  Atomically thin two-dimensional layer of honeycomb crystalline carbon known
as graphene is a promising system for electronics. It has a point-like Fermi
surface, which is very sensitive to external potentials. In particular, Zeeman
magnetic field parallel to the graphene layer splits electron bands and creates
fully spin-polarized and geometrically congruent circular Fermi surfaces of
particle and hole type. In the presence of electric field, particles and holes
with opposite spins drift in opposite direction. These phenomena are likely to
be of interest for developing graphene-based spintronic devices. A domain wall
(DW) separating regions with opposite spin polarizations is a basic element of
such a device. Here we consider a ballistic passage of spin-polarized charge
carriers through DW in graphene. We also discuss the analogy between the
generation of spin currents in graphene and in relativistic quark-gluon plasma,
where the spin-polarized current is responsible for the phenomenon of charge
separation studied recently at RHIC.
