Wave Packet Propagation Through Randomly Distributed Scattering Centers in Graphene

Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)


We numerically investigate the wave packet propagation in graphene in the presence of randomly distributed circular potential steps. The calculations are performed within the continuum model, and the time propagation is made by a simple computational technique, based on the split-operator method. Our results show that, despite the Klein tunnelling effect, the presence of these potential steps significantly reduces the transmission probabilities, specially for higher concentration of scatterers and higher potential heights.


Wave Packet Propagation Exchange Scattering Klein Tunneling Potential Height Transmission Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work of Kh. Rakhimov was supported by Matsumae International Foundation (Ref. Nr. Gno: 12G09) and partially supported by VolkswagenStiftung (Ref. Nr. Az.: 86 140). A. Chaves and G.A. Farias gratefully acknowledge financial support from the Brazilian Council for Research (CNPq).


  1. 1.
    Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of graphene. Rev Mod Phys 81:109ADSCrossRefGoogle Scholar
  2. 2.
    Matulis A, Peeters FM (2008) Quasibound states of quantum dots in single and bilayer graphene. Phys Rev B 77:115423ADSCrossRefGoogle Scholar
  3. 3.
    Martin J, Akerman N, Ulbricht G, Lohmann T, Smet JH, von Klitzing K, Yacoby A (2008) Observation of electron-hole puddles in graphene using a scanning single-electron transistor. Nat Phys 4:144CrossRefGoogle Scholar
  4. 4.
    Schubert G, Fehske H (2012) Metal-to-insulator transition and electron-hole puddle formation in disordered graphene nanoribbons. Phys Rev Lett 108:066402ADSCrossRefGoogle Scholar
  5. 5.
    Palpacelli S, Mendoza M, Herrmann HJ, Succi S (2012) Klein tunneling in the presence of random impurities. Int J Mod Phys C 23:1250080ADSCrossRefGoogle Scholar
  6. 6.
    Chaves A, Covaci L, Rakhimov KY, Farias GA, Peeters FM (2010) Wave-packet dynamics and valley filter in strained graphene. Phys Rev B 82:205430ADSCrossRefGoogle Scholar
  7. 7.
    Rusin TM, Zawadzki W (2010) Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions. Phys Rev D 82:125031ADSCrossRefGoogle Scholar
  8. 8.
    Degani MH, Leburton JP (1991) Single-electron states and conductance in lateral-surface superlattices. Phys Rev B 44:10901ADSCrossRefGoogle Scholar
  9. 9.
    Suzuki M (1990) Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Phys Lett A 146:319MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Rakhimov KY, Chaves A, Farias GA, Peeters FM (2011) Wavepacket scattering of Dirac and Schrodinger particles on potential and magnetic barriers. J Phys Condens Matter 23:275801ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of PhysicsNational University of UzbekistanTashkentUzbekistan
  2. 2.Departamento de FísicaUniversidade Federal do CearáFortaleza-CEBrazil

Personalised recommendations