Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

There has been much interest in pyrochlore iridates A₂Ir₂O₇ where both strong spin-orbital coupling and strong correlation are present. A recent local density approximation calculation [X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.205101 83, 205101 (2011)] suggests that the system is likely in a three-dimensional topological semimetallic phase: a Weyl semimetal. 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 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 wave vector connecting Weyl nodes with opposite chiralities. A general formula of the anomalous Hall coefficients in a Weyl semimetal is also given. Both proposed effects can be probed by experiments in the near future and can be used to detect the Weyl semimetal phase.