1990
DOI: 10.1016/0038-1098(90)90192-e
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Dirac-like behaviour of a non-relativistic tight binding Hamiltonian in one dimension

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Cited by 50 publications
(36 citation statements)
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“…Introducing the vector potential into the Hamiltonian (4) in the way described in Sec. 2 we obtain the following Schrodinger equation, see (4), (5) and (14) ih d dt…”
Section: Appendix B Zb In Monolayer Graphenementioning
confidence: 99%
See 1 more Smart Citation
“…Introducing the vector potential into the Hamiltonian (4) in the way described in Sec. 2 we obtain the following Schrodinger equation, see (4), (5) and (14) ih d dt…”
Section: Appendix B Zb In Monolayer Graphenementioning
confidence: 99%
“…Beginning from 1970 the Zitterbewegung was proposed also for electrons in solids where the velocities are not relativistic [4,5,6,7]. The decisive feature is that the electron energy spectrum consists of at least two bands, so that the interference of upper and lower energy states can take place.…”
Section: Introductionmentioning
confidence: 99%
“…Due to a formal similarity between two interacting bands in a solid and the Dirac equation for relativistic electrons in a vacuum, theoretical investigations have shown that the ZB can also appear even for a nonrelativistic particle moving in a crystal [3,4], or for quasiparticles governed by the Bogoliubov-de Gennes equations in superconductors [5], or for spintronics in some semiconductor nanostructures with spin-orbit coupling [6][7][8][9]. Recently, graphene has become the subject of intensive research due to the successful fabrication experimented by Novoselov et al [10].…”
mentioning
confidence: 99%
“…Zitterbewegung oscillations cannot be directly observed by current experimental techniques for an electron since the amplitude is very small ≈ 10 −12 m. However, it can be seen in a number of solid-state, atomic-physics, photonic-cristal and optical waveguide simulators [43][44][45][46][47]. figure: here the state is a superposition of Hermite functions (the polynomials Hj(x) multiplied by the Gaussian) peaked around k0 = 3π/10.…”
Section: A Zitterbewegungmentioning
confidence: 99%