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 ${\omega }_Z\approx {\mathcal{E}}_g∕\hslash$ and its amplitude is ${\lambda }_Z$, where ${\lambda }_Z=\hslash ∕m_0^{*}u$ corresponds to the Compton wavelength in vacuum (${\mathcal{E}}_g$ is the energy gap, $m_0^{*}$ is the effective mass, and $u\approx 1.3\times {10}^8\mathrm{cm}∕\mathrm{s}$). 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 ${\lambda }_Z$. The magnitude of ${\lambda }_Z$ in narrow gap semiconductors can be as large as $70\mathrm{\AA }$. Possible consequences of the above predictions are indicated.

• Received 16 November 2004

DOI:https://doi.org/10.1103/PhysRevB.72.085217