  Decoherence of electron spins in nanoscale systems is important to quantum
technologies such as quantum information processing and magnetometry. It is
also an ideal model problem for studying the crossover between quantum and
classical phenomena. At low temperatures or in light-element materials where
the spin-orbit coupling is weak, the phonon scattering in nanostructures is
less important and the fluctuations of nuclear spins become the dominant
decoherence mechanism for electron spins. Since 1950s, semiclassical noise
theories have been developed for understanding electron spin decoherence. In
spin-based solid-state quantum technologies, the relevant systems are in the
nanometer scale and the nuclear spin baths are quantum objects which require a
quantum description. Recently, quantum pictures have been established to
understand the decoherence and quantum many-body theories have been developed
to quantitatively describe this phenomenon. Anomalous quantum effects have been
predicted and some have been experimentally confirmed. A systematically
truncated cluster correlation expansion theory has been developed to account
for the many-body correlations in nanoscale nuclear spin baths that are built
up during the electron spin decoherence. The theory has successfully predicted
and explained a number of experimental results in a wide range of physical
systems. In this review, we will cover these recent progresses. The limitations
of the present quantum many-body theories and possible directions for future
development will also be discussed.
