在傳統超導體中金屬介化物(intermetallic compound)因其在傳統超導體中，較高的超導溫度(???)而被廣泛的研究，其中A3B 結構的化合物是超導溫度最高的家族之一。V3Ga作為其中的一員，因其高臨界磁場和接近17 K的超導溫度受到關注及研究；相比之下，與其組成元素相同的V2Ga5因其超導溫度為3.5 K而相對沒有受到甚麼關注，僅有一些關於其電阻、磁導率和比熱的測量研究，並且其比熱測量僅在3.5K 發生超導相變後測量至1.8 K。為了更深入了解V2Ga5 的超導特性，低溫比熱實驗是研究塊材超導性的重要工具，它可以提供超導體的配對機制以及樣品整體的超導效應。我們透過電阻、磁導率量測確認了V2Ga5為超導溫度3.5 K的Type-II超導體，臨界磁場在垂直晶體c軸及平行c軸分別為6.5 kO e及4.1 kOe，同時發現了當磁場垂直晶體c軸時存在peak effect；高壓下的電阻量測表現出超導溫度隨壓力增加而呈線性下降，並在20 GPa時趨近0K。隨後我們對V2Ga5進行了4 K-0.05 K的比熱量測，結果顯示V2Ga5 類似於MgB2，是雙能隙超導體。通過擬合，我們得到兩個超導能隙分別為0.543 meV 和0.226 meV。同時我們進行了角分辨光電子能譜(ARPES)量測，並進行能帶計算以得到在費米面的能帶分布。結合高壓實驗的結果，我們得出V2Ga5為聲子介導的雙能隙超導體。

In traditional superconductors, intermetallic compounds are known for having relatively high superconducting transition temperatures (???) and are thus widely studied. Among these, A3B compounds have the highest ???. V3Ga, a member of this group, has attracted attention and research due to its high critical magnetic field and superconducting temperature close to 17 K. In contrast, V2Ga5, composed of the same elements and exhibiting a superconducting temperature of 3.5 K, has received much scarce attention. Previous studies have only measured its resistivity, magnetic susceptibility, and specific heat, confirming a superconducting transition at 3.5 K, with measurements extending down only to 2 K. To gain a comprehensive understanding of the superconducting properties of V2Ga5, low-temperature specific heat experiments are invaluable. They can provide insights into the pairing mechanism and the overall superconducting behavior of the material.
We have confirmed through resistivity and magnetic susceptibility measurements that V2Ga5 is a Type-II superconductor with a superconducting temperature (???) of 3.5 K. The critical magnetic fields perpendicular and parallel to the c-axis are 6.5 kOe and 4.1 kOe, respectively (??2,⊥? = 6.5 kOe, ??2,| |? = 4.1 kOe). Additionally, we observed a peak effect when H⊥c. High-pressure resistivity measurements show a linear decrease in ??? with increasing pressure, approaching zero at 20 GPa.
Subsequently, we conducted specific heat measurements from 4 K to 0.05 K and found that V2Ga5 is a two-gap superconductor similar to MgB2. Fitting the specific heat data revealed two superconducting gap values of 0.543 meV and 0.226 meV. Furthermore, we performed angle-resolved photoemission spectroscopy (ARPES) measurements and band structure calculations to acquire the bands near the Γ and Z point on the Fermi surface. Combined with the high-pressure measurement, we conclude that V2Ga5 is a phonon-mediated two-gap superconductor.

[1] H. Kamerlingh-Onnes. The resistance of pure mercury at helium temperatures. Communications from the Physical Laboratory of the University of Leiden, 122:13–15,1911.
[2] R. Meissner, W.and Ochsenfeld. Ein neuer effekt bei eintritt der supraleitfahigkeit. Naturwissenschaften, 21(44):787–788, 1933.
[3] V. L. Ginzburg and L. D. Landau. On the Theory of superconductivity. Zh. Eksp. Teor.Fiz., 20:1064–1082, 1950.
[4] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 5 - Ginzburg–Landau Theory. Academic Press, 1995.
[5] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 9 - Type II Superconductivity. Academic Press, 1995.
[6] J. Bardeen, L. N. Cooper, and J. R. Schrieffer. Theory of superconductivity. Phys. Rev., 108:1175–1204, 1957.
[7] J. G. Bednorz and K. A. Muller. Possible high-?? superconductivity in the BaLaCuO system. Zeitschrift fur Physik B Condensed Matter, 64(2):189–193, 1986.
[8] M. K.Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu. Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure. Phys. Rev. Lett., 58:908–910, 1987.
[9] Kazumi Maki. Introduction to d-wave superconductivity. AIP Conference Proceedings, 438(1):83–128, 1998.
[10] D Aoki, J-P Brison, J Flouquet, K Ishida, G Knebel, Y Tokunaga, and Y Yanase. Unconventional superconductivity in UTe2. Journal of Physics: Condensed Matter, 34(24):243002, 2022.
[11] Sheng Ran, Chris Eckberg, Qing-Ping Ding, Yuji Furukawa, Tristin Metz, Shanta R Saha, I-Lin Liu, Mark Zic, Hyunsoo Kim, Johnpierre Paglione, and Nicholas P Butch. Nearly ferromagnetic spin-triplet superconductivity. Science, 365(6454):684–687, 2019.
[12] JunNagamatsu,NorimasaNakagawa, Takahiro Muranaka,Yuji Zenitani, and Jun Akimitsu. Superconductivity at 39K in magnesium diboride. Nature, 410(6824):63–64, 2001.
[13] P. Szabo, P. Samuely, J. Kačmarč璭, T. Klein, J. Marcus, D. Fruchart, S. Miraglia, C. Marcenat, and A. G. M. Jansen. Evidence for two superconducting energy gaps in MgB2 by point-contact spectroscopy. Phys. Rev. Lett., 87:137005, 2001.
[14] J. W. Quilty, S. Lee, S. Tajima, and A. Yamanaka. ?-axis raman scattering spectra of MgB2: Observation of a dirty-limit gap in the ? bands. Phys. Rev. Lett., 90:207006, 2003.
[15] F. Bouquet, Y. Wang, R. A. Fisher, D. G. Hinks, J. D. Jorgensen, A. Junod, and N. E. Phillips. Phenomenological two-gap model for the specific heat of MgB2. Europhysics Letters, 56(6):856, 2001.
[16] F. Bouquet, R. A. Fisher, N. E. Phillips, D. G. Hinks, and J. D. Jorgensen. Specific heat of Mg11B2: Evidence for a second energy gap. Phys. Rev. Lett., 87:047001, 2001.
[17] S. Souma,Y. Machida, T. Sato, T.Takahashi, H. Matsui, S.-C.Wang, H. Ding, A. Kaminski, J. C. Campuzano, S. Sasaki, and K. Kadowaki. The origin of multiple superconducting gaps in MgB2. Nature, 423(6935):65–67, 2003.
[18] Y. Nakajima, T. Nakagawa, T. Tamegai, and H. Harima. Specific-heat evidence for two-gap superconductivity in the ternary-iron silicide Lu2Fe3Si5. Phys. Rev. Lett., 100:157001, 2008.
[19] Kim C Lobring, Catherine E Check, Jianhua Zhang, Shoujian Li, Chong Zheng, and Krzysztof Rogacki. Single crystal growth, bonding analysis and superconductivity of V2Ga5. Journal of Alloys and Compounds, 347(1):72–78, 2002.
[20] Atsushi Teruya, Masataka Takeda, Ai Nakamura, Hisatomo Harima, Yoshinori Haga, Kiyoharu Uchima,Masato Hedo, Takao Nakama, and Yoshichika O¯ nuki. Characteristic fermi surface properties of V2Ga5, CoGa3, TiGa3, ZrGa3, and ZrAl3 with different tetragonal structures. Journal of the Physical Society of Japan, 84(5):054703, 2015.
[21] Bruker technology. D2 phaser, 2024.
[22] Elena gabriela Udriştioiu Andrei A. Bunaciu and Hassan Y. Aboul-Enein. X-ray diffraction: Instrumentation and applications. Critical Reviews in Analytical Chemistry, 45(4):289–299, 2015. PMID: 25831472.
[23] Bruker technology. Bruker D2 phaser user manual (120 pages), 2015.
[24] Hector Castro, Jose Galvis, and Sonia Castro. Automated setup for van der pauw hall measurements. Instrumentation and Measurement, IEEE Transactions on, 60:198–205, 2011.
[25] F.S. Oliveira, R.B. Cipriano, and F.T. et al. da Silva. Simple analytical method for determining electrical resistivity and sheet resistance using the van der pauw procedure. Sci Rep, 10:16379, 2020.
[26] L. J. van der Pauw. A method of measuring specific resistivity and hall effect of discs of arbitrary shape. Philips Research Report, 13:1–9, 1958.
[27] L. J. van der Pauw. Van der pauw, l.j. (1958) a method of measuring the resistivity and hall coefficient on lamellae of arbitrary shape. Philips Technical Review, 20:220–224, 1958.
[28] H. C. Montgomery. Method for Measuring Electrical Resistivity of Anisotropic Materials. Journal of Applied Physics, 42(7):2971–2975, 1971.
[29] B. F. Logan, S. O. Rice, and R. F. Wick. Series for Computing Current Flow in a Rectangular Block. Journal of Applied Physics, 42(7):2975–2980, 1971.
[30] G. Teleberg G. Batey. Principles of dilution refrigeration. 2015.
[31] R. Bachmann, Jr. DiSalvo, F. J., T. H. Geballe, R. L. Greene, R. E. Howard, C. N. King, H. C. Kirsch, K. N. Lee, R. E. Schwall, H.-U. Thomas, and R. B. Zubeck. Heat capacity measurements on small samples at low temperatures. Review of Scientific Instruments, 43(2):205–214, 1972.
[32] T. L. Hung, C. H. Huang, L. Z. Deng, M. N. Ou, Y. Y. Chen, M. K. Wu, S. Y. Huyan, C. W. Chu, P. J. Chen, and T. K. Lee. Pressure induced superconductivity in MnSe. Nature Communications, 12(1):5436, 2021.
[33] A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Nature, 525(7567):73–76, 2015.
[34] A. Jayaraman. Diamond anvil cell and high-pressure physical investigations. Rev. Mod. Phys., 55:65–108, 1983.
[35] Chengwei Zhang, Jung Fu Lin, Ying Liu, Shaomin Feng, Changqing Jin, Mingqiang Hou, and Takashi Yoshino. Electrical resistivity of Fe-C alloy at high pressure: Effects of carbon as a light element on the thermal conductivity of the earth’s core. Journal of Geophysical Research: Solid Earth, 123(5):3564–3577, 2018. Publisher Copyright: c2018. American Geophysical Union. All Rights Reserved.
[36] Friedrich Reinert and Stefan Hufner. Photoemission spectroscopy—from early days to recent applications. New Journal of Physics, 7(1):97, 2005.
[37] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 6 - BCS Theory. Academic Press, 1995.
[38] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 4 – Thermodynamic Properties. Academic Press, 1995.
[39] Norman E. Phillips. Heat capacity of aluminum between 0.1 K and 4.0 K. Phys. Rev., 114:676–685, 1959.
[40] C. L. Huang, J.-Y. Lin, C. P. Sun, T. K. Lee, J. D. Kim, E. M. Choi, S. I. Lee, and H. D. Yang. Comparative analysis of specific heat of YNi2B2C using nodal and two-gap models. Phys. Rev. B, 73:012502, 2006.
[41] J.Μ.REDDY, A.R. STORM, andΚ.KNOX. The crystal structure ofV2Ga5. Zeitschrift fur Kristallographie - Crystalline Materials, 121(1-6):441–448, 1965.
[42] E. Cruceanu, G. Antesberger, and C. Papastaikoudis. Low-temperature electrical properties of V2Ga5. Solid State Communications, 15(6):1047–1049, 1974.
[43] W. J. Kitchingman and P. L. Norman. X-ray diffraction studies of the ternary alloys (V,Mn)2Ga5. Acta Crystallographica Section B, 28(4):1311–1312, 1972.
[44] C. Q. Xu, C. C. Zhao, Y. Shen, D. Ratkovski, X. Ma, W. Zhou, Xunqing Yin, B. Li, A. F. Bangura, Chao Cao, Baomin Wang, Ziming Zhu, X. Ke, Dong Qian, Shiyan Li, and Xiaofeng Xu. Multigap nodeless superconductivity in the dirac intermetallic alloy V2Ga5 with one-dimensional vanadium chains. Phys. Rev. B, 109:L100506, 2024.
[45] Alan A. Coelho. TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. Journal of Applied Crystallography, 51(1):210–218, 2018.
[46] Aveek Bid, Achyut Bora, and A. K. Raychaudhuri. Temperature dependence of the resistance of metallic nanowires of diameter ⩾ 15 nm: Applicability of bloch-gruneisen theorem. Phys. Rev. B, 74:035426, 2006.
[47] N.R. Dilley, J. Herrmann, S.H. Han, M.B. Maple, S. Spagna, J. Diederichs, and R.E. Sager. Anomalous electrical resistivity in the superconducting state of CeRu2. Physica C: Superconductivity, 265(1):150–158, 1996.
[48] C. V. Tomy, G. Balakrishnan, and D. McK. Paul. Observation of the peak effect in the superconductor Ca3Rh4Sn13. Phys. Rev. B, 56:8346–8350, 1997.
[49] C.V. Tomy, G. Balakrishnan, and D.McK. Paul. Regions of enhanced pinning in the mixed state of the superconductor Yb3Rh4Sn13. Physica C: Superconductivity, 280(1):1–8, 1997.
[50] Charles P. Poole, Horacio A. Farach, and Richard J. Creswick. 10 - Magnetic Properties.Academic Press, 1995.
[51] C. Kittel. Introduction to solid state physics. NY: John Wiley & Sons, 2004.
[52] T. F. Smith and C. W. Chu. Will pressure destroy superconductivity? Phys. Rev., 159:353–358, 1967.
[53] B. Lorenz and C.W. Chu. High Pressure Effects on Superconductivity. Springer Berlin Heidelberg, Berlin, Heidelberg, 2005.
[54] E. R. Margine and F. Giustino. Anisotropic migdal-eliashberg theory using wannier functions. Phys. Rev. B, 87:024505, 2013.
[55] W. L. McMillan. Transition temperature of strong-coupled superconductors. Phys. Rev., 167:331–344, 1968.
[56] P. B. Allen and R. C. Dynes. Transition temperature of strong-coupled superconductors reanalyzed. Phys. Rev. B, 12:905–922, 1975.