  There have been lots of interest in pyrochlore Iridates A2Ir2O7 where both
strong spin-orbital coupling and strong correlation are present. A recent LDA
calculation suggests that the system is likely in a novel three dimensional
topological semi-metallic phase: a Weyl semi-metal. Such a system has zero
carrier density and arrives at the quantum limit even in a weak magnetic field.
In this paper we discuss two novel quantum effects of this system in a magnetic
field: a pressure-induced anomalous Hall effect and a magnetic field induced
charge density wave at the pinned wavevector connecting Weyl nodes with
opposite chiralities. A general formula of the anomalous hall coefficients in a
Weyl semi-metal is also given. Both proposed effects can be probed by
experiments in the near future, and can be used to detect the Weyl semi-metal
phase.

Strongly Correlated Electrons