认为类比于“FFLO”态的配对密度波.

    图 1 配对密度波(a)与拆对杂质散射(b)造成的超导能隙振荡\r\nFig. 1. Superconducting gap modulations induced by pair density waves (a) and pair-breaking scatterings (b).
    图 1  配对密度波(a)与拆对杂质散射(b)造成的超导能隙振荡
    Fig. 1.  Superconducting gap modulations induced by pair density waves (a) and pair-breaking scatterings (b).

    同样在20世纪60年代初, 我国理论学者于渌在国内有限的科研条件下发现了超导体内磁性杂质的拆对行为, 即超导能隙内形成局域束缚态[13]. 这项工作在国际上被广泛认为是超导领域内的经典之作. 于渌先生的论文附录中详细推导了能隙在杂质周围的周期性振荡行为(图1(b)), 并指出了这种变化的量级在1/15(图2). 这在当时来看确实是一个可以忽略的小量, 然而却与当前实验观测到的能隙振荡幅度的数量级吻合. 近期, 李东海等[14]则进一步指出了在多种情况下(包括磁性杂质、非磁性杂质、相位变化的超导序参量、磁性超导体等), 多个杂质的拆对散射形成干涉后可以形成全局的能隙的周期性振荡. 这样的振荡行为可能不涉及相位调制, 并区别于配对密度波.

    图 2 于渌对磁性杂质周围能隙振荡的推导与量级估算, 节选自文献[13]\r\nFig. 2. Results on superconducting gap modulations near the magnetic impurities by Lu Yu from Ref. [13].
    图 2  于渌对磁性杂质周围能隙振荡的推导与量级估算, 节选自文献[13]
    Fig. 2.  Results on superconducting gap modulations near the magnetic impurities by Lu Yu from Ref. [13].

    量子世界中, 对立往往隐喻着统一. 上述两种振荡机制的确又有着深刻的联系. 例如, “FFLO”态中引入的磁场是明确破缺时间反演对称性的[2,3]; 磁性杂质也是因为明确破坏了时间反演对称性, 从而破坏超导电性, 并产生局域束缚态和能隙振荡[13]; 当超导材料存在自发性的时间反演对称性破缺时, 非磁性杂质也可破坏超导并激发出能隙振荡[14]. 因此, 配对密度波与拆对散射似乎都与时间反演对称性破缺有着统一的内禀联系. 进一步, 二者在关联体系内甚至可能存在着混合: 当杂质拆对散射在某个特定波矢特别强且呈现发散趋势时, 往往也意味着此处费米面的失稳, 有可能在相同波矢涌现出丰富的密度波态.

    目前发表的大多数论文把已有的实验数据都解释成配对密度波. 如此是否准确, 成为领域内值得深思的问题. 我们从扫描隧道显微谱学技术和理论层面对这个难题进行一些抛砖引玉的剖析. 在实验中, 扫描隧道显微镜一般是对超导样品的某一个小的区域进行能隙的谱学成像, 对实空间数据傅里叶变换后得到能隙振荡的波矢. 另一种测量方法是利用超导针尖与超导样品实现约瑟夫森隧道结, 对约瑟夫森电流或者是约瑟夫森零能电导峰进行空间成像, 再对实空间数据进行傅里叶变换后得到所谓配对电子密度振荡的波矢. 值得注意的是, 这里配对电子密度并不直接对应于超流密度, 而是一个唯象局域波函数的密度, 实则经过严格推导后对应于超导能隙的一个复杂函数[15], 近似与能隙大小的平方值成比例. 这样, 约瑟夫森扫描隧道显微镜测量到的信号仍然是超导能隙的空间振荡行为, 并不能被夸大认为是通常意义上的配对电子超流密度的波动. 这样, 两种实验方法实则都是测量超导能隙振荡行为, 我们也无法用后者严格区分配对密度波和拆对杂质散射.

    拆对杂质散射机理一般要求存在杂质或者晶体缺陷, 而配对密度波则是发生在不依赖杂质的纯洁晶格中电子结构的行为. 因此, 实验中如果在没有杂质或缺陷的干净区域测量到能隙振荡, 则很大可能是来自配对密度波. 实验中如果只在杂质或缺陷附近测量到能隙振荡, 而在干净区域振荡消失, 则很大可能是拆对散射; 在这种情况下, 振荡信号在倒空间中一般呈现弧形或者圆形结构, 部分反映出费米面的几何. 当测量到的能隙振荡在杂质附近出现, 且在倒空间结构呈现为点状信号时, 则既可能来自配对密度波, 又可能来自能带结构中态密度比较大的点状区域(hot spot)间的散射(杂质拆对散射), 亦或是二者的混合.

    在这种最难的情况下, 如果信号真的是来自纯净的配对密度波, 在理论上有可能利用博戈留波夫(Bogoliubov)费米面(如文献[16])对配对密度波的存在进行确认. 在有限动量配对下, 超导能隙并不严格在所有费米波矢打开在费米能, 在某些动量位置, 超导能隙打开在费米能旁边, 这样会有残留的费米面形成博戈留波夫费米面. 博戈留波夫费米面在动量空间的几何形状应当与配对电子的波动波矢有着严格的倒空间-实空间对应关系. 如果探测到这样的对应关系, 则可以锁定配对密度波起源. 值得注意的是, “FFLO”意义下的配对密度波都是针对可以局部定义的配对序参量而言的. 在许多强关联系统中, 由于局域库仑排斥, 配对更可能发生在近邻键上. 这种情况下, 配对密度波与谱学能隙或约瑟夫森电流的关系更为复杂, 值得在理论和实验上进一步厘清. 但这种复杂性不影响利用博戈留波夫费米面来判断配对密度波的准确性, 因此后者具有更好的通用性优势. 近期, 我们利用以上原则在笼目超导材料KV3Sb5和CsV3Sb5中用(约瑟夫森)扫描隧道显微镜对两种类型的能隙振荡进行了初步的区分, 并尝试把来自配对密度波的振荡和可能存在的博戈留波夫费米面进行联系[17], 希望能对深刻理解两种机制的区别和联系起到推动作用.

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  • 图 1  配对密度波(a)与拆对杂质散射(b)造成的超导能隙振荡

    Figure 1.  Superconducting gap modulations induced by pair density waves (a) and pair-breaking scatterings (b).

    图 2  于渌对磁性杂质周围能隙振荡的推导与量级估算, 节选自文献[13]

    Figure 2.  Results on superconducting gap modulations near the magnetic impurities by Lu Yu from Ref. [13].

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    Bardeen J, Cooper L N, Schrieffer J R 1957 Phys. Rev. 108 1175Google Scholar

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    Fulde P, Ferrell R A 1964 Phys. Rev. 135 A550Google Scholar

    [3]

    Larkin A I, Ovchinnikov Y N 1965 Sov. Phys. JETP 20 762

    [4]

    Hamidian M, Edkins S D, Joo S H, et al. 2016 Nature 532 343Google Scholar

    [5]

    Du Z Y, Li H, Joo S H, Donoway E P, Lee J, Séamus Davis J C, Gu G D, Johnson P D, Fujita K 2020 Nature 580 65Google Scholar

    [6]

    Chen H, Yang H T, Hu B, et al. 2021 Nature 599 222Google Scholar

    [7]

    Liu X, Chong Y X, Sharma R, Davis J C S 2021 Science 372 1447Google Scholar

    [8]

    Zhao H, Blackwell R, Thinel M, et al. 2023 Nature 618 940Google Scholar

    [9]

    Liu Y Z, Wei T C, He G Y, Zhang Y, Wang Z Q, Wang J 2023 Nature 618 934Google Scholar

    [10]

    Aishwarya A, May-Mann J, Raghavan A, Nie L M, Romanelli M, Ran S, Saha S R, Paglione J, Butch N P, Fradkin E, Madhavan V 2023 Nature 618 928Google Scholar

    [11]

    Gu Q, Carroll J P, Wang S Q, Ran S, Broyles C, Siddiquee H, Butch N P, Saha S R, Paglione J, Séamus Davis J C, Liu X L 2023 Nature 618 921Google Scholar

    [12]

    Agterberg D F, Séamus Davis J C, Edkins S D, et al. 2020 Annu. Rev. Condens. Matter Phys. 11 231Google Scholar

    [13]

    于渌 1965 物理学报 21 75Google Scholar

    Yu L 1965 Acta Phys. Sin. 21 75Google Scholar

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    Gao Z Q, Lin Y P, Lee D H 2023 arXiv: 2310.06024 [cond-mat.supr-con]

    [15]

    Ambegaokar V, Baratoff A 1963 Phys. Rev. Lett. 11 104Google Scholar

    [16]

    Jin J T, Jiang K, Yao H, Zhou Y 2022 Phys. Rev. Lett. 129 167001Google Scholar

    [17]

    Deng H B, Qin H L, Liu G W, et al. 2024 Nature DOI: 10.1038/s41586-024-07798-y

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Publishing process
  • Received Date:  06 June 2024
  • Accepted Date:  04 July 2024
  • Available Online:  13 July 2024
  • Published Online:  05 August 2024

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