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## Kagome superconductors

Feng Xi-Lin, Jiang Kun, Hu Jiang-Ping
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• #### 摘要

钒基笼目超导体的发现为研究拓扑物态、超导以及几何阻挫等物理特性提供了全新平台. 自发现钒基笼目超导体以来, 国内很多研究组对其超导、电荷密度波、配对密度波、电子向列相以及时间反演对称性破缺多方面特性进行了研究, 并取得了重要进展, 引发了极大的关注. 这些新进展展示了钒基笼目超导体有极其丰富的基本物理机制. 本文简略讨论国内研究组取得的进展及其对理解钒基笼目超导体性质的意义, 并介绍目前领域内值得关注的重要问题.

#### Abstract

The newly discovered Kagome superconductors $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}(A=\mathrm{K},\mathrm{R}\mathrm{b},\mathrm{C}\mathrm{s})$ provide a platform to investigate the interplay of the topological property, superconductivity and geometrical frustration. Since their discovery, many research groups, especially many groups in China, have made tremendous progress in this field, including time-reversal-symmetry-breaking (TRSB), charge density wave (CDW), electronic nematicity, superconductivity properties and pair density wave (PDW). In this paper, we introduce the $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$properties, discuss the recent research progress and highlight the future focus of this Kagome superconductor.The paper is organized as follows. We start from the exotic normal states of $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$, where a CDW emerges at the temperature around 70–100 K depending on $A$. This CDW enlarges the unit cell size to 2×2 with additional c-direction modulation as observed by scanning tunneling microscope (STM) and X-ray scattering experiments. Interestingly, this CDW behaves differently under opposite magnetic fields. Namely, this CDW may break the time reversal symmetry. To confirm this property, the zero field muon spin relaxation (ZFμSR) experiment is performed with increasing relaxation rates after the CDW transition. Additionally, the intrinsic anomalous Hall effect is also observed, which may relate to this time reversal symmetry breaking (TRSB). Since there are no long-range magnetic orders observed in the elastic neutron scattering experiment and μSR, the TRSB is not related to the electron spin degree of freedom. To explain the TRSB, the chiral flux phase (CFP) with orbital magnetism is theoretically proposed. Moreover, the electronic nematicity is also observed at about 30–50 K below the CDW transition temperature. This phase breaks the ${C}_{6}$ rotation symmetry of the Kagome lattice as confirmed by STM and nuclear magnetic resonance (NMR). What is the microscopic origin of this nematicity is still under investigation.Then, we move to the superconducting properties of $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$. Combining the inversion symmetry property found in optical measurement and decreasing of the spin susceptibility found in NMR, the $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$ superconductor is proven to be a spin-singlet superconductor. Experiments in NMR, angle-resolved photoemission, superfluid density and specific heat further confirm the superconductivity in Kagome superconductors is a conventional s-wave superconductor. Although this superconductor is conventional, $A{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$ also contains the unconventional property. Importantly, a PDW is observed in $\mathrm{C}\mathrm{s}{\mathrm{V}}_{3}{\mathrm{S}\mathrm{b}}_{5}$ by high-resolution STM. What is the PDW origin or microscopic mechanism is still an open question. These new progress reveal the intriguing physical properties behind the Kagome superconductors and also bring many unsolved questions, which calls for further investigations.

#### 施引文献

• 图 1  (a) 笼目结构示意图; (b) CsV3Sb5元胞结构示意图[4]; (c) 仅考虑最近邻原子间电子跃迁时, 笼目晶格的电子能谱; (d) 常压下笼目超导体随温度变化的相图

Fig. 1.  (a) Schematic diagram of the Kagome lattice structure; (b) schematic diagram of the primitive unit cell structure of CsV3Sb5[4]; (c) the electronic energy spectrum of the Kagome lattice when electrons hop between the nearest neighbor atoms; (d) the Kagome superconductor’s phase diagram as a function of temperature under ambient pressure.

图 2  (a) CsV3Sb5比热随温度的变化[4], 其中ZFC代表零场条件, FC代表有场条件; (b) STM下KV3Sb5的电荷密度分布图, 内嵌图为其傅里叶变换的结果表现出2×2有序的特性[5]

Fig. 2.  (a) The specific heat of CsV3Sb5 varies with temperature[4], ZFC means zero field case, and FC means finite field case; (b) the charge density distribution of KV3Sb5 observed by STM, the inset image is the result of Fourier transform which shows the characteristic of 2×2 order[5].

图 3  μSR测量和光学SHG结果[6]

Fig. 3.  μSR measurement and optical SHG results[6].

图 4  (a) CFP实空间示意图[10,11]; (b) CFP的局域轨道磁矩分布及电荷分布[10]

Fig. 4.  (a) Schematic diagram of CFP in real space[10,11]; (b) local orbital magnetic moment distribution and charge distribution of CFP[10].

图 5  由核磁共振结果分析得出的笼目超导体各相的相变示意图, 浅蓝色代表电子结构[12]

Fig. 5.  Schematic diagram of phase transition of each phase of Kagome superconductor obtained from the analysis of NMR results. Light blue represents the electronic structure[12]

图 6  (a) CsV3Sb5材料在各方向的奈特位移随温度的变化; (b) 超导转变温度附近自旋晶格弛豫率的Hebel-Slicheter共振峰[13]

Fig. 6.  (a) The Knight shift of CsV3Sb5 material in all directions as a function of temperature; (b) Hebel-Slicheter resonance peak of the spin lattice relaxation rate near the superconducting transition temperature[13].

图 7  (a) BCS超导电子配对示意图(左)与FFLO态配对示意图(右); (b) CsV3Sb5的零场STM结果快速傅里叶变换图, 绿色圈中的峰对应于2×2的CDW相, 粉色圈中的峰对应于PDW相[16]

Fig. 7.  (a) Cooper pair for BCS superconductor (left) and for FFLO state (right); (b) Fourier transform of the STM diagram of CsV3Sb5 under zero field, the green cycle shows the 2×2 CDW phase, the pink cycle shows the PDW phase[16].

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##### 出版历程
• 收稿日期:  2022-05-06
• 修回日期:  2022-06-04
• 上网日期:  2022-06-07
• 刊出日期:  2022-06-05

## 钒基笼目超导体

• 1. 中国科学院物理研究所, 北京　100190
• 2. 中国科学院大学物理科学学院, 北京　100049
• 3. 松山湖材料实验室, 东莞　523808

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