外界磁场进入超导体的磁穿透深度随超导体的温度变化而变化，特别是在超导转变温度附近，穿透深度变化尤为剧烈。探测穿透深度变化可实现对温度变化的高分辨率测量，是重要的深低温温度测量原理。基于该基本原理，提出一种基于超导体穿透深度变化、闭合超导回路磁通量子化和超导量子干涉器件(SQUID)的温度测量方案，进行理论分析和仿真，有望在液氦温区实现nK/$\sqrt{\mathrm{Hz}}$量级的温度分辨率，并给出具体的实验装置设计。该方法分辨率高且不引入额外热流，不需要外部持续的电流激励，可通过在被测物体表面镀超导膜等方法消除传统温度测量方法中温度计的自热效应、接触热阻等对测量的不利影响。
The magnetic penetration depth of the external magnetic field into the superconductor varies with the temperature, especially near the superconducting transition temperature, the penetration depth changes dramatically. Detecting the change of the penetration depth can achieve high-resolution measurement of temperature changes, which is an important principle of deep and low temperature measurement. Based on this basic principle, this work studies a temperature measurement scheme using the change of superconductor penetration depth, the quantization of closed superconducting loop magnetic flux and the superconducting quantum interference device (SQUID), carries out theoretical analysis and simulation, which is expected to achieve a temperature resolution of nK/$\sqrt{\mathrm{Hz}}$ in the liquid helium temperature region, and gives the specific experimental device design. This method offers high resolution, does not introduce additional heat flow, and does not require continuous current excitation. It can greatly reduce the adverse effects of the traditional temperature measurement caused by thermometer self-heating effect and contact thermal resistance. By plating superconducting film on the surface of the object，which is beneficial to temperature measurement experiments and applications below 10 K.
[1] Ventura G, Risegari L. Temperature scales and temperature fixed points [M]//The Art of Cryogenics: Low-Temperature Experimental Techniques. Elsevier, 2008. DOI: https://doi.org/10.1016/B978-008044479-6.50009-1.
[2] Moldover M R, Tew W L, Yoon H W. Advances in thermometry [J]. Nature Physics, 2016, 12(1): 7-11.DOI: 10.1038/nphys3618.
[3] Moldover M R, Gavioso R M, Mehl J B, et al. Acoustic gas thermometry [J]. Metrologia, 2014, 51(1): R1-R19.DOI: 10.1088/0026-1394/51/1/r1.
[4] Gugan D, Michel G W. Dielectric constant gas thermometry from 4.2 to 27.1 K [J]. Metrologia, 1980, 16(4): 149-167.DOI: 10.1088/0026-1394/16/4/002.
[5] Kirste A, Engert J. A SQUID-based primary noise thermometer for low-temperature metrology [J]. Philosophical Transactions.Series A, Mathematical, Physical, and Engineering Sciences, 2016, 374(2064): 20150050. DOI:10.1098/rsta.2015.0050.
[6] Peruzzi A, Bosma R, de Groot M J, et al. 4He interpolating constant-volume gas thermometry in the range 3.0 K to 24.556 1 K [J]. Metrologia, 2010, 47(3): 325-333.DOI: 10.1088/0026-1394/47/3/024.
[7] Pitre L, Moldover M R, Tew W L. Acoustic thermometry: new results from 273 K to 77 K and progress towards 4 K[J]. Metrologia, 2006, 43(1): 142-162.DOI: 10.1088/0026-1394/43/1/020.
[8] Greywall D S. 3He melting-curve thermometry at millikelvin temperatures [J]. Physical Review B, Condensed Matter 1985, 31(5): 2675-2683.DOI: 10.1103/physrevb.31.2675.
[9] Lusher C P, Li J Y, Maidanov V A, et al. Current sensing noise thermometry using a low Tc DC SQUID preamplifier [J]. Measurement Science and Technology, 2001, 12(1): 1-15.DOI: 10.1088/0957-0233/12/1/301.
[10] Merlone A, Moro F, Zandt T, et al. Construction and start-up of a large-volume thermostat for dielectric-constant gas thermometry [J]. International Journal of Thermophysics, 2010, 31(7): 1386-1395.DOI: 10.1007/s10765-010-0708-x.
[11] DiPirro M J, Tuttle J G, Shirron P J. Development of a high-resolution penetration depth thermometer [M]//Advances in Cryogenic Engineering. Boston, MA: Springer. 1996: 1723-1730. 10.1007/978-1-4613-0373-2_216.
[12] McDonald D G. Novel superconducting thermometer for bolometric applications [J]. Applied Physics Letters, 1987, 50(12): 775-777.DOI: 10.1063/1.98042.
[13] Sauvageau J E, McDonald D G. Superconducting kinetic inductance bolometer [J]. IEEE Transactions on Magnetics, 1989, 25(2): 1331-1334.DOI: 10.1109/20.92541.
[14] Shirron P J, DiPirro M J. Concept for a high-resolution thermometer utilizing the temperature dependence of the magnetic penetration depth [J]. IEEE Transactions on Applied Superconductivity, 1993, 3(1): 2140-2143.DOI: 10.1109/77.233925.
[15] Meissner W. Messungen mit hilfe von flüssigem helium. Ⅵ[J]. Zeitschrift Für Physik, 1930, 60(3): 181-183.DOI: 10.1007/BF01339823.
[16] Chan H A. Null test of the gravitational inverse square law with a superconducting gravity gradiometer [D]. College Park, MD, USA: University of Maryland, College Park, 1982.
[17] Wasserbäch W. Electron-phonon scattering and low-temperature thermal conductivity of niobium and tantalum single crystals [J]. Physica Status Solidi (b) Research, 1985, 127(2): 481-492.DOI: 10.1002/pssb.2221270207.
[18] Bodryakov V Y, Bashkatov A N. Heat capacity of tantalum in the normal and superconducting states: identification of the contributions [J]. Russian Metallurgy, 2013, (9): 671-675.DOI: 10.1134/s0036029513090048.
[19] Touloukian Y S. Thermal expansion: metallic elements and alloys [M]. New York: IFI/Plenum, 1975.
[20] 王迪昌,廉曾妍,王沛,等.界面平均温度和压力对DD5和1Cr11Ni2W2MoV材料接触热阻影响的实验研究 [J].中国科学院大学学报，2023，40(6)：726-734. DOI：10.7523/j.ucas.2022.044.
[21] Zhang H H, Han S Y, Fan L F. Modeling 2D transient heat conduction problems by the numerical manifold method on Wachspress polygonal elements [J]. Applied Mathematical Modelling, 2017, 48: 607-620.DOI: 10.1016/j.apm.2017.03.043.
