Zitterbewegung and its effects on electrons in semiconductors

TL;DR

This paper explores the analogy between semiconductor band structures and relativistic electrons, demonstrating that electrons in narrow gap semiconductors exhibit Zitterbewegung, affecting their effective size and behavior.

Contribution

It introduces a novel analogy linking semiconductor electrons to relativistic particles, predicting Zitterbewegung effects in semiconductors based on band structure similarities.

Findings

Electrons in narrow gap semiconductors experience Zitterbewegung with specific frequency and amplitude.

Electrons should be considered as extended objects of size λ_Z due to Zitterbewegung.

Implications for electron behavior and properties in semiconductors are discussed.

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 $\omega_Z \approx {\cal E}_g/\hbar$ and its amplitude is $\lambda_Z$, where $\lambda_Z = \hbar/m^*_0 u$ 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 $\lambda_Z$. Possible consequences of the above predictions are indicated.