Quantum oscillations in the Luttinger model with quadratic band touching: Applications to pyrochlore iridates

Abstract

Motivated by recent experiments on ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, we provide a theory of quantum oscillations in the Luttinger model with quadratic band touching, modeled 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 inter-Landau-level crossing, nonuniform Landau level spacings, and nonparabolic dispersions along the applied magnetic-field direction. The aperiodic SdH signals observed in the paramagnetic state of ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ 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 developments in these systems.