  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.
