Velocity-modulation control of electron-wave propagation in graphene

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 7, 2010, Pages

  Raoux, Arnaud ^a,e   Polini, Marco ^a   Asgari, Reza ^b   Hamilton, A R ^c   Fazio, Rosario ^a   MacDonald, A H ^d  

^a INFM   (Italy)

^b INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES IPM   (Iran)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

^d UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^e ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954853537     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.073407     Document Type: Article

References (33)

1. J. D. Joannopoulos, Photonic Crystal: Molding the Flow of Light (Princeton University Press, Princeton NJ, 1995) and work cited therein.
2. See for example M. M. Sigalas and E. N. Economou, Solid State Commun. 86, 141 (1993). 10.1016/0038-1098(93)90888-T
3. A. H. Castro Neto, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys.81. 109
4. See for example V. V. Cheianov, Science 315, 1252 (2007) 10.1126/science.1138020
5. C. W. J. Beenakker, Phys. Rev. Lett. 102, 146804 (2009). 10.1103/PhysRevLett.102.146804
6. For a review see B. J. LeRoy, J. Phys.: Condens. Matter 15, R1835 (2003). 10.1088/0953-8984/15/50/R02
7. While this work was being written we learned that scattering of MDFs against a velocity barrier has also been studied by A. Concha and Z. Teanovic, arXiv:0912.0493 (unpublished).
8. N. M. R. Peres, J. Phys: Condens. Matter 21, 095501 (2009) 10.1088/0953-8984/21/9/095501
9. a position-dependent velocity has also been considered by F. de Juan, Phys. Rev. B 76, 165409 (2007) in the context of curved graphene. 10.1103/PhysRevB.76.165409
10. M. I. Katsnelson, Nat. Phys. 2, 620 (2006) 10.1038/nphys384
11. for recent experimental studies of Klein tunneling see A. F. Young and P. Kim, Nat. Phys. 5, 222 (2009) 10.1038/nphys1198
12. N. Stander, Phys. Rev. Lett. 102, 026807 (2009). 10.1103/PhysRevLett.102. 026807
13. The reflection coefficient r in Eq. is given by r η, ξ (θ 1) = (ξ - 1) exp (i θ 1) sin (q x η / k) sin (θ 1) / D η, ξ (θ 1), with D η, ξ (θ 1) = (ξ q x / k) cos (q x η / k) cos (θ 1) - i sin (q x η / k) [1 - ξ sin 2 (θ 1)].
14. ) 2 in the function C η, ξ (θ 1), with s = sgn (E) sgn (E - V 0). This implies that for any velocity v 2 we can find a value of the barrier height, V 0 = E - | E | / ξ, which gives the same transmission probability. On the other hand, not every problem of scattering through a potential barrier can be mapped into a velocity-barrier problem: the mapping exists only if s = 1.
15. M. Polini, Phys. Rev. B 77, 081411 (R) (2008). 10.1103/PhysRevB.77.081411
16. E. H. Hwang and S. Das Sarma, Phys. Rev. B 77, 081412 (R) (2008). 10.1103/PhysRevB.77.081412
17. Y. Barlas, Phys. Rev. Lett. 98, 236601 (2007). 10.1103/PhysRevLett.98. 236601
18. The impact of screening due to metal gates or high-density 2D electron gases on Fermi-liquid parameters has been recently studied experimentally in the context of the metal-insulator transition: L. H. Ho, Phys. Rev. B 77, 201402 (R) (2008). 10.1103/PhysRevB.77.201402
19. M. Polini, Solid State Commun. 143, 58 (2007). 10.1016/j.ssc.2007.04.035
20. G. Li, Phys. Rev. Lett. 102, 176804 (2009). 10.1103/PhysRevLett.102. 176804
21. See, e.g., G. F. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005), Chap..
22. / 2 evaluated at z = 0 (where the graphene sheet is located). The electrostatic potential Φ (ρ, z) can be simply obtained from the method of image charges and satisfies the boundary condition Φ (ρ, d) = 0. This simple form of V d (q) is true if no dielectric media other than air are located underneath or above the graphene flake [see inset in Fig.]. For the sake of simplicity the data reported in Fig. have been obtained for such suspended sheets [K. I. Bolotin, Solid State Commun. 146, 351 (2008) 10.1016/j.ssc.2008. 02.024
23. X. Du, Nature Nanotech. 3, 491 (2008)]. In this case, apart from electron density n and metal-graphene distance d, the only parameter that controls v / v is the fine structure constant α ee = e 2 / (v) 2.2. 10.1038/nnano.2008. 199
24. J. Moore, Nat. Phys. 5, 378 (2009) 10.1038/nphys1294
25. Y. Xia, Nat. Phys. 5, 398 (2009) 10.1038/nphys1274
26. H. Zhang, Nat. Phys. 5, 438 (2009). 10.1038/nphys1270
27. C.-H. Park and S. G. Louie, Nano Lett. 9, 1793 (2009). 10.1021/nl803706c
28. M. Gibertini, Phys. Rev. B 79, 241406 (R) (2009). 10.1103/PhysRevB.79. 241406
29. See also C. Flindt, Nano Lett. 5, 2515 (2005) for a discussion of antidot lateral superlattices for quantum computation. 10.1021/nl0518472
30. S. L. Zhu, Phys. Rev. Lett. 98, 260402 (2007) 10.1103/PhysRevLett.98. 260402
31. B. Wunsch, New J. Phys. 10, 103027 (2008). 10.1088/1367-2630/10/10/103027
32. F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008) 10.1103/PhysRevLett.100.013904
33. R. A. Sepkhanov, Phys. Rev. B 78, 045122 (2008). 10.1103/PhysRevB.78. 045122