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.

arXiv comment5 pages + 8 pages of Supplementary Material, 3 figures + 1 supplementary figure

References in corpus (24)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Cuba - a library for multidimensional numerical integration
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum Excitations in Quantum Spin Ice
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Pseudogap state from quantum criticality
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Emergence of magnetic long-range order in frustrated pyrochlore Nd${}_2$Ir${}_2$O${}_7$ with metal-insulator transition
• Giant Magnon Gap in Bilayer Iridate Sr3Ir2O7: Enhanced Pseudo-dipolar Interactions Near the Mott Transition
• Dimensionality Driven Spin-Flop Transition in Layered Iridates
• Magnetic orders and topological phases from f-d exchange in pyrochlore iridates
• Renormalization group theory of nematic ordering in d-wave superconductors
• Magnetic Order in the Pyrochlore Iridates A2Ir2O7 (A = Y, Yb)
• Pyrochlore electrons under pressure, heat and field: shedding light on the iridates
• Renormalization group analysis of quantum critical points in d-wave superconductors
• RKKY interactions and anomalous Hall effect in metallic rare-earth pyrochlores
• Chiral RKKY interaction in Pr2Ir2O7
• Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario

Cited by in corpus (78)

• Metallic Quantum Ferromagnets
• Recent progress on correlated electron systems with strong spin-orbit coupling
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• All-in all-out magnetic order and propagating spin-waves in Sm2Ir2O7
• Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Phase diagram of pyrochlore iridates: all-in-all-out magnetic ordering and non-Fermi liquid properties
• Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
• Superconducting quantum criticality in three-dimensional Luttinger semimetals
• An anisotropic local modification of crystal field levels in Pr-based pyrochlores: a muon-induced effect modelled using density functional theory
• Quasi-Local Strange Metal
• Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Supermetal
• Competing orders and topology in the global phase diagram of pyrochlore iridates
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Exponent relations at quantum phase transitions, with applications to metallic quantum ferromagnets
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Pressure and magnetic-field effects on metal-insulator transitions of bulk and domain-wall states in pyrochlore iridates
• A magnetic Weyl semimetallic phase in thin films of Eu${}_2$Ir${}_2$O${}_7$
• d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals
• Sound waves and resonances in electron-hole plasma
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
• Multiferroicity in spin ice: towards a magnetic crystallography of Tb2Ti2O7 in a field
• Multi-$Q$ hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
• Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
• Anomalous lattice contraction and emergent electronic phases in Bi-doped Eu${}_2$Ir${}_2$O${}_7$
• Correlated triple-Weyl semimetals with Coulomb interactions
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• Pr${}_2$Ir${}_2$O${}_7$: when Luttinger semimetal meets Melko-Hertog-Gingras spin ice state
• Topological d+s wave superconductors in a multi-orbital quadratic band touching system
• 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
• Instability of $j=3/2$ Bogoliubov Fermi-surfaces
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram
• Modulated Helical Metals at Magnetic Domain Walls of Pyrochlore Iridium Oxides
• Magnetic field induced topological semimetals near a quantum critical point of pyrochlore iridates
• Approaching the quantum critical point in a highly-correlated all-in-all-out antiferromagnet
• The Magnetic Grüneisen Parameter for Model Systems
• Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching
• Topological Phase Transitions in Line-nodal Superconductors
• Quantum criticality preempted by nematicity
• Optical response of Luttinger semimetals in the normal and superconducting states
• Incommensurate spin density wave at a ferromagnetic quantum critical point in a three-dimensional parabolic semimetal
• Evolution of structure and magnetism across the metal-insulator transition in the pyrochlore iridate $($Nd${}_{1-x}$Ca${}_x{)}_2$Ir${}_2$O${}_7$
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• Bogoliubov Fermi surfaces from pairing of emergent $j=3/2$ fermions on the pyrochlore lattice
• Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
• Competing magnetic orders and multipolar Weyl fermions in 227 pyrochlore iridates
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Monopole-limited nucleation of magnetism in Eu${}_2$Ir${}_2$O${}_7$
• Identification of Griffiths-like phase and its evolution in Cr substituted pyrochlore iridates $Y_{2}I{r}_2{O}_7$
• Multi-scale Quantum Criticality driven by Kondo-lattice Coupling in Pyrochlore Systems
• Incommensurate magnetic states induced by ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{N}{\mathrm{a}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• The Future of the Correlated Electron Problem
• Quantum field theories of relativistic Luttinger fermions
• Mapping the structural, magnetic and electronic behavior of (Eu${}_{1-x}$Ca${}_x$)${}_2$Ir${}_2$O${}_7$ across a metal-insulator transition
• Metal-insulator transitions in pyrochlore oxides
• Infrared fixed points of higher-spin fermions in topological semimetals
• Correlated interaction effects in three-dimensional semi-Dirac semimetal
• 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
• Emergence of Spinon Fermi Arcs in the Weyl-Mott Metal-Insulator Transition
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Quantum-critical electrodynamics of Luttinger fermions
• 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
• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
• Anomalous Hall effect and quantum criticality in geometrically frustrated heavy fermion metals
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals