Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(12): 127401    DOI: 10.1088/1674-1056/20/12/127401
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

The Wiedemann–Franz law in a normal metal–superconductor junction

R Ghanbari and G Rashedi
Department of Physics, Faculty of Sciences, University of Isfahan, 81744 Isfahan, Iran
Abstract  In this paper the influence of superconducting correlations on the thermal and charge conductances in a normal metal-superconductor (NS) junction in the clean limit is studied theoretically. First we solve the quasiclassical Eilenberger equations, and using the obtained density of states we can acquire the thermal and electrical conductances for the NS junction. Then we compare the conductance in a normal region of an NS junction with that in a single layer of normal metal (N). Moreover, we study the Wiedemann-Franz (WF) law for these two cases (N and NS). From our calculations we conclude that the behaviour of the NS junction does not conform to the WF law for all temperatures. The effect of the thickness of normal metal on the thermal conductivity is also theoretically investigated in the paper.
Keywords:  quasiclassical approach      Eilenberger equations      Wiedemann-Franz law      thermal and charge conductances  
Received:  05 June 2011      Revised:  26 July 2011      Accepted manuscript online: 
PACS:  74.45.+c (Proximity effects; Andreev reflection; SN and SNS junctions)  
  74.45.+r  
  74.25.Fy  
  74.25.Bt (Thermodynamic properties)  

Cite this article: 

R Ghanbari and G Rashedi The Wiedemann–Franz law in a normal metal–superconductor junction 2011 Chin. Phys. B 20 127401

[1] Guron S, Pothier H, Birge N O, Esteve D and Devoret M H 1996 Phys. Rev. Lett. 77 3025
[2] Courtois H, Charlat P, Gandit Ph, Mailly D and Pannetier B 1999 J. Low Temp. Phys. 116 187
[3] Pannetier B and Courtois H 2000 J. Low Temp. Phys. 188 599
[4] Moussy N, Courtois H and Pannetier B 2001 Europhys. Lett. 55 861
[5] Dubos P, Courtois H, Pannetier B, Wilkhelm F K, Zaikin A D and Schn G 2001 Phys. Rev. B 63 064502
[6] Rashedi G and Kolesnichenko Yu A 2004 Phys. Rev. B 69 024516
[7] Rashedi G 2010 Chin. Phys. B 19 107303
[8] Taddei F, Giazotto F and Fazio R 2005 J. Comput. Theor. Nanosci. 2 329
[9] Del Maestro A, Rosenow B, Shah N and Sachdev S 2008 Phys. Rev. B 77 180501
[10] Linder J, Yokoyama Y, Tanaka Y, Asano Y and Sudbupphi A 2008 Phys. Rev. B 77 174505
[11] Durst A C and Sachdev S 2009 Phys. Rev. B 80 054518
[12] Levchenko A 2010 Phys. Rev. B 81 012507
[13] Andersson A and Lidmar J 2010 Phys. Rev. B 81 060508
[14] Golubev D S and Zaikin A D 2010 Phys. Rev. B 82 134508
[15] Ruiz H S, Lopez C and Badia-Majos A 2011 Phys. Rev. B 83 134508
[16] Mahmoodi R, Shevchenko S N and Kolesnichenko Yu A 2002 Low Temp. Phys. 28 184
[17] Mahmoodi R, Shevchenko S N and Kolesnichenko Yu A 2002 Fiz. Nizk. Temp. 28 262
[18] Rashedi G and Kolesnichenko Yu A 2005 Low Temp. Phys. 31 481
[19] Rashedi G and Kolesnichenko Yu A 2005 Fiz. Nizk. Temp. 31 634
[20] Kittel C 2004 Introduction to Solid State Physics (Berkeley: University of California Press)
[21] Jones W and March N H 1685 Theoretical Solid State Physics (New York: Courier Dover Publications)
[22] Poole C P, Farach H A, Creswick R J and Prozorov R 2007 Superconductivity 2nd edn. (London: Academic Press)
[23] Poole C P 2000 Handbook of Superconductivity (San Diego: Academic Press)
[24] Alidoust M, Rashedi G, Linder J and Sudbo A 2010 Phys. Rev. B 82 014532
[25] Rahnavard Y, Rashedi G and Yokoyama T 2010 J. Phys: Condens. Matter 22 415701
[26] Rashedi G, Rahnavard Y and Kolesnichenko Yu A 2010 Low Temp. Phys. 36 205
[27] Rashedi G, Rahnavard Y and Kolesnichenko Yu A 2010 Fiz. Nizk. Temp. 36 262
[28] Golubov A A, Kupriyanov M Y and Il'ichev E 2004 Rev. Mod. Phys. 76 411
[29] Belzig W, Bruder C and Schon G 1996 Phys. Rev. B 54 9443
[30] Scheer E, Belzig W, Naveh Y, Devoret M H, Esteve D and Urbina C 2001 Phys. Rev. Lett. 86 284
[31] Rubio-Bollinger G, de las Heras C, Bascones E, Agrat N, Guinea F and Vieira S 2003 Phys. Rev. B 67 121407(R)
[32] Clarke J 1969 Proc. R. Soc. London. A 308 447
[33] Ishida S, Nakajima M, Tomioka Y, Ito T, Miyazawa K, Kito H, Lee C H, Ishikado M, Shamoto S, Iyo A, Eisaki H, Kojima K M and Uchida S 2010 Phys. Rev. B 81 094515
[34] Koerting V, Andersen B M, Flensberg K and Paaske J 2010 Phys. Rev. B 82 245108
[35] de Gennes P G 1964 Rev. Mod. Phys. 36 255
[36] de Gennes P G 1996 Superconductivity of Metals and Alloys (New York: Benjamin)
[37] Buzdin A I 2005 Rev. Mod. Phys. 77 935
[38] Graf M J, Yip S K, Sauls J A and Rainer D 1996 Phys. Rev. B 53 15147
[39] Wiedemann G and Franz R 1853 Ann. Phys. 89 497
[40] Ronning F, Hill R W, Sutherland M, Hawthorn D G, Tanatar M A, Paglione J, Taillefer L, Graf M J, Perry R S, Maeno Y and Mackenzie A P 2006 Phys. Rev. Lett. 97 067005
[41] Hill R W, Proust C, Taillefer L, Fournier P and Greene R L 2001 Nature (London) 414 711
[42] van Harlingen D J, Heidel D F and Garland J C 1980 Phys. Rev. B 20 1842
[43] Tanatar M A, Reid J P, Shakeripour H, Luo X G, Doiron-Leyraud N, Ni N, Bud'ko S L, Canfield P C, Prozorov R and Taillefer L 2010 Phys. Rev. Lett. 104 067002
[44] Mattis D C and Bardeen J 1958 Phys. Rev. 111 412
[45] Geilikman B T 1958 Zh. Eksp. Teor. Fiz. 34 1042 [1958 Sov. Phys. JETP 34 L721]
[46] Kadanoff L P and Martin P 1961 Phys. Rev. 124 670
[47] Tewordt L 1962 Phys. Rev. 128 12
[48] Eckern U 1983 J. Low Temp. Phys. 50 489
[49] Machida Y, Sakai S, Izawa K, Okuyama H and Watanabe T 2011 Phys. Rev. Lett. 106 107002
[50] Kopnin N B, Mel'nikov A S, Pozdnyakova V I, Ryzhov D A, Shereshevskii I A and Vinokur V M 2007 Phys. Rev. B 57 024514
[51] Rabani H, Taddei F, Bourgeois O, Fazio R and Giazotto F 2008 Phys. Rev. B 78 012503
[52] Tewordt L and Fay D 2003 Phys. Rev. B 67 134524
[53] Spivak B, Oreto P and Kivelson S A 2008 Phys. Rev. B 77 214523
[54] Podolsky D, Vishwanath A, Moore J and Sachdev S 2007 Phys. Rev. B 75 014520
[55] Houghton A, Lee S and Marston J B 2002 Phys. Rev. B 65 220503
[56] Blonder G E, Tinkham M and Klapwijk T M 1982 Phys. Rev. B 25 4515
[57] Andreev A F 1964 Sov. Phys. JETP 19 1228
[58] Bardas A and Averin D 1995 Phys. Rev. B 52 12873
[59] Devyatov I A, Kuprianov M Y, Kuzmin L S, Golubov A A and Willander M 2000 J. Exp. Theor. Phys. 90 1050
[60] Kohen A and Deutscher G 2001 Phys. Rev. B 64 060506
[61] Eilenberger G 1968 Z. Phys. 214 195
[62] Larkin A I and Ovchinnikov Y N 1968 Sov. Phys. JETP 26 1200
[63] Amin M H S, Omelyanchouk A N, Rashkeev S N, Coury M and Zagoskin A M 2002 Physica B: Condens. Matter 318 162
[64] Schmidt V V, Muller P and Ustinov A V (eds.) 1997 The Physics of Superconductors (New York: Springer)
[65] Zareyan M, Belzig W and Nazarov Y V 2002 Phys. Rev. B 65 184505
[66] Bennemann K H and Ketterson J B (eds.) 2008 Superconductivity: Conventional and Unconventional Superconductors Vol. 1 (New York: Springer) pp. 280-283
[1] Thermoelectric signature of Majorana zero modes in a T-typed double-quantum-dot structure
Cong Wang(王聪) and Xiao-Qi Wang(王晓琦). Chin. Phys. B, 2023, 32(3): 037304.
[2] Spin transport properties in ferromagnet/superconductor junctions on topological insulator
Hong Li(李红) and Xin-Jian Yang(杨新建). Chin. Phys. B, 2022, 31(12): 127301.
[3] Strain-modulated anisotropic Andreev reflection in a graphene-based superconducting junction
Xingfei Zhou(周兴飞), Ziming Xu (许子铭), Deliang Cao(曹德亮), and Fenghua Qi(戚凤华). Chin. Phys. B, 2022, 31(11): 117403.
[4] Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V5S8
Juewen Fan(范珏雯), Bingyan Jiang(江丙炎), Jiaji Zhao(赵嘉佶), Ran Bi(毕然), Jiadong Zhou(周家东), Zheng Liu(刘政), Guang Yang(杨光), Jie Shen(沈洁), Fanming Qu(屈凡明), Li Lu(吕力), Ning Kang(康宁), and Xiaosong Wu(吴孝松). Chin. Phys. B, 2022, 31(5): 057402.
[5] Electronic properties and interfacial coupling in Pb islands on single-crystalline graphene
Jing-Peng Song(宋靖鹏) and Ang Li(李昂). Chin. Phys. B, 2022, 31(3): 037401.
[6] Dynamic vortex Mott transition in triangular superconducting arrays
Zi-Xi Pei(裴子玺), Wei-Gui Guo(郭伟贵), and Xiang-Gang Qiu(邱祥冈). Chin. Phys. B, 2022, 31(3): 037404.
[7] Cross correlation mediated by distant Majorana zero modes with no overlap
Lupei Qin(秦陆培), Wei Feng(冯伟), and Xin-Qi Li(李新奇). Chin. Phys. B, 2022, 31(1): 017402.
[8] Anomalous Josephson current in quantum anomalous Hall insulator-based superconducting junctions with a domain wall structure
Qing Yan(闫青), Yan-Feng Zhou(周彦峰), Qing-Feng Sun(孙庆丰). Chin. Phys. B, 2020, 29(9): 097401.
[9] Magnetic field enhanced single particle tunneling in MoS2-superconductor vertical Josephson junction
Wen-Zheng Xu(徐文正), Lai-Xiang Qin(秦来香), Xing-Guo Ye(叶兴国), Fang Lin(林芳), Da-Peng Yu(俞大鹏), Zhi-Min Liao(廖志敏). Chin. Phys. B, 2020, 29(5): 057502.
[10] Probing the minigap in topological insulator-based Josephson junctions under radio frequency irradiation
Guang Yang(杨光), Zhaozheng Lyu(吕昭征), Xiang Zhang(张祥), Fanming Qu(屈凡明), Li Lu(吕力). Chin. Phys. B, 2019, 28(12): 127402.
[11] Topological superconductivity in a Bi2Te3/NbSe2 heterostructure: A review
Hao Zheng(郑浩), Jin-Feng Jia(贾金锋). Chin. Phys. B, 2019, 28(6): 067403.
[12] The nonlocal transport and switch effect in light- and electric-controlled silicene-superconductor hybrid structure
Fenghua Qi(戚凤华), Jun Cao(曹军), Jie Cao(曹杰), Lifa Zhang(张力发). Chin. Phys. B, 2018, 27(12): 127401.
[13] Distinction between critical current effects and intrinsic anomalies in the point-contact Andreev reflection spectra of unconventional superconductors
Ge He(何格), Zhong-Xu Wei(魏忠旭), Jérémy Brisbois, Yan-Li Jia(贾艳丽), Yu-Long Huang(黄裕龙), Hua-Xue Zhou(周花雪), Shun-Li Ni(倪顺利), Alejandro V Silhanek, Lei Shan(单磊), Bei-Yi Zhu(朱北沂), Jie Yuan(袁洁), Xiao-Li Dong(董晓莉), Fang Zhou(周放), Zhong-Xian Zhao(赵忠贤), Kui Jin(金魁). Chin. Phys. B, 2018, 27(4): 047403.
[14] Coherent charge transport in ferromagnet/semiconductor nanowire/ferromagnet double barrier junctions with the interplay of Rashba spin–orbit coupling, induced superconducting pair potential, and external magnetic field
Li-Jie Huang(黄立捷), Lian Liu(刘恋), Rui-Qiang Wang(王瑞强), Liang-Bin Hu(胡梁宾). Chin. Phys. B, 2017, 26(7): 077201.
[15] Transition from tunneling regime to local point contact realized on Ba0.6K0.4Fe2As2 surface
Xingyuan Hou(侯兴元), Yunyin Jie(揭云印), Jing Gong(巩靖), Bing Shen(沈冰), Hai Zi(子海), Chunhong Li(李春红), Cong Ren(任聪), Lei Shan(单磊). Chin. Phys. B, 2017, 26(6): 067402.
No Suggested Reading articles found!