Chiral tunneling in single-layer and bilayer graphene

Physica Scripta

Volumn , Issue T146, 2012, Pages

  Tudorovskiy, T ^a   Reijnders, K J A ^a   Katsnelson, M I ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL FORMULAS; BERRY PHASE; BI-LAYER; COMPLEX POTENTIALS; DINGER EQUATION; DIRAC EQUATIONS; NORMAL INCIDENCE; NUMERICAL RESULTS; ONE-DIMENSIONAL GEOMETRY; PHASE SPACES; SEMICLASSICAL THEORIES; SINGLE LAYER; TOTAL TRANSMISSION;

LINEAR EQUATIONS; PHASE SPACE METHODS; SEMICONDUCTOR JUNCTIONS;

GRAPHENE;

EID: 84857425217     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/2012/T146/014010     Document Type: Article

References (53)

1. Geim A K and Novoselov K S 2007 The rise of graphene Nature Mater. 6 183
2. Katsnelson M I 2007 Graphene: carbon in two dimensions Mater. Today 10 20
3. Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109
4. Beenakker C W J 2008 Colloquium: Andreev reflection and Klein tunneling in graphene Rev. Mod. Phys. 80 1337
5. Geim A K 2009 Graphene: status and prospects Science 324 1530
6. Peres N M R 2010 Colloquium: the transport properties of graphene: an introduction Rev. Mod. Phys. 82 2673
7. Vozmediano M A H, Katsnelson M I and Guinea F 2010 Gauge fields in graphene Phys. Rep. 496 109
8. Katsnelson M I, Novoselov K S and Geim A K 2006 Chiral tunnelling and the Klein paradox in graphene Nature Phys. 2 620-5 (Pubitemid 44328348)
9. Klein O 1929 Die reflexion von elektronen an einem potentialsprung nach der relativistischen dynamik von Dirac Z. Phys. 53 157-65
10. Calogeracos A and Dombey N 1999 History and physics of the Klein paradox Contemp. Phys. 40 313
11. Dombey N and Calogeracos A 1999 Seventy years of the Klein paradox Phys. Rep. 315 41
12. Greiner W and Schramm S 2008 Resource letter QEDV-1: the QED vacuum Am. J. Phys. 76 509
13. Vonsovsky S V and Svirsky M S 1993 The Klein paradox and the zitterbewegung of an electron in a field with a constant scalar potential Usp. Fiz. Nauk 163 115
14. Su R-K, Siu G G and Chou X 1993 Barrier penetration and Klein paradox J. Phys. A: Math. Gen. 26 1001
15. Stratton J A 1941 Electromagnetic Theory (New York: McGraw-Hill)
16. Landau L D and Peierls R 1931 Erweiterung des unbestimmtheitsprinzips für die relativistische quantentheorie Z. Phys. 69 56
17. Berestetskii V B, Lifshitz E M and Pitaevskii L P 1971 Relativistic Quantum Theory (Course of Theoretical Physics) vol 4 (Oxford: Pergamon)
18. Calogeracos A, Dombey N and Imagawa K 1996 Spontaneous fermion production by a supercritical potential well Phys. At. Nucl. 59 1275
19. Krekora P, Su Q and Grobe R 2005 Klein paradox with spin-resolved electrons and positrons Phys. Rev. A 72 064103
20. Ando T, Nakanishi T and Saito R 1998 Berry's phase and absence of back scattering in carbon nanotubes J. Phys. Soc. Japan 67 2857
21. Yennie D R, Ravenhall D G and Wilson R N 1954 Phase-shift calculation of high-energy electron scattering Phys. Rev. 95 500
22. Lifshitz I M, Gredeskul S A and Pastur L A 1998 Introduction to the Theory of Disordered Systems (New York: Wiley)
23. Newton R G 1966 Scattering Theory of Waves and Particles (New York: McGraw-Hill)
24. Greiner W, Mueller B and Rafelski J 1985 Quantum Electrodynamics of Strong Fields (Berlin: Springer)
25. Grib A A, Mamaev S V and Mostepanenko V M 1994 Vacuum Effects in Strong Fields (St Petersburg: Friedmann)
26. Stander N, Huard B and Goldhaber-Gordon D 2009 Evidence for Klein tunneling in graphene p-n junctions Phys. Rev. Lett. 102 026807
27. Young A F and Kim P 2009 Quantum interference and Klein tunnelling in graphene heterojunctions Nature Phys. 5 222
28. Esaki L 1958 New phenomenon in narrow germanium para-normal-junctions Phys. Rev. 109 603
29. Meyer J R, Hoffman C A, Bartoli F J and Rammohan L R 1995 Type-II quantum-well lasers for the midwavelength infrared Appl. Phys. Lett. 67 757
30. Teissier R, Finley J J, Skolnick M S, Cockburn J W, Pelouard J-L, Grey R, Hill G, Pate M-A and Planel R 1996 Experimental determination of Γ-X intervalley transfer mechanisms in GaAs/AlAs heterostructures Phys. Rev. B 54 8329
31. Dresselhaus M S and Dresselhaus G 2002 Intercalation compounds of graphite Adv. Phys. 51 1
32. Kuzmenko A B, Crassee I, van der Marel D, Blake P and Novoselov K S 2009 Determination of the gate-tunable band gap and tight-binding parameters in bilayer graphene using infrared spectroscopy Phys. Rev. B 80 165406
33. McCann E and Falko V I 2006 Landau-level degeneracy and quantum Hall effect in a graphite bilayer Phys. Rev. Lett. 96 086805
34. Novoselov K S, McCann E, Morozov S V, Falko V I, Katsnelson M I, Zeitler U, Jiang D, Schedin F and Geim AK 2006 Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene Nature Phys. 2 177
35. McCann E, Abergel D S L and Falko V I 2007 Electrons in bilayer graphene Solid State Commun. 143 110
36. Foldy L and Wouthuysen S 1950 On the Dirac theory of spin 1/2 particles and its non-relativistic limit Phys. Rev. 78 29-36
37. Blount E I 1961 Bloch electrons in a magnetic field Phys. Rev. 126 1636-53
38. Berlyand L V and Dobrokhotov Y S 1987 Operator separation of variables in problems of short-wave asymptotics for differential equations with rapidly oscillating coefficients Dokl. Akad. Nauk SSSR 296 80-4
39. Belov V V, Dobrokhotov Y S and Tudorovskiy Y T 2006 Operator separation of variables for adiabatic problems in quantum and wave mechanics J. Eng. Math. 55 183-237
40. Maslov V P 1972 Perturbation Theory and Asymptotic Methods (Paris: Dunod)
41. Maslov V P and Fedoryuk M V 1981 Semi-Classical Approximation in Quantum Mechanics (Dordrecht: Reidel)
42. Shytov A V, Rudner M S and Levitov L S 2008 Klein backscattering and Fabry-Pérot interference in graphene heterojunctions Phys. Rev. Lett. 101 156804
43. Carmier P and Ullmo D 2008 Berry phase in graphene: semiclassical perspective Phys. Rev. B 77 245413
44. Cheianov V V and Fal'ko V I 2006 Selective transmission of Dirac electrons and ballistic magnetoresistance of n-p junctions in graphene Phys. Rev. B 74 041403
45. Abramowitz M and Stegun I A (ed) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover) chapter 19, p 686
46. http://functions.wolfram.com/HypergeometricFunctions/ParabolicCylinderD - ref-separator -
47. Evgrafov M A and Fedoryuk M V 1966 Asymptotic behaviour as λ→∞ of the solution of the equation w″ (z)p(z,)w(z)=0 in the complex z-plane Russ. Math. Surv. 21 1
48. Landau L D and Lifshitz E M 1977 Quantum Mechanics, Non-relativistic Theory (Course of Theoretical Physics) vol3 2nd edn (Oxford: Pergamon)
49. Heading J 1962 An Introduction to Phase-Integral Methods (Methuen's Monographs on Physical Subjects) (Methuen: London) (a Russian translation with an appendix by V P Maslov on the WKB method in the multi-dimensional case was published in 1965 by MIR, Moscow)
50. Fröman N and Fröman P O 1962 JWKB Approximation, Contributions to the Theory (Amsterdam: North-Holland)
51. Berry M V and Mount K E 1972 Semiclassical approximations in wave mechanics Rev. Prog. Phys. 35 315-97
52. Fröman N and Fröman P O 2002 Physical Problems Solved by the Phase-Integral Method (Cambridge: Cambridge University Press)
53. Goldstein H, Poole C P and Safko J L 2002 Classical Mechanics 3rd edn (San Fransisco, CA: Addison-Wesley)