臺灣博碩士論文加值系統

在本論文中我們操作了一個可調式的石墨烯-超導垂直穿隧結，主要是在探討無質量狄拉克費米子(Massless Dirac fermion)與庫珀對(Cooper pair)之間的穿隧行為，我們的樣品主要由兩個鈮-石墨烯結串聯而成，並在其上塗佈離子凝膠作為閘極電極，此閘極電極用來控制室溫下的石墨烯費米能階(Fermi level)的位置，當溫度低於鈮臨界溫度(~9K)且石墨烯費米能階被調整到遠離石墨烯中性點(或稱狄拉克點)時，我們觀察到在零源極-汲極電壓(VSD)附近的微分電導有一個明顯的下沉結構，且其下沉結構的特徵接近超導能隙，其明確的表明了超導鈮與石墨烯結的物理穿隧行為，上述特徵會隨著費米能階的改變而產生變化，令人感興趣的是當費米能階被調整到靠近中性點時，其微分電導受到石墨烯起伏的影響變得明顯，我們數據分析指出所當費米能階遠離中性點時，所觀察到的穿隧行為與巴格翏夫方程(Bogoliubov-de Gennes equation)的理論預測一致，而在靠近中性點時，其穿隧行為主要是受到石墨烯不均勻(disorder)的影響與鏡像安德列夫反射(Specular Andreev reflection)。

We implement a tunable vertical graphene-superconductor tunnel junction and aim to investigate the tunneling behaviors between Dirac fermions and Cooper pairs. Our device consists with two serial coupled Niobium (Nb)-Graphene junctions, which are coated with an ionic gel as a top-gate electrode for controlling the Fermi-level (EF) of grapheme at room temperature. When EF is tuned away from the charge-neutral point (CNP or called the Dirac point) of grapheme and the temperature is lower to the critical temperature of Nb (~ 9 K), we observe a clear dip structure of differential conductance in the vicinity of zero-bias source-drain voltage (VSD), and peak features as VSD approaches the superconducting gap, which indicate clear behaviors of a superconducting Nb-graphene junction. The general features aforementioned evolve with EF ; intriguingly the differential conductance becomes fluctuating as EF is tuned closed CNP. Our data analysis suggests the observed tunneling behaviors are consistent with the theoretical predictions based on the approaches of Bogoliubov-de-Genn equation when EF is away from CNP. Near CNP, the tunneling behaviors are dominated by the combinations of the effects of interfacial disorders and specular Andreev reflection.

目錄
摘要 i
Abstract ii
誌謝 iii
目錄 iv
第一章 導論 1
1.1超導體的基本特性與發展歷史 1
1.2安德列夫反射(Andreev Reflection) 3
1.3 BTK理論 4
1.4石墨烯的基本特性與發展歷史 6
1.5石墨烯的電子能帶與狀態密度 7
1.6超導與石墨烯穿隧結的電子傳輸機制 9
第二章 文獻回顧與實驗動機 12
2.1石墨烯正常金屬-絕緣體-超導結的穿隧電導理論 12
2.2石墨烯約瑟芬結的不均勻 14
2.3彈道型超導電流在懸浮石墨烯的約瑟夫弱連結 17
2.4約瑟芬耦合在石墨基底的垂直結中實現 19
2.5石墨烯的帶間鏡像安德列夫反射 21
2.6本論文實驗動機 23
第三章 實驗樣品的設計構想與樣品製備 25
3.1樣品設計構想 25
3.2光學微影技術(Photolithography) 26
3.3離子研磨系統(Ionic-Milling System) 26
3.4電子槍蒸鍍系統(E-gun Evaporation System ) 27
3.5熱蒸鍍系統(Thermal Evaporation System) 27
3.6化學氣象沉積法成長石墨烯 28
3.6.1銅箔的實驗前處理 29
3.6.2化學氣象沉積法 30
3.6.3石墨烯轉移術 32
3.7液態閘極( Liquid gate ) 34
3.8樣品製作過程總結 34
第四章 量測結果與討論 35
4.1電阻對溫度量測( RT ) 35
4.2液態閘極對石墨烯改變費米能階的電阻結果 36
4.3拉曼光譜檢測 37
4.4 Nb-Gr結電阻量測 38
4.5 Nb-Gr結的電流對電壓量測 40
4.6 Nb-Gr結的微分電導 41
4.7數據歸納與定性分析 44
第五章 結論 50
5.1結論 50
5.2展望 52
參考文獻 53
附件 56

參考文獻
[1] H. Kamerlingh Onnes, Leiden Comm. 120b, 122b, 124c (1911)
[2] J. Bardeen, L. N. Cooper, J.R. Schrieffer. Microscopic Theory of superconductivity, Phys. Rev. 106, 162 (1957)
[3] A. F. Andreev, Thermal conductivity of the intermediate state of superconductors, Phys. JETP, 19, 1228(1964)
[4] G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent convention, Phys. Rev B 25, 4515(1982)
[5] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438, 197 (2005)
[6] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric Field Effect in Atomically Thin Carbon Films, Science 306, 666 (2004)
[7] Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature 438, 201 (2005)
[8] Jahan M. Dawlaty, Shriram Shivaraman, Mvs Chandrashekhar, Farhan Rana and Michael G. Spencer, Measurement of ultrafast carrier dynamics in epitaxial graphene ,Applied Physics Letters 92, 042116 (2008)
[9] Kuan-chun Lin, Ultrafast Carrier Dynamics of Chemical Vapor Deposited Graphene, Doctoral dissertation(2013)
[10] S. H. R. Sena, J.M. Pereira Jr, G.A. Farias, F. M. Peeters, R. N. Costa Filho, The electronic properties of graphene and graphene ribbons under simple shear strain, J. Phys.: Condens. Matter 24 375301
[11] C. W. J. Beenakker, Specular Andreev reflection in graphene, Phys. Rev. Lett. 97, 067007(2006)
[12] Subhro Bhattacharjee, Moitri Maiti, and K. Sengupta, Theory of tunneling conductance of graphene normal metal-insulator-superconductor junctions, PHYSICAL REVIEW B 76, 184514 (2007)
[13] W. A. Munoz, L. Covaci, and F. M. Peeters, Disordered graphene Josephson junctions, PHYSICAL REVIEW B 91, 054506 (2015)
[14] Naomi Mizuno, Bent Nielsen, and Xu Du, Ballistic-like supercurrent in suspended graphene Josephson weak links, Nature Commun. 4, 2716 (2013)
[15] Gil-Ho Lee and Hu-Jong Lee, Josephson Coupling Realized in Graphite-Based Vertical Junction, Appl. Phys. Express 6 025102
[16] D. K. Efetov, L. Wang, C. Handschin, K. B. Efetov, J. Shuang, R. Cava,
T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean and P. Kim, Specular interband Andreev reflections at van der Waals interfaces between graphene and NbSe2, Nature Physics 12. 328-332(2016)