Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
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).
A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nature Mater. 6, 183 (2007).
A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
M. I. Katsnelson, “Graphene: carbon in two dimensions,” Mater. Today 10, 20 (2007).
M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620 (2006).
A. V. Rozhkov, G. Giavaras, Y. P. Bliokh, V. Freilikher, and F. Nori, “Electronic properties of mesoscopic graphene structures: Charge confinement and control of spin and charge transport,” Phys. Rep. 77, 503 (2011).
A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332, 1291 (2011).
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).
M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627 (2012).
C. Dean, A. Young, L. Wang, I. Meric, G.-H. Lee, K. Watanabe, T. Taniguchi, K. Shepard, P. Kim, and J. Hone, “Graphene based heterostructures,” Solid State Commun. 152, 1275 (2012).
Y. P. Bliokh, V. Freilikher, S.Savel’ev, and F. Nori, “Transport and localization in periodic and disordered graphene superlattices,” Phys. Rev. B 79, 075123 (2009).
L. Brey and H. A. Fertig, “Emerging Zero Modes for Graphene in a Periodic Potential,” Phys. Rev. Lett. 103, 046809 (2009).
P. Burset, A. L. Yeyati, L. Brey, and H. A. Fertig, “Transport in superlattices on single-layer graphene,” Phys. Rev. B 83, 195434 (2011).
S. P. Milovanović, D. Moldovan, and F. M. Peeters, “Veselago lensing in graphene with a p-n junction: Classical versus quantum effects,” J. Appl. Phys. 118, 154308 (2015).
M. Barbier, F. M. Peeters, P. Vasilopoulos, and J. M. Pereira, Jr., “Dirac and Klein-Gordon particles in one-dimensional periodic potentials,” Phys. Rev. B 77, 115446 (2008).
L.-G. Wang and S.-Y. Zhu, “Electronic band gaps and transport properties in graphene superlattices with one-dimensional periodic potentials of square barriers,” Phys. Rev. B 81, 205444 (2010).
C. H. Park, L. Yang, Y. W. Son, M. L. Cohen, and S. G. Louie, “New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials,” Phys. Rev. Lett. 101, 126804 (2008).
C.-H. Park, L. Yang, Y.-W. Son, M. L. Cohen, and S. G. Louie, “Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials,” Nat. Phys. 4, 213 (2008).
C.-H. Park, Y.-W. Son, L. Yang, M. L. Cohen, and S. G. Louie, “Electron Beam Supercollimation in Graphene Superlattices,” Nano Lett. 9, 2920 (2008).
J. C. Meyer, C.O. Girit, M. F. Crommie, and A. Zettl, “Hydrocarbon lithography on graphene membranes,” Appl. Phys. Lett. 92, 123110 (2008).
M. Barbier, P. Vasilopoulos, and F. M. Peeters, “Extra Dirac points in the energy spectrum for superlattices on single-layer graphene,” Phys. Rev. B 81, 075438 (2010).
M. Barbier, P. Vasilopoulos, and F. M. Peeters, “Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines,” Phil. Trans. R. Soc. A 368, 5499 (2010).
M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoyet, “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride,” Nat. Phys. 8, 382 (2012).
L. A. Ponomarenko, R. V. Gorbachev, G. L. Yu, D. C. Elias, R. Jalil, A. A. Patel, A. Mishchenko, A. S. Mayorov, C. R. Woods, J. R. Wallbank, M. Mucha-Kruczynski, B. A. Piot, M. Potemski, I. V. Grigorieva, K. S. Novoselov, F. Guinea, V. I. Fal’ko, and A. K. Geim, “Cloning of Dirac fermions in graphene superlattices,” Nature 497, 594 (2013).
J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000).
A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
M. G. Silveirinha and N. Engheta, “Effective medium approach to electron waves: Graphene superlattices,” Phys. Rev. B 85, 195413 (2012).
M. G. Silveirinha and N. Engheta, “Spatial Delocalization and Perfect Tunneling of Matter Waves: Electron Perfect Lens,” Phys. Rev. Lett 110, 213902 (2013).
D. E. Fernandes, N. Engheta, and M. G. Silveirinha, “Wormhole for electron waves in graphene,” Phys. Rev. B 90, 041406(R) (2014).
M. S. Jang, H. Kim, H. A. Atwater, and W. A. Goddard III, “Time dependent behavior of a localized electron at a heterojunction boundary of graphene,” Appl. Phys. Lett. 97, 043504 (2010).
M. S. Jang, H. Kim, Y.-W. Son, H. A. Atwater, and W. A. Goddard III, “Graphene field effect transistor without an energy gap,” Proc. Natl. Acad. Sci. U.S.A 110, 8786 (2013).
F. Fillion-Gourdeau, E. Lorin, and A. D. Bandrauk, “Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling,” Comput. Phys. Commun. 183, 1403 (2012).
V. Ya. Demikhovskii, G. M. Maksimova, A. A. Perov, and E. V. Frolova, “Space-time evolution of Dirac wave packets,” Phys. Rev. A 82, 052115 (2010).
A. Matulis, M. R. Masir, and F. M. Peeters, “Application of optical beams to electrons in graphene,” Phys. Rev. B 83, 115458 (2011).
Kh. Y. Rakhimov, A. Chaves, G. A. Farias, and F. M. Peeters, “Wavepacket scattering of Dirac and Schrödinger particles on potential and magnetic barriers,” J. Phys.: Condens. Matter 23, 275801 (2011).
S. T. Park, “Propagation of a relativistic electron wave packet in the Dirac equation,” Phys. Rev. A 86, 062105 (2012).
D. A. Stone, C. A. Downing, and M. E. Portnoi, “Searching for confined modes in graphene channels: The variable phase method,” Phys. Rev. A 86, 075464 (2012).
C. A. Downing, A. R. Pearce, R. J. Churchill, and M. E. Portnoi, “Optimal traps in graphene,” Phys. Rev. B 92, 165401 (2015).
X. Li, X. Duan, and K. W. Kim, “Controlling electron propagation on a topological insulator surface via proximity interactions,” Phys. Rev. B 89, 045425 (2014).
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
G.-H. Lee, G.-H. Park, and H.-J. Lee, “Observation of negative refraction of Dirac fermions in graphene,” Nat. Phys. 11, 925 (2015).
R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine Structure Constant Defines Visual Transparency of Graphene,” Science 320, 1308 (2008).
J. C. W. Song, P. Samutpraphoot, and L. S. Levitov, “Topological Bloch bands in graphene superlattices,” Proc. Natl Acad. Sci. USA 112, 10879 (2015).
M. G. Silveirinha and N. Engheta, “Transformation Electronics: Tailoring the Effective Mass of Electrons,” Phys. Rev. B 86, 161104(R) (2012).
See supplementary material at for (i) validation of the FDTD algorithm in simple graphene heterostructures, (ii) the time animations of the electronic states propagating in the graphene superlattices for the examples of Figs. 8(b), 8(c) and 8(d).[Supplementary Material]
S. Lannebère and M. G. Silveirinha, “Effective Hamiltonian for electron waves in artificial graphene: A first-principles derivation,” Phys. Rev. B 91, 045416 (2015).
E. Schrödinger, “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 24, 418 (1930).
B. Thaller, Visualizing the kinematics of relativistic wave packets, arXiv:quant-ph/0409079 (unpublished).
G. M. Maksimova, V. Ya. Demikhovskii, and E. V. Frolova, “Wave packet dynamics in a monolayer graphene,” Phys. Rev. B 78, 235321 (2008).
G. Dávid and J. Cserti, “General theory of Zitterbewegung,” Phys. Rev. B 81, 121417(R) (2010).
A. Chaves, L. Covaci, Kh. Yu. Rakhimov, G. A. Farias, and F. M. Peeters, “Wave-packet dynamics and valley filter in strained graphene,” Phys. Rev. B 82, 205430 (2010).
A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, MA, 2005).

Data & Media loading...


Article metrics loading...



The time evolution of electron waves in graphene superlattices is studied using both microscopic and “effective medium” formalisms. The numerical simulations reveal that in a wide range of physical scenarios it is possible to neglect the granularity of the superlattice and characterize the electron transport using a simple effective Hamiltonian. It is verified that as general rule the continuum approximation is rather accurate when the initial state is less localized than the characteristic spatial period of the superlattice. This property holds even when the microsocopic electric potential has a strong spatial modulation or in presence of interfaces between different superlattices. Detailed examples are given both of the time evolution of initial electronic states and of the propagation of stationary states in the context of wave scattering. The theory also confirms that electrons propagating in tailored graphene superlattices with extreme anisotropy experience virtually no diffraction.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd