Semirelativity in semiconductors: a review

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Relativistic Physics

Background:

• A known analogy exists between electrons in narrow-gap semiconductors (NGS) and relativistic electrons in vacuum.
• Special relativity for vacuum is analogous to a two-band description for NGS.

Purpose of the Study:

• To review the analogy between electrons in NGS and relativistic electrons in vacuum.
• To emphasize the correspondence between NGS energy band structures and the energy-momentum relation in special relativity.
• To explore relativistic quantum phenomena in semiconductor systems.

Main Methods:

• Analysis of energy band structures in various NGS materials.
• Introduction of effective mass for charge carriers in semiconductors.
• Calculation of statistical properties of electron gas in NGS.
• Theoretical and experimental description of interband electron tunneling.
• Investigation of relativistic analogy for orbital and spin properties in magnetic fields.
• Theoretical and experimental study of electrons in crossed electric and magnetic fields.
• Consideration of Zitterbewegung (ZB) for electrons in NGS.
• Analysis of graphene, carbon nanotubes, and topological insulators within the relativistic analogy framework.

Main Results:

• Maximum electron velocity in NGS corresponds to the speed of light.
• Effective mass in NGS depends on electron energy, similar to free relativistic electrons.
• Vanishing energy gap in alloys leads to massless Dirac fermions.
• A characteristic wavelength in NGS is comparable to the Compton wavelength.
• Statistical properties of electron gas in NGS resemble Jüttner gas.
• Interband electron tunneling in NGS is analogous to Dirac equation predictions.
• Spin magnetic moment approaches zero with increasing energy for both NGS and relativistic electrons.
• Two-band description for NGS accurately accounts for experimental results in crossed fields.
• Transverse Doppler shift indicates time dilation in NGS.
• ZB in NGS has lower frequency and higher amplitude than in vacuum, facilitating observation.
• Semiconductor systems offer easier observation of semirelativistic effects compared to vacuum.

Conclusions:

• The relativistic analogy provides a powerful framework for understanding electron behavior in NGS.
• NGS systems serve as accessible experimental platforms for exploring relativistic quantum mechanics.
• The analogy holds for various phenomena including tunneling, spin properties, and Zitterbewegung.
• Graphene, carbon nanotubes, and topological insulators represent extreme semirelativistic regimes.
• While approximations exist, the relativistic analogy significantly enhances our understanding of condensed matter physics.