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

Abstract

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.

References in corpus (13)

• Topological Insulators
• Topological insulators and superconductors
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Correlated quantum phenomena in the strong spin-orbit regime
• Mott physics and band topology in materials with strong spin-orbit interaction
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Topological insulators and metal-insulator transition in the pyrochlore iridates
• Metal-Nonmetal Changeover in Pyrochlore Iridates
• Correlation effects on 3D topological phases: from bulk to boundary
• Competing Exotic Topological Insulator Phases in Transition Metal Oxides on the Pyrochlore Lattice with Distortion
• Anisotropic hysteretic Hall-effect and magnetic control of chiral domains in the chiral spin states of Pr${}_2$Ir${}_2$O${}_7$
• Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

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• Recent progress on correlated electron systems with strong spin-orbit coupling
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• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Incommensurate spin density wave at a ferromagnetic quantum critical point in a three-dimensional parabolic semimetal
• Propagation of longitudinal acoustic phonons in ZrTe${}_5$ exposed to a quantizing magnetic field
• Hybrid Dispersion Dirac semimetal and Hybrid Weyl phases in Luttinger Semimetals: A dynamical approach
• RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems
• Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism
• Electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors
• Quantum-critical electrodynamics of Luttinger fermions