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测量物质在不同外加磁场方向下的电输运性质是近年来研究拓扑量子材料的一种重要实验方法, 为探索物质的新奇特性提供了独特的视角和手段. 研究表明, 在超高强度的脉冲强磁场下, 材料的电输运研究可能扩展至量子极限区域, 将观察到更加丰富的物理现象. 而现有的电输运测量系统中, 稳态场下的样品测量杆受限于尺寸和材料, 难以适应脉冲场测量要求; 脉冲场下的传统样品测量杆的角度分辨率和空间利用率较低, 亟需研制更高性能的转角测量系统. 为此, 本文提出一种拉杆式转角样品杆, 基于该转角样品杆的脉冲强磁场电输运测量系统, 能够在极低温、强磁场的极端环境下, 于脉冲磁体中心通孔的微型样品腔内开展磁场方向190°范围内任意变化的电输运性质测量实验, 其旋转结构稳定性良好, 转角控制精度达到0.1°; 通过合理设计集成电路布局、前置补偿放大和数字锁相提取等信号处理环节, 电输运测量结果的精确度优于0.1 mΩ. 本文详细阐述了该测量系统的组成、转角测量杆的设计与研制、校准原理与信号处理过程, 并简要介绍了该测量系统在费米面重构、拓扑绝缘体表面态、量子极限输运、超导电性等前沿研究领域的应用.In recent years, measuring the electrical transport properties of materials in different directions of applied magnetic field has become an important experimental study of topological quantum materials. With the development of condensed matter physics, scientific research has shown that under the ultra-high intensity pulsed magnetic field, the electrical transport study of materials may extend to the quantum limit region, and more abundant physical phenomena will be observed. However, in the existing electric transport measurement system, the rotation sample rod under the action of steady-state field presents a large size and significant eddy current effect, which makes it difficult to meet the requirements for pulsed field measurement, and the current commercial physical property measurement system (PPMS) can only operate under ±16 T steady magnetic field. In addition, the conventional rotation sample rod encounters the problems of insufficient angular resolution and space utilization when used in pulsed high magnetic environment. So there is an urgent need to develop a higher performance rotation measurement system. In view of the above background, in this paper we present a kind of electrical transport measurement system designed by Wuhan National High Magnetic Field Center (WHMFC), which consists of five modules: pulse power supply, pulse magnet, control center, cryogenic system, and signal measurement. The key component is the sample measuring rod with rotation function, which restricts the movement of the drawbar through a double-groove structure to achieve an angular change in a range from –5° to 185°. An angle calibration coil is mounted on the back of the sample stage. Based on the double-calibration method, the angle control accuracy of 0.1° is achieved. The temperature, magnetoresistance and Hall resistance signal are collected by the integrated circuit on sample stage and extracted by compensation circuit and virtual digital lock-in amplifier, and the accuracy of electric transport measurement is better than 0.1 mΩ. Furthermore, the effect of eddycurrent and material deformation at low temperatures are completely eliminated by using polyetheretherketone material, which effectively improves the stability and reliability of the rotation sample rod. Using this measuring rod, we complete a series of experiments in the 8 mm sample cavity in the center of the pulse magnet: the minimum ambient temperature reaches 1.3 K, the maximum magnetic field strength arrives at 65 T, and the direction angle of the magnetic field is able to change in a 190° range. Thus the universally applicable measurement system of electric transport experiment in pulsed high magnetic field is successfully established. In this paper, we elaborate the principle and device components of the measurement system, the design and fabrication of the angle measuring rod, and the calibration principle and measurement process. Relevant experimental results show that the system has important application value in the research of 3D Fermi surface, topological insulator surface state, quantum limit transport, superconductivity analysis, etc. Based on this system, the electrical transport experimental system at WHMFC provides an effective means for the relevant research teams (home and abroad) engaged in the exploration of the intrinsic physical characteristics of quantum materials in extremely pulsed high magnetic field and low temperature environment.
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[30] Zhu Z W, Lin X, Liu J, Fauque B, Tao Q, Yang C L, Shi Y G, Behnia K 2015 Phys. Rev. Lett. 114 176601
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图 1 脉冲强磁场电输运测量系统
Fig. 1. Electrical transport measurement system in pulsed high magnetic field.
图 2 国内外已有转角样品杆 (a) 稳态强磁场中使用的探测样品杆; (b) 美国国家脉冲强磁场中心样品杆
Fig. 2. Rotation sample rod in: (a) Steady-state strong magnetic field; (b) NHMFL (National High Magnetic Field Laboratory).
图 3 武汉强磁场中心转角样品杆 (a)机械结构图; (b) 转角示意图; (c) 角度标定原理图
Fig. 3. Rotation sample rod in WHMFC (Wuhan National High Magnetic Field Center): (a) Mechanical structure diagram; (b) situation at different angles; (c) principle of angle calibration.
图 4 转角样品测量杆实物图 (a) 杆件顶部旋钮及引线罗盘; (b) 底部样品台正面; (c) 底部样品台背面
Fig. 4. Physical diagram rotation sample rod: (a) Top part; (b) the front of the bottom sample stage; (c) the back of the bottom sample stage.
图 5 60 T脉冲强磁场下转角电输运实验相关数据处理过程
Fig. 5. Signal processing of angular-dependent electrical transport experiment in 60 T pulsed high magnetic field.
图 6 Cd3As2三维嵌套各向异性费米面构造图 (a) 不同晶轴方向的费米面最大横截面; (b) B[112]方向上的量子振荡
Fig. 6. 3D nested anisotropic Fermi surface construction of Cd3As2: (a) Largest cross section of Fermi surface versus the magnetic field orientation; (b) quantum oscillation for B[112] direction.
图 8 脉冲强磁场下的半金属材料量子极限输运研究 (a) TaP; (b) Bi
Fig. 8. Quantum limit electrical transport of semi-metal materials in pulsed high magnetic fields: (a) TaP; (b) Bi.
图 9 超导材料K2Cr3As3的转角电输运实验结果 (a) π/2处出现上方临界场(Hc2)的最大值表明了泡利极限的缺失; (b) 极坐标图则体现了Hc2的三重调制性
Fig. 9. Electrical transport of the superconducting material K2Cr3As3: (a) The maximum value of the upper critical field (Hc2) at π/2 indicates the absence the Pauli paramagnetic effect; (b) the polar map of Hc2 shows a unique three fold modulation.
表 1 不同样品杆技术参数比较
Table 1. Technical parameters of different kind of measurement rod.
样品杆类型及参数 角度范围θ/(°) 角度分辨率θ/(°) 磁场范围B/T 适应孔径d/mm 样品台空间 PPMS商用样品杆 –10—370 0.05 ± 16 (稳态) 25 相对孔径较大 传统拉绳式样品杆 0—180 1.00 > 60 (脉冲) 9 相对孔径较小 新型拉杆式样品杆 –5—185 0.10 > 60 (脉冲) 8 相对孔径较大 
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[1] Li G, Xiang Z, Yu F, Asaba T, Lawson B, Cai1 P, Tinsman C, Berkley A, Wolgast S, Eo Y S, Kim D J, Kurdak C, Allen J W, Sun K, Chen X H, Wang Y Y, Fisk Z, Li L 2014 Science 346 1208
Google Scholar
[2] Huang X C, Zhao L X, Long Y J, Wang P P, Chen D, Yang Z H, Liang H, Xue M Q, Wen H M, Fang Z, Dai X, Chen G F 2015 Phys. Rev. X 5 031023
Google Scholar
[3] Wang Y J, Yu J H, Wang Y Q, Xi C Y, Ling L S, Zhang S L, Wang J R, Xiong Y M, Han T, Han H, Yang J, Gong J X, Luo L, Tong W, Zhang L, Qu Z, Han Y Y, Zhu W K, Pi L, Wan X G, Zhang C J, Zhang Y H 2018 Phys. Rev. B 97 115133
Google Scholar
[4] Ramshaw B J, Vignolle B, Day J, Liang R X, Hardy W N, Proust C, Bonn D A 2011 Nature Phys. 7 234
Google Scholar
[5] Sebastian S E, Harrison N, Altarawneh M M, Liang R X, Bonn D A, Hardy W N, Lonzarich G 2011 Nat. Commun. 2 471
Google Scholar
[6] Murphy J, Tanatar M A, Graf D, Brooks J S, Bud’ko S L, Canfield P C, Kogan V G, Prozorov R 2013 Phys. Rev. B 87 094505
Google Scholar
[7] Qu D X, Hor Y S, Xiong J, Cava R J 2010 Science 329 821
Google Scholar
[8] Quantun Design PPMS Specification https://www.qdusa.Com/sitedocs/productBrochures/1070-002.pdf [2019-7-12]
[9] Doan N N, James M, Chuck H M 2016 IEEE Trans. Appl. Supercond. 26 4300905
Google Scholar
[10] Fritz H, Miura N 2003 Magnetic Fields Science and Technology (Vol. 1) (New Jersey: World Scientific Publishing) pp285−316
[11] Han X T, Peng T, Ding H F, Ding T H, Zhu Z W, Xia Z C, Wang J F, Han J B, Ouyang Z W, Han Y B, Xiao H X, Cao Q L, Lü Y L, Pan Y, Li L 2017 Matter and Radiation at Extremes 2 278
Google Scholar
[12] 王绍良, 李亮, 欧阳钟文, 夏正才, 夏念明, 彭涛, 张凯波 2012 61 107601
Google Scholar
Wang S L, Li L, Ouyang Z W, Xia Z C, Xia N M, Peng T, Zhang K B 2012 Acta Phys. Sin. 61 107601
Google Scholar
[13] Li L, Lü Y L, Xiao H X, Pan Y, Peng T 2016 IEEE Trans. Appl. Supercond. 26 4303204
Google Scholar
[14] 刘永杰, 林梓泉, 王俊峰 2016 物理 45 19
Google Scholar
Liu Y J, Lin Z Q, Wang J F 2016 Physics 45 19
Google Scholar
[15] Cheng K Q, Wang L, Xu Y J, Yang F, Zhu H P, Ke J Z, Lu X F, Xia Z C, Wang J F, Shi Y G, Yang Y F, Luo Y K 2019 Phys. Rev. Mater. 3 021402(R)
Google Scholar
[16] Wang H C, Liu H W, Li Y N, Liu Y J, Wang J F, Liu J, Dai J Y, Wang Y, Li L, Yan J Q, Mandrus D, Xie X C, Wang J 2018 Sci. Adv. 4 5096
Google Scholar
[17] Zhao L X, Xu L C, Zuo H K, Wu X M, Gao G Y, Zhu Z W 2018 Phys. Rev. B 98 085137
Google Scholar
[18] Shi J T, Han X T, Xie J F, Li L 2016 IEEE Trans. Appl. Supercond. 26 4300604
Google Scholar
[19] Zuo H K, Xia Z C, Li L 2014 CN Patent for Utility Model 203704948 U
[20] Coldea A I, Andrew C M J, Analytis J G, McDonald R D, Bangure A F, Chu J H, Fisher I R, Canrrinton A 2009 Phys. Rev. Lett. 103 026404
Google Scholar
[21] Torque Magnetometry in Pulsed Fields, National High Magnetic Field Laboratory https://nationalmaglab.Org/user-facilities/pulsed-field-facility/pff-measurement-techniques/torque-magnetometry-pff [2019-7-12]
[22] Wang K F, Graf D, Lei H C, Tozer S W, Petrovic C 2011 Phys. Rev. B 84 220401
Google Scholar
[23] Wang K F, Graf D, Wang L M, Lei H C, Tozer S W, Petrovic C 2012 Phys. Rev. B 85 041101
Google Scholar
[24] Liu Q Y, Zhang S Z, Ding L C, Zuo H K, Han X T 2019 IEEE International Instrumentation and Measurement Technology Conference Proceedings Auckland, New Zealand, May 20–23, 2019 p504
[25] Zhao Y F, Liu H W, Zhang C L, Wang H C, Wang J F, Lin Z Q, Xing Y, Lu H, Liu J, Wang Y, Brombosz S M, Xiao Z L, Jia S, Xie X C, Wang J 2015 Phys. Rev. X 5 031037
Google Scholar
[26] Gotze K, Klotz J, Gnida D, Harima H, Aoki D, Demuer A, Elgazzar S, Wosnitza J, Kaxzorowski D, Sheikin I 2015 Phys. Rev. B 92 115141
Google Scholar
[27] Arnold F, Shekhar C, Wu S C, Sun Y, Reis R D, Kumar N, Naumann M, Ajeesh M O, Schmidt M, Grushin A G, Bardarson J H, Baenitz M, Sokolov D, Borrmann H, Nicklas M, Felser C, Hassinger E, Yan B H 2016 Nat. Commun. 7 11615
Google Scholar
[28] Zhang C L, Schindler F, Liu H W, Chang T R, Xu S Y, Chang G Q, Hua W, Jiang H, Yuan Z J, Sun J L, Jeng H T, Lu H Z, Lin H, Hasan M Z, Xie X C, Nerpert T, Jia S 2017 Phys. Rev. B 96 165148
Google Scholar
[29] Kim H, Wang K F, Nakajima Y, Hu R W, Ziemak S, Syers P, Wang L M, Hodovanets H, Denlinger J D, Brydon P M, Agterberg D F, Tanatar M A, Prozorov R, Paglione J 2018 Sci. Adv. 4 4513
Google Scholar
[30] Zhu Z W, Lin X, Liu J, Fauque B, Tao Q, Yang C L, Shi Y G, Behnia K 2015 Phys. Rev. Lett. 114 176601
Google Scholar
[31] Analytis J G, McDonald R D, Riggs S C, Chu J H, Boebinger G S, Fisher L R 2010 Nature Phys. 6 960
Google Scholar
[32] Petrushevsky M, Lahoud E, Ron A, Maniv E, Diamant I, Neder I, Wiedmann S, Guduru V K, Chiappini F, Zeitler U, Maan J C, Chashka K, Kanigel A, Dagan Y 2012 Phys. Rev. B 86 045131
Google Scholar
[33] Zhang C L, Xu S Y, Wang C M, Lin Z Q, Du Z Z, Guo C, Lee C C, Lu H, Feng Y Y, Huang S M, Chang G Q, Hsu C H, Liu H W, Li L, Zhang C, Zhang J L, Xie X C, Neupert T, Hasan M Z, Lu H Z, Wang J F, Jia S 2017 Nature Phys. 13 979
Google Scholar
[34] Fauque B, Yang H, Sheikin I, Balicas L, Issi J P, Behnia K 2009 Phys. Rev. B 79 245124
Google Scholar
[35] Fauque B, Vignolle B, Proust C, Issi J P, Behnia K 2009 New J. Phys. 11 113012
Google Scholar
[36] Zuo H K, Bao J K, Liu Y, Wang J H, Jin Z, Xia Z C, Li L, Xu Z, Kang J, Zhu Z W, Cao G H 2017 Phys. Rev. B 95 014502
Google Scholar
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