非中心对称材料中的超导电性和自旋轨道耦合：综述

1. Smidman

中国杭州浙江大学物理系关联物质研究中心，邮编310058

M.B. Salamon

美国德克萨斯大学纳米技术机构，德克萨斯大学邮编750830688

H.Q. Yuan

中国杭州浙江大学物理系关联物质研究中心，浙大紫金港邮编310058

中国南京大学人工微结构科学与技术协同创新中心，南京大学仙林校区邮编210093

1. F. Agterberg

密尔沃基威斯康星大学物理系，威斯康星大学邮编53201

摘要：在非中心对称超导体中，晶体结构缺乏反演中心，因为宇称不再是一个好量子数，基于对称性，一种电子型的反对称自旋轨道耦合（ASOC）就允许出现了。如果这个ASOC的强度足够大，会对超导态产生非常重大的影响。例如，它通常会导致自旋单态和自旋三重态混合的超导配对态。这种奇特的配对状态以及可能会观察到的反常（超导）行为，引发了大量的理论和实验的研究。这里我们将回顾缺失反演对称的超导体系的理论和实验结果。随后我们将回顾强关联和弱关联体材料以及二维体系中的实验特性。本文的中心在于评估ASOC对超导性质的影响，以及（ASOC的强度）到何种程度会有自旋单态和三重态混合的证据。随后将会有非中心对称超导理论方面的更细节的概述。包括ASOC对配对对称性、超导的磁响应、磁电效应、超导有限动量配对态，以及非中心对称超导体表现出拓扑超导电性的可能性。

正文选段：

E拓扑体系中的非中心对称超导电性

半赫斯勒合金是最近备受关注的一系列化合物。由于电子结构中能带倒置的出现，这些缺少反演对称中心的化合物，已经有很多被预言说拥有非平凡拓扑表面态。就是其中一种，其超导临界温度为。在低温下对横向磁场磁阻的测量表明自旋单态和三重态的混合使费米面劈裂成两个大小相似的Fermi sheets, 并且其载流子浓度比起其他超导体系出奇的低。基于超导理论的计算表明需要更大的载流子密度来解释超导转变温度。这也表明了的超导电性不能用传统的电声子配对机制来解释，而是有一种非传统的配对。基于超导理论的计算表明需要更大的载流子密度来解释超导转变温度。这也表明了的超导电性不能用传统的电声子配对机制来解释，而是有一种非传统的配对。虽然的测量不能提供足够精确的，在低温下对的测量出现的线性行为，表明线节点的存在。由于费米面附近能带倒置和能带的四重简并，这表明库珀对可能由自旋总角动量为的费米子构成，而不是普遍认为的总角动量为的费米子。所以，拥有更高角动量的五重态（）和七重态（）都有可能发生，除了自旋单态（）和自旋三重态（）是由配对引起的。这表明超导状态可能和这类具有高角动量状态的混合的宇称配对态有关，而线节点可能由自旋单态和三重态的混合引起的。其他同时表现出能带倒置和超导电性的半赫斯勒合金有RPdBi (R=Ho,Er,Tm or Lu) (Tc~1.2-1.7K), LuPtBi (Tc~1.0K) 和 LaPtBi (Tc~0.9K)。同时表现出超导电性的其他半赫斯勒化合物包括RPdBi （R=Sm, Dy, Tb or Y)，虽然这些化合物的电子结构被预言不会产生能带倒置，但是会产生平凡拓扑性。RPdBi还有另一个有趣的性质，当R是磁性元素时，该化合物会同时表现出磁序和超导电性。RPdBi还有另一个有趣的性质，当R是磁性元素时，该化合物会同时表现出磁序和超导电性。在这些化合物中超导电性和磁相之间的关系还不是很明朗，还需要进一步的详细测量。对于大部分半赫斯勒合金来说，超导能隙结构尚未得到表征。除了先前讨论的YPtBi这个例子，LuPdBi在Tc~1.7K的比热也通过一个各向同性、全能隙的单能带模型（其能隙大于弱耦合BCS理论给出的的值）拟合出来，并且由NQR测出的也在略低于S波超导Tc的温度下表现出相干态。因此对更多的半赫斯勒合金进行能带结构的测量变得更加重要，而由于在某些比热测量中缺少超导转变，（半赫斯勒合金能带结构的测量）变得更具有挑战性。另一个有前景的拓扑超导材料是NCS PbTaSe₂，其超导转变温度为3.7K。先前认为NCS可能是观察马约拉纳模型的理想体系，只要三重态分量比单态比重大。PbTaSe₂就不可能是这一类化合物，其穿透深度和超流密度可以用单间隙S波模型解释，表明任何三重态的成分应该很小。但是根据Ref.204上报道，PbTaSe₂有非平凡拓扑狄拉克表面状，所以全能隙的超导电性诱导的这些态已足够使马约拉纳束缚态的出现。因为有大量的实验测量证据PbTaSe₂中有全能隙的超导电性，所以一直很期望在这个体系中找到马约拉纳费米子的特征。事实上，对三重态主导的化合物的需求比超导能隙完全打开要严格的多，因此，识别这种非平凡表面态的NCS可能会是一种观察这类新奇现象的途径。

二维超导体：界面，单层和异质结构

近年来，表现出一系列反常现象的低维体系的性质一直是凝聚态研究的重要课题。例如，在两个绝缘体的表面可以形成一个二维导电层，以及在类似LaAlO₃/SrTio₃和LaTiO₃/SrTiO₃等物质的体系表面观察到超导电性。另一种了解二维体系的超导电性的的途径是通过单层的材料，这些材料在块状时可能是不显超导电性的，比如MoS₂半导体或者有体超导电性的NbS₂。在很多情况下,这些体系中的超导电性要么因为施加的栅极电压而产生，要么得到加强。这些界面或表面的一个重要的性质是反演对称性的破缺并且电子会受到一种Rashba形式的自旋轨道耦合作用，其强度可由施加在其上的栅极电压来改变。因此这些体系为研究ASOC对超导性质的影响提供了很珍贵的机会。这种现象的一个例子就是最近在施加了栅极电压的单层NbSe2和MoS₂中观察到了超导电性。对于这些体系的单层结构，在平面内的中心反演对称性是破缺的，所以不是Rashba形式的相互作用，导致ASOC的主要原因是因为引起了一个等效磁场，这个磁场使得自旋锁定在了垂直于平面的方向上。这将会在第三部分详细介绍。如前所述，一个外加的场超过泡利顺磁极限会引发塞曼分裂，从而破坏自旋单态的库珀对。然而，因为这些体系的费米自旋被锁定在垂直平面的方向上。他们会对平面内的磁场表现出不平常的弹力。

图14是由依赖于温度的面内上临界场。对于14(a)图中的NbSe₂，原子层薄的样品和同样超过了平面上临界场的体材料进行了比较。这些例子里，与温度的关系是线性的，并且相比起要低。随着维数的降低，，有两个方面会加强面内上临界场。首先，一旦材料的厚度比要小，平面轨道配对的破缺将会明显削弱。其次，面内上临界场远远超过，在单层NbSe2中超过了，在MoS₂中超过了。但没有观察到面内上临界场与温度线性的关系，而是成平方根关系。当施加的外场比ASOC产生的有效场要大的多时，自旋就会向平面倾斜，顺磁配对的破裂也会发生。从配置数据看(图14(a)中的实线)，在单层NbSe₂中的等效磁场大约有660T，而在MoS₂中大约有114T，这与理论上计算的能带分裂是一致的。因此这些结果都对ASOC在低维超导体系产生的重要影响提供了强有力的证据。一系列新奇的超导电性被认为可能是由加强的ASOC引起的，包括一种FFLO的配对态和拓扑超导电性。通过CeCoIn₅层和 YbCoIn₅层组成的异质层结构，在二维近藤晶格中观察到了超导电性。CeCoIn₅是中心对称的重费米子超导体，并且由填充了无超导电性的YbCoIn₅ 的n层CeCoIn₅ 构成的超导晶格也可以生长。在对所有的层（CeCoIn₅）进行电阻测量时可以观察到超导的转变，但是零电阻只有在对nge;3层测量时才观察的到，以及两种材料中费米速度的巨大差异表明二维的超导电性是可以实现。因为反演对称性的破缺在两种材料的接触面更明显，ASOC的强度可以由材质层的厚度来改变。在 CeCoIn₅ 中3-5层间测量以角动量为变量的上临界场。对于，在时的上临界场里，临界温度附近观察到一个尖峰，与平面内的方向有关。越大，这种尖峰就会变得平缓而且越不明显，对于，还会随着温度的降低而减弱。这种尖峰预期会在轨道配对破缺的二维超导体中出现，因此随着n的增大而减弱就可以用决定了体材料中上临界场的泡利顺磁性有限性的增加来解释。随着温度的降低，的尖峰形状发生变化的情况，只有在的样品中观察到，这被理解为是类似FFLO态的一种标志，这种状态的超导序参量有一个真实空间的调制。事实上这被认为是一种混合宇称的密度波函数，自旋三重态的成分在空间是均匀分布的，但是自旋单态的成分在各层之间相差很大。在插图14(C)中，根据不同的标绘了上临界场（theta;=pi;/2），由零温的轨道极限场归一化。可以发现对于所有n，数据都介于强泡利极限（实线）的体行为和纯轨道极限情况（虚线）之间。随着的减少，数据更趋向于轨道极限，表明泡利极限在减弱。更多复杂的超晶格在被制造出来，YbCoIn₅层不再是同样的厚度，而是可以在m和mrsquo;层之间改变，比例为（n：m：n：mrsquo;）。正如图14（c）主要展示的那样，当n固定的时，泡利极限也会随着的增加而减小。这些结果证明反演对称性破缺的程度会相应的降低顺磁极限，并且也证明了用异质结来控制ASOC的可能性。

参考文献：

[1]Emmanuel I. Rashba. Properties of semiconductors with an extreum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phus. Solid, 2:1109, 1960.

[2]Lev P. Gorrsquo;kov and Emmanuel I. Rashba. Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state. Phys. Pev. Lett, 87:037004, 2001.

[3]P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist. Superconductivity without invention symmetry: MnSi versus CePt3Si. Phys. Rev. Lett, 92:097001, 2004. See also Erratum 93, 099909(E) (2004).

[4]I. A. Sergienko and S. H. Curnoe. Order parameter in superconductors with nondegenerate bands. Phys. Rev. B, 70:214510, 2004.

[5]Manfred Srigrist ang Kazuo Ueda. Phenomennological theory of unconventional superconductivity. Rev. Mod. Phys, 63:239311, 1991.

[6]P A Frigeri, D F Agterberg, and M Sigrist. Spin susceptibility in superconductors without inversion symmetry. New J. Phys.6(1):115, 2004.

[7]G. E. Volovik. An analog of the quantum hall effect in a superfluid 3He film. JETP, 67:1804, 1988.

[8]Chi-Ken Lu and Sungkit Yip. Zero-energy vortex bound states in noncentrosymmetric superconductors. Phys. Rev. B, 78:132502, 2008.

[9]K. V. Samokin, E. S. Zijlstra, and S. K. Bose. CePt3Si: an unconventional superconductor without inversion center. Phys. Rev. B, 69:094514, 2004.

[10]G Motoyama, M Shiotsuki, Y Oda, A Yamaguchi, A Sumiyama, T Takeuchi, R Settai, and Y Onuki. Specific heat study of the non-centrosymmetric superconductor LaPt3Si in magnetic fields. J. Phys. Conf. Ser, 400(2):022079, 2012.

[11]Ikuto Kawasaki, Isao Watanabe, Hiroshi Amitsuka, Keisuke Kunimori, Hiroshi Tanida, and Yoshichika Onuki. Superconducting propert

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Superconductivity and spin-ordit coupling in non-centrosymmetric materials:a review

1. Smidman

Center for Correlated matter and Department of Physics, Zhejiang University, Hangzhou 310058, china

M.B. Salamon

UTD-NanoTech Institude, The University of Texas at Dalls, Richardson,

Texas 750830688, USA

H.Q. Yuan

Center for Correlated Matter and Department of Physics,

Zhejiang University, Hangzhou 310058, China and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China*

D.F. Agterberg

Department of physics, University of Wisconsin, Milwaukee, WI 53201, USA

(Dated: August 18, 2016)

摘要：

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling(ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviours, led to intensive theoretical and experimental inverstigations. Here we review the experimental and the theoretical results for superconducting systems lacking inversion symmetry. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effect of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

正文选段：

1. Non-centrosymmetric superconductivity in topological systems

The half Heusler alloys are a series of compounds which have recently attracted particular attention. These compounds lack inversion symmetry and many have been predicted to have topologically non-trivial surface states, due to the presence of a band inversion in the electronic structure. One such compound is which becomes superconducting at . Measurements of the transverse field magnetoresistance at low temperatures reveal that the spin-orbit coupling splits the Fermi surface into two similar sized sheets and the carrier density is surprisingly low compared to most other superconducting systems. Calculations on the basis of the theory of superconductivity indicate that much larger values of are necessary to account for the value of , which was taken to suggest that the superconductivity of can not be explained within the framework of the conventional electron-phonon pairing mechanism, but rather that there is unconventional pairing. Meanwhile remains linear to low temperatures, in excess of the orbital limiting field of calculated from theory, but it can be extrapolated to a zero temperature value of ~, close to the weak coupling Pauli limit. Although measurements were unable to provide of sufficient precision, recent measurements of showed linear behaviour at low temperatures, indicating the presence of line nodes. Due to the band inversion and the four fold degeneracy of the bands near the Fermi level, it was suggested that the Cooper pairs may form between fermions with , instead of the commonly considered . As a result, pairing states with higher angular momentum such as quintet() and septet () states may occur, in addition to the singlet() and triplet () states arising from pairing. It was suggested that the superconducting state may correspond to mixed-parity pairing involving these higher angular momentum states, where the line nodes may arise from a mixture of singlet-septet pairing. Other half Heusler alloys displaying both band inversion and superconductivity are RPdBi (R=Ho,Er,Tm or Lu) (Tc~1.2-1.7K), LuPtBi (Tc~1.0K) and LaPtBi (Tc~0.9K). Meanwhile other half heusler compounds showing superconductivity include RPdBi （R=Sm, Dy, Tb or Y), although for these compounds, the electronic structures are predicted not to show band inversion,but to be topologically trivial. Another interesting feather of the RPdBi superconductors is that when R is a magnetic element, the compound diaplays both magnetic order and superconductivity. The relationship between the superconducting and magnetic phases in these compounds is yet to be determined and requires further detailed measurements. For most of the superconducting half Heulser alloys, the superconducting gap structure has yet to be characterized. Besides the case of YPtBi discussed previously, the specific heat below Tc~1.7K of LuPdBi was fitted by an isotropic, fully gapped single band model with a gap larger than the weakly coupled BCS value and obtained from NQR measurements of LaPtBi shows the coherence peak just below Tc expected for s-wave superconductivity. It is therefore important for the gap structure of a wider range of half Heusler alloys to be measured, which is made more challenging in some instances by a lack of a superconducting transition observed in specific heat measurements. Another promising candidate for topological superconductivity is the NCS PbTaSe₂, which has a Tc of 3.7K. It was previously proposed that NCS may be ideal systems for observing Majorana modes, as long as the triplet component is larger than the singlet one. This is unlikely to be the case for PbTaSe₂, where the penetration depth and superfluid density are well accounted for by a single-gap s-wave model, indicating that any

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