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.
Time evolution of electron waves in graphene superlattices
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. 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).
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).
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, “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).
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).
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).
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).
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
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).
See supplementary material at http://dx.doi.org/10.1063/1.4959190
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)
E. Schrödinger, “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik,” Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 24, 418 (1930).
A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Norwood, MA, 2005).
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...
Most read this month