A New Type of Quantum Criticality in the Pyrochlore Iridates

Abstract

Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero temperature phase transitions - quantum critical points - in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials, and in the formation of unconventional superconductors. Here we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formulate and solve a field theory for this quantum critical point by renormalization group techniques, show that electrons and antiferromagnetic fluctuations are strongly coupled, and that both these excitations are modified in an essential way. This quantum critical point has many novel features, including strong emergent spatial anisotropy, a vital role for Coulomb interactions, and highly unconventional critical exponents. Our theory motivates and informs experiments on pyrochlore iridates, and constitutes a singular realistic example of a non-trivial quantum critical point with gapless fermions in three dimensions.

5 pages + 8 pages of Supplementary Material, 3 figures + 1 supplementary figure

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Cited by in corpus (25)

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• Quasi-Local Strange Metal
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Multiferroicity in spin ice: towards a magnetic crystallography of Tb2Ti2O7 in a field
• Anomalous lattice contraction and emergent electronic phases in Bi-doped Eu${}_2$Ir${}_2$O${}_7$
• Magnetic and transport properties in pyrochlore iridates (Y${}_{1-x}$Pr${}_x$)${}_2$Ir${}_2$O${}_7$: The role of $f$-$d$ exchange interaction and $d$-$p$ orbital hybridization
• Identification of Griffiths-like phase and its evolution in Cr substituted pyrochlore iridates $Y_{2}I{r}_2{O}_7$
• Mapping the structural, magnetic and electronic behavior of (Eu${}_{1-x}$Ca${}_x$)${}_2$Ir${}_2$O${}_7$ across a metal-insulator transition
• Quantum field theories of relativistic Luttinger fermions
• Infrared fixed points of higher-spin fermions in topological semimetals
• Metal-insulator transitions in pyrochlore oxides
• Emergence of Spinon Fermi Arcs in the Weyl-Mott Metal-Insulator Transition
• Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates
• Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism
• Optical conductivity of the metallic pyrochlore iridate Pr${}_2$Ir${}_2$O${}_7$: Influence of spin-orbit coupling and electronic correlations on the electronic structure
• Quantum-critical electrodynamics of Luttinger fermions
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction