1990
DOI: 10.1103/physrevb.42.7454
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Nonrelativistic zitterbewegung in two-band systems

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Cited by 52 publications
(45 citation statements)
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“…The factor k D is a measure for the summation in momentum space and is considered to be analogous to the measure dk of an integral. Since momentum space is spaced equidistantly in our approach, we write down a sum in (14) with measure Δ k and focus on the plane wave solution in this more fundamental theory part. The spacing of Δ k and its relation to position space is discussed in the section on numerical implementation 4.…”
Section: Time Evolution Of Maxwell Equationsmentioning
confidence: 99%
See 1 more Smart Citation
“…The factor k D is a measure for the summation in momentum space and is considered to be analogous to the measure dk of an integral. Since momentum space is spaced equidistantly in our approach, we write down a sum in (14) with measure Δ k and focus on the plane wave solution in this more fundamental theory part. The spacing of Δ k and its relation to position space is discussed in the section on numerical implementation 4.…”
Section: Time Evolution Of Maxwell Equationsmentioning
confidence: 99%
“…Nevertheless, the Zitterbewegung can be modelled in various other effective systems and its appearance has been subject of diverse investigations. It has been discussed for superconductors [12] in 1970, for onedimensional chains [13] in 1990 and many considerations set in on semiconductors [14][15][16][17][18][19][20]. In 2005 renewed discussions on Zitterbewegung in Spintronics [21,22], Graphene [23,24] and carbon nanotubes [25,26] were raised, (see also [27]).…”
Section: Introductionmentioning
confidence: 99%
“…Dirac cones and Dirac points owe their names to the formal analogy existing between the two-dimensional Helmholtz equation describing the electromagnetic behavior of photons near these points and the Dirac equation for the motion of relativistic, free electrons in the absence of external fields. The subject is well-rooted in solid state physics, in which Dirac cones appear in a great variety of scenarios such as non-relativistic motion of particles in a crystal 8 and semiconductor nanostructures for spintronic applications. 9 Particularly important in this framework is the recent discovery of graphene, 10 a purely two-dimensional electronic system in which the conduction band and the valence band touch each other at the Dirac point, leading to remarkable electronic transport properties.…”
Section: Introductionmentioning
confidence: 99%
“…The theoretical existence of the quivering motion has been evidenced by numerical simulations of the Dirac equation and of quantum field theory. While Zitterbewegung oscillations cannot be directly observed by current experimental techniques for a Dirac electron since the amplitude should by very small (equal to the Compton wavelengthh/mc with m the rest mass of the relativistic particle, namely ≈ 10 −12 m for an electron), solid state and atomic physics provide physical hardware to simulate the phenomenon [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], and they have recently boosted a renewed interest in the Dirac equation features.…”
Section: Introductionmentioning
confidence: 99%