  Zitterbewegung is a striking consequence of relativistic quantum mechanics
which predicts that free Dirac electrons exhibit a rapid trembling motion even
in the absence of external forces. The trembling motion of an electron results
from the interference between the positive and the negative-energy solutions of
the Dirac equation, separated by one MeV, leading to oscillations at extremely
high frequencies which are out of reach experimentally. Recently, it was shown
theoretically that electrons in III-V semiconductors are governed by similar
equations in the presence of spin-orbit coupling. The small energy splittings
up to meV result in Zitterbewegung at much smaller frequencies which should be
experimentally accessible as an AC current. Here, we demonstrate the
Zitterbewegung of electrons in a solid. We show that coherent electron
Zitterbewegung can be triggered by initializing an ensemble of electrons in the
same spin states in strained n-InGaAs and is probed as an AC current at GHz
frequencies. Its amplitude is shown to increase linearly with both the
spin-orbit coupling strength and the Larmor frequency of the external magnetic
field. The latter dependence is the hallmark of the dynamical generation
mechanism of the oscillatory motion of the Zitterbewegung. Our results
demonstrate that relativistic quantum mechanics can be studied in a rather
simple solid state system at moderate temperatures. Furthermore, the large
amplitude of the AC current at high precession frequencies enables ultra-fast
spin sensitive electric read-out in solids.
