# Semirelativity in Semiconductors: a Review

## TL;DR

This review explores the analogy between electron behavior in narrow-gap semiconductors and relativistic particles, highlighting how semiconductors can simulate relativistic effects and provide accessible platforms for studying such phenomena.

## Contribution

It systematically reviews the semirelativistic analogy in semiconductors, emphasizing experimental evidence and theoretical models that connect semiconductor physics with relativistic quantum mechanics.

## Key findings

- Electrons in narrow-gap semiconductors exhibit velocities up to 10^8 cm/s, analogous to light speed.
- Vanishing energy gaps in HgCdTe alloys lead to massless Dirac fermions.
- Semirelativistic effects are observable and sometimes easier to study in semiconductors than in vacuum.

## Abstract

Analogy between behavior of electrons in narrow-gap semiconductors (NGS) and relativistic electrons is reviewed. Energy bands in NGS correspond to special relativity, the latter is analogous to two-band k.p description for NGS. Maximum electron velocity in NGS is u=(okolo)1x 10^8 cm/s corresponding to the light velocity. An effective mass of electrons in semiconductors is introduced relating their velocity to quasimomentum. This mass depends on energy similarly to the mass of relativistic electrons. In Hg_(1-x)Cd_(x)Te alloys one can reach vanishing energy gap at which electrons and light holes are 3D massless Dirac fermions. Wavelength lam_z is defined for NGS, in analogy to the Compton wavelength, lam_z is around tens of Angstroms in semiconducting materials, in agreement with tunneling experiments. Interband electron tunneling in NGS is in close analogy to tunneling between negative and positive energies of the Dirac equation. Relativistic analogy holds for orbital and spin properties of electrons in an external magnetic field. The spin magnetic moment of both NGS electrons and relativistic electrons approaches zero with increasing energy. Electrons in crossed electric and magnetic fields are described. It is the semirelativistic two-band description that gives a correct account of experiments in this situation. A transverse Doppler shift is observed in crossed fields indicating that there exists a time dilatation between an electron and an observer. Phenomenon of Zitterbewegung (ZB, trembling motion) for semiconductor electrons follows an analogy to free relativistic electrons. Graphene, carbon nanotubes, topological insulators illustrate extreme semirelativistic regime. Approximations and restrictions of the relativistic analogy are emphasized. It is often easier to observe semirelativistic effects in semiconductors than relativistic effects in vacuum.