The split-operator technique for the study of spinorial wavepacket dynamics

Communications in Computational Physics

Volumn 17, Issue 3, 2015, Pages 850-866

  Chaves, A ^a   Farias, G A ^a   Peeters, F M ^a,b   Ferreira, R ^a,c  

^a FEDERAL UNIVERSITY OF CEARÁ   (Brazil)

^b UNIVERSITY OF ANTWERP   (Belgium)

^c LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

graphene; semiconductor heterostructures; spin orbit coupling; Wave packet propagation

Indexed keywords

EID: 84961290475     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.110914.281014a     Document Type: Article

References (39)

1. M. H. Degani and M. Z. Maialle, Numerical Calculations of the Quantum States in Semiconductor Nanostructures, J. Comp. Theor. Nanosci. 7 (2010) 454.
2. S. Yuan, H. De Raedt, and M. I. Katsnelson, Modeling electronic structure and transport properties of graphene with resonant scattering centers, Phys. Rev. B 82 (2010) 115448.
3. A. Weisse, G. Wellein, A. Alvermann, and H. Fehske, The Kernel Polynomial Method, Rev. Mod. Phys. 78 (2006) 275.
4. B. Szafran and F.M. Peeters, Lorentz-force induced asymmetry in the Aharonov-Bohmeffect in a three-terminal semiconductor quantum ring, Europhys. Lett. 70 (2005) 810.
5. T Chwiej and B Szafran, Fractional conductance oscillations in quantum rings: wave packet picture of transport in a few-electron system, J. Phys.: Condens. Matter 25 (2013) 155802.
6. A. Chaves, G. A. Farias, F. M. Peeters, and B. Szafran, Wave packet dynamics in semiconductor quantum rings of finite width, Phys. Rev. B 80 (2009) 125331.
7. R. Romo, J. Villavicencio, and M. L. Ladrón de Guevara, Trapping effects in wave-packet scattering in a double-quantum-dot Aharonov-Bohm interferometer, Phys. Rev. B 86 (2012) 085447.
8. M. D. Petrović, F. M. Peeters, A. Chaves, and G. A. Farias, Conductance maps of quantum rings due to a local potential perturbation, J. Phys.: Condens. Matter 25 (2013) 495301.
9. R. Kalina, B. Szafran, S. Bednarek, and F. M. Peeters,Magnetic-Field Asymmetry of Electron Wave Packet Transmission in Bent Channels Capacitively Coupled to a Metal Gate, Phys. Rev. Lett. 102 (2009) 066807.
10. C. Kreisbeck, T. Kramer, S. S. Buchholz, S. F. Fischer, U. Kunze, D. Reuter, and A. D. Wieck, Phase shifts and phase π jumps in four-terminal waveguide Aharonov-Bohm interferometers, Phys. Rev. B 82 (2010) 165329.
11. F. Fillion-Gourdeau, E. Lorin, and A. D. Bandrauk, A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry, J. Comp. Phys. 272 (2014) 559.
12. V. Ya. Demikhovskii, G.M. Maksimova, A. A. Perov, and E. V. Frolova, Space-time evolution of Dirac wave packets, Phys. Rev. A 82 (2010) 052115.
13. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, Electric Field Effect in Atomically Thin Carbon Films, Science 306 (2004) 666-669.
14. E. Schrödinger, Sitzungsber. Preuss. Akad.Wiss. Phys. Math. Kl. 24 (1930) 418.
15. T. M. Rusin and W. Zawadzki, Zitterbewegung of electrons in graphene in a magnetic field, Phys. Rev. B 78 (2008) 125419.
16. W. Zawadzki and T. M. Rusin, Zitterbewegung (trembling motion) of electrons in semiconductors: a review, J. Phys.: Condens. Matter 23 (2011) 143201.
17. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Chiral tunneling and the Klein paradox in graphene, Nat. Phys. 2 (2006) 620.
18. U. Peskin, R. Kosloff, and N. Moiseyev, The solution of the time dependent Schrdinger equation by the (t,t') method: The use of global polynomial propagators for time dependent Hamiltonians, J. Chem. Phys. 100 (1994) 8849.
19. A. Alvermann and H. Fehske, High-order commutator-free exponential time-propagation of driven quantum systems, J. Comp. Phys. 230 (2011) 5930.
20. H. Tal-Ezer and R. Kosloff, An accurate and efficient scheme for propagating the time dependent Schrödinger equation, J. Chem. Phys. 81 (1984) 3967.
21. H. Fehske, J. Schleede, G. Schubert, G. Wellein, V. S. Filinov, and A. R. Bishop, Numerical approaches to time evolution of complex quantum systems, Phys. Lett. A 373 (2009) 2182.
22. R. I. McLachlan and G. R. W. Quispel, Splitting methods, Acta Numerica 11 (2002) 341.
23. G. Dattoli, P. L. Ottaviani, A. Segreto, and A. Torre, Symmetric-split-operator techniques and finite-differencemethods for the solution of classical and quantum evolution problems, Il Nuovo Cimento B 111 (1996) 825.
24. J. Schliemann, Cyclotron motion and magnetic focusing in semiconductor quantum wells with spin-orbit coupling, Phys. Rev. B 77 (2008) 125303.
25. T. Biswas and T. K. Ghosh, Wave packet dynamics and zitterbewegung of heavy holes in a quantizing magnetic field, J. Appl. Phys. 115 (2014) 213701.
26. V. Ya. Demikhovskii, G. M. Maksimova, and E. V. Frolova, Wave packet dynamics in a twodimensional electron gas with spin orbit coupling: Splitting and zitterbewegung, Phys. Rev. B 78 (2008) 115401.
27. N. Watanabe and M. Tsukada, Fast and stable method for simulating quantum electron dynamics, Phys. Rev. E 62 (2000) 2914.
28. M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations, Phys. Lett. A 146 (1990) 319.
29. William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, 1992, pp. 22-99.
30. A.H. CastroNeto, F. Guinea, N.M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109.
31. S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. CastroNeto, and A. Lanzara, Substrate-induced band gap opening in epitaxial graphene, Nat. Mat. 6 (2007) 770.
32. S. M. Badalyan, A. Matos-Abiague, G. Vignale, and J. Fabian, Beating of Friedel oscillations induced by spin-orbit interaction, Phys. Rev. B 81 (2010) 205314.
33. S. Badalyan and J. Fabian, Spin Edge Helices in a Perpendicular Magnetic Field, Phys. Rev. Lett. 105 (2010) 186601.
34. Kh. Yu. 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 (2011) 275801.
35. G.M. Maksimova, V. Ya. Demikhovskii and E. V. Frolova,Wave packet dynamics in a monolayer graphene, Phys. Rev. B 78 (2008) 235321.
36. P. E. Allain and J.N. Fuchs, Klein tunneling in graphene: optics with massless electrons, Eur. Phys. J. B 83 (2011) 301.
37. C. W. J. Beenakker, Colloquium: and reev reflection and Klein tunneling in graphene, Rev. Mod. Phys. 80 (2008) 1337.
38. J. M. Pereira, A. Chaves, G. A. Farias, and F. M. Peeters, Klein tunneling in single and multiple barriers in graphene, Semic. Sci. Tech. 25 (2010) 033002.
39. A. Matulis and F. M. Peeters, Quasibound states of quantum dots in single and bilayer graphene, Phys. Rev. B 77 (2008) 115423.