Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects
arXiv:cond-mat/0609005 · doi:10.1103/PhysRevB.75.205314
Abstract
In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.
11 pages, 1 figure, various minor clarifying changes (final version)
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- Magnetic focusing of charge carriers from spin-split bands: Semiclassics of a Zitterbewegung effect
- Cyclotron motion and magnetic focusing in semiconductor quantum wells with spin-orbit coupling
- Weak momentum scattering and the conductivity of graphene
- Wave packet dynamics in monolayer MoS with and without a magnetic field
- Wave packet dynamics in various two-dimensional systems: a unified description
- Nanospintronics meets relativistic quantum physics: Ubiquity of Zitterbewegung effects