Journal
PHYSICS LETTERS A
Volume 374, Issue 34, Pages 3533-3537Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2010.06.028
Keywords
Zitterbewegung; Periodic potential; Instantaneous velocity; Kronig-Penney model; Two-band model
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We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. We show that the two-band k.p model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description of ZB in solids. Our results unambiguously indicate that the trembling motion is the basic way of electron propagation in periodic potentials and, as such, it is certainly observable. A recent experimental simulation of ZB with the use of trapped ions is in good agreement with our calculations. (C) 2010 Elsevier B.V. All rights reserved.
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