  Motivated by recent experiments on Pr2Ir2O7, we provide a theory of quantum
oscillations in the Luttinger model with quadratic band touching, modelled for
the spin-orbit-coupled conduction electrons in pyrochlore iridates. The
magneto- and Hall resistivities are computed for electron- and hole-doped
systems, and the corresponding Shubnikov de Haas (SdH) signals are
investigated. The SdH signals are characterized by aperiodic behaviors that
originate from the unconventional Landau level structures of the Luttinger
model near the neutrality point, such as the inter-Landau level crossing,
nonuniform Landau level spacings and non-parabolic dispersions along the
applied magnetic-field direction. The aperiodic SdH signals observed in the
paramagnetic state of Pr2Ir2O7 are shown to be consistent with such behaviors,
justifying the use of the Luttinger model and the quadratic band touching
spectrum as excellent starting points for physics of pyrochlore iridates. The
implications of these results are discussed in light of recent theoretical and
experimental devel- opments in these systems.
