Colloquium: Andreev reflection and Klein tunneling in graphene

Reviews of Modern Physics

Volumn 80, Issue 4, 2008, Pages 1337-1354

  Beenakker, C W J ^a  

^a UNIVERSITEIT LEIDEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC CONDUCTIVITY; ELECTRIC CURRENTS; GALVANOMAGNETIC EFFECTS; HALL EFFECT; QUANTUM THEORY; REFLECTION; SEMICONDUCTOR JUNCTIONS; SUPERCONDUCTIVITY; TUNNELING (EXCAVATION);

A CARBONS; ANDREEV REFLECTIONS; BIPOLAR JUNCTIONS; CONDUCTANCE PLATEAUX; ELECTRONIC PROCESSES; ELECTROSTATIC POTENTIALS; GRAPHENE; ISOSPIN; JOSEPHSON JUNCTIONS; MASSLESS DIRAC FERMIONS; NEGATIVE REFRACTIONS; NORMAL INCIDENCES; P-N JUNCTIONS; PAIR POTENTIALS; QUANTUM HALL EFFECTS; QUANTUM MECHANICS; UNIT EFFICIENCIES;

MAGNETIC FIELD EFFECTS;

EID: 56549126981     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.80.1337     Document Type: Article

References (122)

1. Abanin, D. A., P. A. Lee, and L. S. Levitov, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.176803 96, 176803.
2. Abanin, D. A., and L. S. Levitov, 2007, Science SCIEAS 0036-8075 10.1126/science.1144672 317, 641.
3. Akhmerov, A. R., and C. W. J. Beenakker, 2007a, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.045426 75, 045426.
4. Akhmerov, A. R., and C. W. J. Beenakker, 2007b, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.157003 98, 157003.
5. Akhmerov, A. R., and C. W. J. Beenakker, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.085423 77, 085423.
6. Aleiner, I. L., and K. B. Efetov, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.236801 97, 236801.
7. Anderson, P. W., 1963, in Ravello Lectures on the Many-Body Problem, edited by, E. R. Gianello, (Academic, New York).
8. Ando, T., T. Nakanishi, and R. Saito, 1998, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.2857 67, 2857.
9. Andreev, A. F., 1964, Sov. Phys. JETP SPHJAR 0038-5646 19, 1228.
10. Andreev, A. V., 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.247204 99, 247204.
11. Aronov, A. G., and G. E. Pikus, 1967a, Sov. Phys. JETP SPHJAR 0038-5646 24, 188.
12. Aronov, A. G., and G. E. Pikus, 1967b, Sov. Phys. JETP SPHJAR 0038-5646 24, 339.
13. Beenakker, C. W. J., 1997, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.69.731 69, 731.
14. Beenakker, C. W. J., 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.067007 97, 067007.
15. Beenakker, C. W. J., A. R. Akhmerov, P. Recher, and J. Tworzydło, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.075409 77, 075409.
16. Beenakker, C. W. J., and M. Büttiker, 1992, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.1889 46, 1889.
17. Beenakker, C. W. J., and H. van Houten 1992, in Nanostructures and Mesoscopic Systems, edited by, W. P. Kirk, and, M. A. Reed, (Academic, New York).
18. Berry, M. V., and R. J. Mondragon, 1987, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1987.0080 412, 53.
19. Bhattacharjee, S., M. Maiti, and K. Sengupta, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.184514 76, 184514.
20. Bhattacharjee, S., and K. Sengupta, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.217001 97, 217001.
21. Blanter, Ya. M., and I. Martin, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.155433 76, 155433.
22. Bostwick A., T. Ohta, T. Seyller, H. K. Horn, and E. Rotenberg, 2007, Nat. Phys. ZZZZZZ 1745-2473 3, 36.
23. Brey, L., and H. A. Fertig, 2006a, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.195408 73, 195408.
24. Brey, L., and H. A. Fertig, 2006b, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.235411 73, 235411.
25. Büttiker, M., Y. Imry, and R. Landauer, 1983, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(83)90011-7 96A, 365.
26. Calogeracos, A., and N. Dombey, 1999, Contemp. Phys. CTPHAF 0010-7514 10.1080/001075199181387 40, 313.
27. Capelle, K., and E. K. U. Gross, 1995, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)01010-R 198, 261.
28. Capelle, K., and E. K. U. Gross, 1999a, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.7140 59, 7140.
29. Capelle, K., and E. K. U. Gross, 1999b, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.7155 59, 7155.
30. Castro Neto, A. H., F. Guinea, and N. M. R. Peres, 2006, Phys. World PHWOEW 0953-8585 19, 33 (2006).
31. Castro Neto, A. H., F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, 2007, e-print arXiv:0709.1163.
32. Cheianov, V. V., and V. I. Fal'ko, 2006, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.041403 74, 041403 (R).
33. Cheianov, V. V., V. I. Fal'ko, and B. L. Altshuler, 2007, Science SCIEAS 0036-8075 10.1126/science.1138020 315, 1252.
34. Cheianov, V. V., V. I. Fal'ko, B. L. Altshuler, and I. L. Aleiner, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.176801 99, 176801.
35. Cserti, J., A. Pályi, and C. Péterfalvi, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.246801 99, 246801.
36. Cuevas, J. C., and A. Levy Yeyati, 2006, Capelle, K., and E. K. U. Gross, 1999, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.180501 74, 180501 (R).
37. Danneau, R., F. Wu, M. F. Craciun, S. Russo, M. Y. Tomi, J. Salmilehto, A. F. Morpurgo, and P. J. Hakonen, 2008, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.196802 100, 196802.
38. De Gennes, P. G., and D. Saint-James, 1963, Phys. Lett. PHLTAM 0031-9163 10.1016/0031-9163(63)90148-3 4, 151.
39. De Jong, M. J. M., and C. W. J. Beenakker, 1995, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1657 74, 1657.
40. DiVincenzo, D. P., and E. J. Mele, 1984, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.29.1685 29, 1685.
41. Dorokhov, O. N., 1984, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(84)90117-0 51, 381.
42. Du, X., I. Skachko, and E. Y. Andrei, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.184507 77, 184507.
43. Fagas, G., G. Tkachov, A. Pfund, and K. Richter, 2005, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.224510 71, 224510.
44. Fistul, M. V., and K. B. Efetov, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.256803 98, 256803.
45. Fogler, M. M., L. I. Glazman, D. S. Novikov, and B. I. Shklovskii, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.075420 77, 075420.
46. Garcia-Pomar, J. L., A. Cortijo, and M. Nieto-Vesperinas, 2008, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.236801 100, 236801.
47. Geim, A. K., and K. S. Novoselov, 2007, Nature Mater. NMAACR 1476-1122 10.1038/nmat1849 6, 183.
48. Ghaemi, P., and F. Wilczek, 2007, e-print arXiv:0709.2626.
49. Ghosh, T. K., A. De Martino, W. Häusler, L. Dell'Anna, and R. Egger, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.081404 77, 081404 (R).
50. González, J., and E. Perfetto, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.155404 76, 155404.
51. Greenbaum, D., S. Das, G. Schwiete, and P. G. Silvestrov, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.195437 75, 195437.
52. Gusynin, V. P., S. G. Sharapov, and J. P. Carbotte, 2007, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979207038022 21, 4611.
53. Haldane, F. D. M., and S. Raghu, 2008, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.013904 100, 013904.
54. Heersche, H. B., P. Jarillo-Herrero, J. B. Oostinga, L. M. K. Vandersypen, and A. F. Morpurgo, 2007, Nature NATUAS 0028-0836 10.1038/nature05555 446, 56.
55. Huard, B., J. A. Sulpizio, N. Stander, K. Todd, B. Yang, and D. Goldhaber-Gordon, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 98.236803 98, 236803.
56. Imry, Y., 1997, Introduction to Mesoscopic Physics (Oxford University Press, Oxford).
57. Jiang, Y., D.-X. Yao, E. W. Carlson, H.-D. Chen, and J.-P. Hu, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.235420 77, 235420.
58. Josephson, B. D., 1964, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.36.216 36, 216.
59. Kane, E. O., and E. Blount, 1969, in Tunneling Phenomena in Solids, edited by, E. Burstein, and, S. Lundqvist, (Plenum, New York).
60. Katsnelson, M. I., 2006, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006-00203-1 51, 157.
61. Katsnelson, M. I., 2007, Mater. Today MTOUAN 1369-7021 10.1016/S1369-7021(06)71788-6 10, 20.
62. Katsnelson, M. I., and K. S. Novoselov, 2007, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2007.02.043 143, 3.
63. Katsnelson, M. I., K. S. Novoselov, and A. K. Geim, 2006, Nat. Phys. ZZZZZZ 1745-2473 2, 620.
64. Klein, O., 1929, Z. Phys. ZEPYAA 0044-3328 10.1007/BF01339716 53, 157.
65. Kulik, I. O., 1970, Sov. Phys. JETP SPHJAR 0038-5646 30, 944.
66. Linder, J., and A. Sudbø, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.147001 99, 147001.
67. Ludwig, T., 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75. 195322 75, 195322.
68. Lukose, V., R. Shankar, and G. Baskaran, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.116802 98, 116802.
69. Maiti, M., and K. Sengupta, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.054513 76, 054513.
70. Martin, J., N. Akerman, G. Ulbricht, T. Lohmann, J. H. Smet, K. von Klitzing, and A. Yacoby, 2008, Nat. Phys. ZZZZZZ 1745-2473 4, 144.
71. McCann, E., and V. I. Fal'ko, 2004, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/16/13/016 16, 2371.
72. McCann, E., and V. I. Fal'ko, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.086805 96, 086805.
73. McCann, E., K. Kechedzhi, V. I. Fal'ko, H. Suzuura, T. Ando, and B. L. Altshuler, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.146805 97, 146805.
74. McClure, J. W., 1956, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.666 104, 666.
75. Miao, F., S. Wijeratne, Y. Zhang, U. C. Coskun, W. Bao, and C. N. Lau, 2007, Science SCIEAS 0036-8075 10.1126/science.1144359 317, 1530.
76. Milton Pereira, J., V. Mlinar, F. M. Peeters, and P. Vasilopoulos, 2006, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.045424 74, 045424.
77. Milton Pereira, J., F. M. Peeters, and P. Vasilopoulos, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.125433 75, 125433.
78. Milton Pereira, J., P. Vasilopoulos, and F. M. Peeters, 2007, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2717092 90, 132122.
79. Moghaddam, A. G., and M. Zareyan, 2006, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.241403 74, 241403 (R).
80. Morozov, S. V., K. S. Novoselov, M. I. Katsnelson, F. Schedin, L. A. Ponomarenko, D. Jiang, and A. K. Geim, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.016801 97, 016801.
81. Morpurgo, A. F., and F. Guinea, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.196804 97, 196804.
82. Müller, J. E., 1992, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.385 68, 385.
83. Notomi, M., 2000, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.10696 62, 10696.
84. Novoselov, K. S., A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, 2005, Nature NATUAS 0028-0836 10.1038/nature04233 438, 197.
85. Novoselov, K. S., A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, 2004, Science SCIEAS 0036-8075 10.1126/science.1102896 306, 666.
86. Ohta, T., A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, 2006, Science SCIEAS 0036-8075 10.1126/science.1130681 313, 951.
87. Oroszlany, L., Rakyta, P., A. Kormanyos, C. J. Lambert, and J. Cserti, 2008, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.081403 77, 081403 (R).
88. Ossipov, A., M. Titov, and C. W. J. Beenakker, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.241401 75, 241401 (R).
89. Özyilmaz, B., P. Jarillo-Herrero, D. Efetov, D. A. Abanin, L. S. Levitov, and P. Kim, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.166804 99, 166804.
90. Pendry, J. B., and D. R. Smith, 2004, Phys. Today PHTOAD 0031-9228 60 (2), 37.
91. Prada, E., P. San-Jose, B. Wunsch, and F. Guinea, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.113407 75, 113407.
92. Robinson, J. P., and H. Schomerus, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.115430 76, 115430.
93. Sauer, T., 2007, Arch. Hist. Exact Sci. AHESAN 0003-9519 10.1007/s00407-006-0122-8 61, 159 (2007).
94. Sauter, F., 1931, Z. Phys. ZEPYAA 0044-3328 10.1007/BF01349862 73, 547.
95. Schomerus, H., 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76. 045433 76, 045433.
96. Semenoff, G. W., 1984, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.2449 53, 2449.
97. Sepkhanov, R. A., Ya. B. Bazaliy, and C. W. J. Beenakker, 2007, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.063813 75, 063813.
98. Shailos, A., W. Nativel, A. Kasumov, C. Collet, M. Ferrier, S. Guéron, R. Deblock, and H. Bouchiat, 2007, EPL EULEEJ 0295-5075 10.1209/0295-5075/79/57008 79, 57008.
99. Shytov, A. V., N. Gu, and L. S. Levitov, 2007, e-print arXiv:0708.3081.
100. Shytov, A. V., M. I. Katsnelson, and L. S. Levitov, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.246802 99, 246802.
101. Silvestrov, P. G., and K. B. Efetov, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.016802 98, 016802.
102. Son, Y.-W., M. L. Cohen, and S. G. Louie, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.216803 97, 216803.
103. Suzuura, H., and T. Ando, 2002, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.266603 89, 266603.
104. Titov, M., and C. W. J. Beenakker, 2006, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.041401 74, 041401 (R).
105. Titov, M., A. Ossipov, and C. W. J. Beenakker, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.045417 75, 045417.
106. Tkachov, G., 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76. 235409 76, 235409.
107. Trauzettel, B., Ya. M. Blanter, and A. F. Morpurgo, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.035305 75, 035305.
108. Tworzydło, J., I. Snyman, A. R. Akhmerov, and C. W. J. Beenakker, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.035411 76, 035411.
109. Tworzydło, J., B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.246802 96, 246802.
110. Uchoa, B., and A. H. Castro Neto, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.146801 98, 146801.
111. Van Delft, D., 2006, Phys. Today PHTOAD 0031-9228 59 (4), 57.
112. Veselago, V. G., 1968, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1968v010n04ABEH003699 10, 509.
113. Volkov, A. F., P. H. C. Magnee, B. J. van Wees, and T. M. Klapwijk, 1995, Physica C PHYCE6 0921-4534 10.1016/0921-4534(94)02429-4 242, 261.
114. Wakabayashi, K., 2003, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.72.1010 72, 1010.
115. Wallace, P. R., 1947, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.71.622 71, 622.
116. Wehling, T. O., H. P. Dahal, A. I. Lichtenstein, and A. V. Balatsky, 2007, e-print arXiv:0704.3115.
117. Weiler, M. H., W. Zawadzki, and B. Lax, 1967, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.163.733 163, 733.
118. Williams, J. R., L. DiCarlo, and C. M. Marcus, 2007, Science SCIEAS 0036-8075 10.1126/science.1144657 317, 638.
119. Zhang, L. M., and M. M. Fogler, 2008, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.116804 100, 116804.
120. Zhang, Y., Y.-W. Tan, H. L. Stormer, and P. Kim, 2005, Nature NATUAS 0028-0836 10.1038/nature04235 438, 201.
121. Zhou, S. Y., G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, 2007, Nature Mater. NMAACR 1476-1122 10.1038/nmat2003 6, 770.
122. Zhou, S. Y., G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, R. D. Diehl, Y. Kopelevich, D.-H. Lee, S. G. Louie, and A. Lanzara, 2006, Nat. Phys. ZZZZZZ 1745-2473 2, 595.