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PNAS reports Jian Wang group and collaborators’ work on the observation of non-trivial superconductivity in topological Weyl semimetal MoTe2-xSx crystals
王健课题组与合作者在拓扑外尔半金属晶体中观测到非平庸的超导特性

Recently, the exotic edge states in topological superconducting materials have drawn broad attention owing to their Majorana fermionic quasiparticles. A Majorana fermion is a particle that is its own antiparticleand displays unusual non-Abelian statistics. Majorana quasiparticle in condensed matter system with its exotic braiding property can be used to build fault-tolerant quantum computer. Prof. Jian Wang and collaborators detected non-trivial superconducting signatures in sulphur doped type-II topological Weyl semimetal MoTe2.ThisMoTe2-xSx (x~0.2)is also a layered transition metal dichalcogenide and thus has potential applications in future topological Weyl semimetal and superconductor nano-devices.

In 1929, physicist Hermann Weyl theoretically predicted that there is a kind of massless fermion whose spin is half-integer and can be described by Weyl equation. It is named as Weyl fermion but hasn’t been observed as a fundamental particle in nature yet. However, researchers recently realized that Weyl fermion can be realized as emergent quasiparticle in condensed matter system like in the electronic crystals. This series of electronic crystals are called topological Weyl semimetal. A Weyl semimetal is a crystal system whose low energy excitation has linear dispersion and can be effectively described by the Weyl equation. Weyl semimetals are also characterized by non-trivial topological invariants, broadeningthe classification of topological phases of condensed matter beyond topological insulator. The Weyl points (WPs) in Weyl semimetals with different chirality locate at different position in momentum space. And the WPs act like monopoles that are either a source or a sink of the Berry curvature. On the crystal boundary, novel metallic non-closed topological surface states (Fermi arcs) connect the projection of the WPs with opposite chirality. In contrast to relativistic fermions, the quasiparticle in the less constrained condensed matter systems doesn’t need to respect Lorentz invariance.

Topological materials that host superconductivity are ideal systems to detect topological superconductivity and Majorana fermions. The superconductivity of topological surface states in topological Weyl semimetals may offer a new opportunity to study topological superconductivity beyond the proximity effect induced superconducting surface states in topological insulators. Based on the paring symmetry of superconductor, there are s wave, p wave and d wave superconductors.  And the strong interband coupling in s wave superconductor can result in the π shift (s+- pairing) between the order parameters on different superconducting bands, such as generally accepted Fe-bases superconductors. Moreover, this kind of sign change of the superconducting gap function between different Fermi surfaces in time reversal invariant topological Weyl semimetal can lead to topological superconductivity (Phys. Rev. B 90(4):045130).

Recently, Prof. Jian Wang, Prof. Ji Feng at Peking University and Prof. Tong Zhang at Fudan University, in collaboration with Prof. Shiyan Li at Fudan University, Prof. Yong Wang at Zhejiang University, Prof. Mingliang Tian and Dr. Langsheng Ling at Heifei High Magnetic Field Laboratory of the Chinese Academy of Sciences, Prof. Nitin Samarth at Pennsylvania State University demonstrated their observations of non-trivial superconducting signatures in topological MoTe2-xSx crystals. The samples are grown by chemical vapor transport method.

Firstly, theyobserved the quasiparticle interference patterns of Fermi arcs at the surface of MoTe2-xSx crystal, which are consistent with the calculated non-trivial band structure. Then, they detected a relatively large superconducting gap on the sample surface and the gap to critical temperature Tc ratio (Δ/kBTc) is 8.6. This value is much larger than that of the conventional weak-coupling superconductors, and also larger than the bulk superconducting gaps fitted from the specific heat measurement.The large superconducting gap they detected might be from superconductivity parity mixing or unconventional paring mechanism on the surface, potentially indicating the non-trivialsuperconductivity from Fermi arc surface states. Moreover, their transport and specific heat measurements show two-band superconductivity with potential s+- wave arising from a dominant interband coupling. Thus, the material could be the other s+- superconductor besides Fe-based superconductors. This s+- paring superconductivity also makes the Weyl semimetal material MoTe2-xSxa promising topological superconductor candidate, the corner stone for future topological quantum computation.The paper was published in PNAS on August 31, 2018. (DOI: 10.1073/pnas.1801650115) (Link:https://doi.org/10.1073/pnas.1801650115)

Prof. Jian Wang, Prof. Ji Feng at Peking University and Prof. Tong Zhang at Fudan University are corresponding authors of this paper. Yanan Li, Qiangqiang Gu at Peking University and Chen Chen at Fudan University contributed equally to this work.

This work was supported by the National Basic Research Program of China, the National Natural Science Foundation of China, and the Strategic Priority Research Program of Chinese Academy of Sciences etc.

Figure 1. Signature of s+- superconductivity in MoTe2-xSx. (A) Schematic structure for electrical transport measurements in MoTe2−xSx. (B) Typical resistivity–temperature curve of MoTe2−xSx showing superconductivity. (C) Magnetoresistance at various temperatures under perpendicular field. (D) Temperature dependence of Hc2from the data in (C). The red curve is the best fit of two-band s-wave model to the experimental data. The fitting parameters showing strong interband coupling, indicates s+- superconductivity in MoTe2-xSx. 

 

Figure 2.Large superconducting gap on the surface of MoTe2-xSx, which reveals the possibility of non-trivial superconductivity from topological surface states. (A) dI/dV spectrum taken on MoTe2-xSx sample. An anomalously large superconducting gap with Δ = 1.7 meV (as marked) was clearly observed at 0.4 K. (B) Comparison of the measured gap (red curve) with a simulated isotropic BCS gap (dashed curve). (C) dI/dV spectrum measured at 0.4 K under various magnetic fields. The superconducting gap is suppressed by increasing the magnetic field.

  近年来,拓扑超导材料因其边界态中存在马约拉纳费米子而引起国际学术界的持续广泛关注。马约拉纳费米子是自身的反粒子,符合非阿贝尔统计,是实现可容错的拓扑量子计算的物质基础。北大量子材料科学中心王健课题组及合作者在掺硫的第二类拓扑外尔半金属二碲化钼晶体中观测到非平庸超导的信号,发现该材料是一种拓扑超导候选材料。同时,因其为层状过渡金属碲化物,具有很大的潜在应用价值。

  1929年物理学家赫尔曼·外尔发现,有一种质量为零,自旋是半整数的费米子的行为满足外尔方程,这种粒子被称为外尔费米子。虽然目前在自然界中尚未观测到这种基本粒子,但是近来人们在晶体中发现了满足外尔方程的这种准粒子激发,这一类晶体被称为拓扑外尔半金属。在拓扑外尔半金属中,费米面附近的准粒子激发满足线性色散关系,可以用外尔方程描述,形状犹如沙漏,被称为外尔锥。与相对论粒子不同,外尔半金属中的准粒子激发可以违反洛伦兹不变性。在拓扑外尔半金属中,手性不同的外尔点成对出现在不同的动量位置。拓扑外尔半金属还具有奇异的表面态,即在表面形成了连接手性不同的外尔点在表面上的投影点的线段态,称为费米弧(Fermi Arc)。当具有拓扑性质的表面态形成超导态时会具有拓扑超导的性质。此外,超导材料根据超导能隙的对称性,可以分为s波,p波,d波超导体等,其中s波超导材料中,如果不同超导能隙的相位不同,被称作s+- 超导。高温超导中的铁基超导就被大多相关专家认为是s+- 超导。理论预言显示,保持时间反演对称性的拓扑外尔半金属的体态若形成s+- 的超导态,会具有拓扑超导的性质(Phys. Rev. B 90(4):045130)。

  近日,北京大学王健教授和冯济教授,复旦大学张童教授及李世燕教授,浙江大学王勇教授,稳态强磁场科学中心(合肥)凌浪生、田明亮研究员,美国宾夕法尼亚州立大学Nitin Samarth教授等人展开合作,通过电输运、扫描隧道谱、比热、抗磁性等系统的实验研究并结合第一性原理计算,在掺硫的第二类拓扑外尔半金属二碲化钼单晶中发现了非平庸超导态的特征。实验中所使用的硫掺杂的高质量二碲化钼晶体是通过化学气相输运的方法合成的,掺杂比例约为0.2。研究组通过准粒子干涉实验与第一性原理计算相结合,在样品表面探测到了费米弧拓扑表面态的存在。随后通过扫描隧道谱学和比热的测量对比,发现样品表面态的超导能隙远大于体态的超导能隙,而且该样品表面态的能隙与临界温度的比值(Δ/kBTc)约为8.6,远大于常规超导材料的能隙与临界温度的比值(约为1.76),表明了表面态具有非常规超导库珀对配对机制,极可能是拓扑超导的普适特征。同时,通过电输运测量和比热测量,发现这种材料为s波超导体,且它的超导能隙的带间耦合很强,超导对称性应为s+- 对称性。这可能是继铁基高温超导之后,又一种新的s+-超导体。而且根据理论预言,拓扑外尔半金属中s+-对称性的超导态会形成拓扑超导态。掺硫的第二类拓扑外尔半金属二碲化钼单晶中拓扑超导特征的发现,证实了外尔半金属中实现拓扑超导的可行性,推动了拓扑超导相关领域的进一步发展,也为拓扑量子计算机的最终实现奠定了前期的科研基础。文章于2018年8月31日在PNAS上在线发表(DOI: 10.1073/pnas.1801650115)。北京大学王健教授、冯济教授和复旦大学张童教授是本文的共同通讯作者。北京大学李亚楠硕士、顾强强博士和复旦大学陈晨博士为共同第一作者。

  这项工作得到了国家重大科学研究计划重点专项,国家自然科学基金,中国科学院战略性先导科技专项等项目的资助。

  

图一. 电磁输运实验观测到的s+- 超导的证据,揭示拓扑超导的可能性。(A) 电磁输运实验的测量示意图。(B) 超导转变温度附近的电阻率-温度关系。(C) 各个温度和磁场下的电阻率。(D) 超导上临界磁场和温度的关系。红色的线是两带超导模型的拟合曲线,拟合结果发现带间耦合比较大,表明该超导行为是s+- 超导。

  

图二.扫描隧道显微镜观发现表面态的超导能隙远超过体态的超导能隙,揭示出拓扑超导的可能性。(A) 4 K和0.4 K下样品表面的微分电导dI/dV谱。在0.4 K下,超导能隙是1.7 meV,远大于体态的超导能隙,且能隙与临界温度的比值约为约为8.6,远大于常规超导材料的能隙与临界温度的比值(1.76)。4 K时样品处于非超导态。(B) 0.4 K超导dI/dV谱和各向同性BCS超导谱的对比。(C) 0.4 K时,不同磁场下的超导dI/dV谱,超导能隙被外加磁场所抑制。