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Zitterbewegung and its effects on electrons in semiconductors

Wlodek Zawadzki
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Abstract

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 $ω_Z \approx {\cal E}_g/\hbar$ and its amplitude is $λ_Z$, where $λ_Z = \hbar/m^*_0 u$ corresponds to the Compton wavelength in vacuum (${\cal E}_g$ is the energy gap, $m^*_0$ is the effective mass and $u \approx 1.3\times10^8$ cm/sec). Once the electrons are described by a two-component spinor for a specific energy band there is no Zitterbewegung but the electrons should be treated as extended objects of size $λ_Z$. Possible consequences of the above predictions are indicated.

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Wlodek Zawadzki. 2004-11-18. Zitterbewegung and its effects on electrons in semiconductors. https://doi.org/10.1103/physrevb.72.085217

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