電子在超導體中以古柏對形式存在，古柏對是量子糾纏電子對，可以透過交叉式安德烈夫反射將古柏對裡的兩個電子分別穿隧至兩個空間上分離的一般金屬，這種空間上分離的糾纏電子對可以應用在固態量子傳輸上。為了提高古柏對分裂的效率，可以利用兩個有不同電荷傳輸載子類型的半導體來取代一般金屬，因為p型半導體(n型半導體)只允許電洞(電子)存在於超導體/半導體介面。
我們製作石墨烯/鋁/石墨烯元件，鋁金屬在溫度1.1K以下為超導體，石墨烯與鋁金屬介面透過穿隧屏障相接，兩塊石墨烯有一個全域的下閘極以及兩個獨立的上閘極來調控其載子種類與濃度。本論文研究元件的二階(2nd order)電子穿隧行為，包括古柏對分裂與彈性共同穿隧。
透過非局部電壓以及電流-電流交互關係量測，分析實驗所得到的數據，我們主要觀察到電子彈性共同穿隧行為，而且鋁在超導狀態下，彈性共同穿隧行為更明顯;另外在下閘極電壓Vbg=10V附近的區域石墨烯分別為p-type與n-type，使元件處於p-type石墨烯/超導體/n-type石墨烯(pSn)狀態，非局部電壓量測的結果，在Vbg=10V，非局部電壓有極小值，可能暗示古柏對分裂，但是由於上閘極品質不佳，無法獨立調控兩個石墨烯載子濃度，使元件處於pSn狀態，所以尚未有系統性的研究石墨烯pSn元件的電荷傳輸行為。

Cooper pair in superconductor is a quantum entangled object and could split into two spatially-separate normal metals via crossed Andreev reflection. Such spatially-separate entangled electron pair may have applications to solid-state quantum teleportation. To achieve high efficiency of Cooper pair splitting (CPS), two semiconductors with opposite polarities are proposed to replace two normal metals due to either electron or hole is missing in both superconductor/semiconductor interfaces.
We fabricated graphene/aluminum/graphene devices. Aluminum becomes superconducting below 1.1K and it links to two graphene grains via tunneling barriers. Each graphene can be tuned electrically by a global bottom-gate and a local top-gate. This thesis reported studies of electrons 2nd-order tunneling events in the devices, including CPS and elastic cotunneling (EC).
According to the non-local voltage and current-current correlation measurements, we mostly observed EC. EC is enhanced when the aluminum becomes superconducting. In a small region near Vbg=10V, two graphene grains have opposite polarities, making a p-type graphene/superconductor/n-type graphene (pSn) device. We found minimum value of non-local voltage when Vbg=10V. The decrease of nonlocal voltage implies CPS. Because the low quality of top-gates, we are unable to vary carrier density of two graphene grains independently. Therefore, we cannot make pSn device reliably. The study of electrons tunneling events in pSn device requires further investigation.

1. Griffiths, D.J. and E.G. Harris, Introduction to quantum mechanics. Vol. 2. 1995: Prentice Hall New Jersey.
2. Blonder, G.E., M. Tinkham, and T.M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion. Physical Review B, 1982. 25(7): p. 4515-4532.
3. Byers, J.M. and M.E. Flatté, Probing Spatial Correlations with Nanoscale Two-Contact Tunneling. Physical Review Letters, 1995. 74(2): p. 306-309.
4. Kleine, A., et al., Contact resistance dependence of crossed Andreev reflection. EPL (Europhysics Letters), 2009. 87(2): p. 27011.
5. Wei, J. and V. Chandrasekhar, Positive noise cross-correlation in hybrid superconducting and normal-metal three-terminal devices. Nat Phys, 2010. 6(7): p. 494-498.
6. Veldhorst, M. and A. Brinkman, Nonlocal Cooper Pair Splitting in a p S n Junction. Physical Review Letters, 2010. 105(10): p. 107002.
7. Novoselov, K.S., et al., Electric Field Effect in Atomically Thin Carbon Films. Science, 2004. 306(5696): p. 666-669.
8. Abergel, D., et al., Properties of graphene: a theoretical perspective. Advances in Physics, 2010. 59(4): p. 261-482.
9. Ferrari, A.C., et al., Raman Spectrum of Graphene and Graphene Layers. Physical Review Letters, 2006. 97(18): p. 187401.
10. Yu, Q., et al., Graphene segregated on Ni surfaces and transferred to insulators. Applied Physics Letters, 2008. 93(11): p. 113103.
11. Li, X., et al., Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science, 2009. 324(5932): p. 1312-1314.
12. Luo, Z., et al., Growth mechanism of hexagonal-shape graphene flakes with zigzag edges. ACS nano, 2011. 5(11): p. 9154-9160.
13. Lin, Y.-C., et al., Graphene annealing: how clean can it be? Nano letters, 2011. 12(1): p. 414-419.
14. Meyer, J.C., et al., The structure of suspended graphene sheets. Nature, 2007. 446(7131): p. 60-63.
15. Miyazaki, H., et al., Resistance modulation of multilayer graphene controlled by the gate electric field. Semiconductor Science and Technology, 2010. 25(3): p. 034008.
16. BlueFors, BF‐LD250 CRYOGEN‐FREE DILUTION REFRIGERATOR SYSTEM User manual. 1.3.1 ed. 2011.
17. Vlassiouk, I., et al., Role of Hydrogen in Chemical Vapor Deposition Growth of Large Single-Crystal Graphene. ACS nano, 2011. 5(7): p. 6069-6076.
18. 陳嘉偉, Research of graphene for transparent conductive film and its growth model, 2012.
19. Losurdo, M., et al., Graphene CVD growth on copper and nickel: role of hydrogen in kinetics and structure. Physical Chemistry Chemical Physics, 2011. 13(46): p. 20836-20843.
20. Yu, Q., et al., Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition. Nat Mater, 2011. 10(6): p. 443-449.
21. Russo, S., et al., Experimental Observation of Bias-Dependent Nonlocal Andreev Reflection. Physical Review Letters, 2005. 95(2): p. 027002.