Wlodek Zawadzki

Zitterbewegung (trembling motion) of electrons in semiconductors: a review.

We review recent research on Zitterbewegung (ZB, trembling motion) of electrons in semiconductors. A brief history of the subject is presented, the trembling motion in semi-relativistic and spin systems is considered and its main features are emphasized. ZB of charge carriers in monolayer and bilayer graphene as well as in carbon nanotubes is elaborated in some detail. We describe the effects of an external magnetic field on ZB using monolayer graphene as an example. The nature of electron ZB in crystalline solids is explained. We also review various simulations of the trembling motion in a vacuum and in semiconductors, and mention ZB-like wave phenomena in sonic and photonic periodic structures. An attempt is made to quote all the relevant literature on the subject.

Transient Zitterbewegung of charge carriers in mono-and bilayer graphene, and carbon nanotubes

Observable effects due to trembling motion [Zitterbewegung (ZB)] of charge carriers in bilayer graphene, monolayer graphene, and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of Gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes. Analytical results for bilayer graphene allow us to investigate phenomena which accompany the trembling motion. In particular, it is shown that the transient character of ZB in graphene is due to the fact that wave subpackets related to positive and negative electron energies move in opposite directions, so their overlap diminishes with time. This behavior is analogous to that of the wave packets representing relativistic electrons in a vacuum.

Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulses

We propose an experiment allowing an observation of Zitterbewegung (ZB, trembling motion) of electrons in graphene in the presence of a magnetic field. In contrast to the existing theoretical work we make no assumptions concerning shape of the electron wave packet. A femtosecond Gaussian laser pulse excites electrons from the valence n=-1 Landau level into three other levels, creating an oscillating electron wave packet with interband and intraband frequencies. Oscillations of an average position of the packet are directly related to the induced dipole moment and oscillations of the average packets acceleration determine emitted electric field. Both quantities can be measured experimentally. A broadening of Landau levels is included to make the description of ZB as realistic as possible. Criteria of realization of a ZB experiment are discussed.

Zitterbewegung and its effects on electrons in semiconductors

An analogy between the band structure of narrow gap semiconductors and the Dirac equation for relativistic electrons in vacuum is used to demonstrate that semiconductor electrons experience a Zitterbewegung (trembling motion). Its frequency is

Zitterbewegung of electrons in graphene in a magnetic field

{\ensuremath{\omega}}_{Z}\ensuremath{\approx}{\mathcal{E}}_{g}∕\ensuremath{\hbar}

One-dimensional semirelativity for electrons in carbon nanotubes

and its amplitude is

Non-parabolicity and anisotropy in the conduction band of GaAs

{\ensuremath{\lambda}}_{Z}

Two-mode resonant polaron in the Hg0.72Cd0.28Te semiconductor

, where

Theory of free-electron optical absorption in n-GaAs

{\ensuremath{\lambda}}_{Z}=\ensuremath{\hbar}∕{m}_{0}^{*}u

Nature of electron Zitterbewegung in crystalline solids

corresponds to the Compton wavelength in vacuum (