  We have recently pointed out that color magnetic field is generated in dense
quark matter, i.e. color ferromagnetic phase of quark matter. Using light cone
quantization, we show that gluons occupying the lowest Landau level under the
color magnetic field effectively form a two dimensional quantum well (layer),
in which infinitely many zero modes of the gluons are present. We discuss that
the zero modes of the gluons form a quantum Hall state by interacting
repulsively with each other, just as electrons do in semiconductors. Such a
ferromagnetic quark matter with the layer structure of the gluons is a possible
origin of extremely strong magnetic field observed in magnetars.
