Colloquium: Hidden Order, Superconductivity, and Magnetism -- The Unsolved Case of URu2Si2

Abstract

This Colloquium reviews the 25 year quest for understanding the continuous (second-order) mean-field-like phase transition occurring at 17.5 K in URu2Si2. About ten years ago, the term hidden order (HO) was coined and has since been utilized to describe the unknown ordered state, whose origin cannot be disclosed by conventional solid-state probes, such as x rays, neutrons, or muons. HO is able to support superconductivity at lower temperatures (Tc ~ 1.5 K), and when magnetism is developed with increasing pressure both the HO and the superconductivity are destroyed. Other ways of probing the HO are via Rh-doping and very large magnetic fields. During the last few years a variety of advanced techniques have been tested to probe the HO state and their attempts will be summarized. A digest of recent theoretical developments is also included. It is the objective of this Colloquium to shed additional light on the HO state and its associated phases in other materials.

25 pages, 16 figures, published in Reviews of Modern Physics

References in corpus (32)

• Quantum criticality
• Nature of the 5f states in actinide metals
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions
• Imaging the Fano Lattice to 'Hidden Order' Transition in URu2Si2
• Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2
• Hidden order in 1D Bose insulators
• The Ground State of the Pseudogap in Cuprate Superconductors
• Exotic Superconducting Properties in the Electron-Hole Compensated Heavy Fermion `Semimetal' URu2Si2
• Gapped itinerant spin excitations account for missing entropy in the hidden order state of URu${}_2$Si${}_2$
• Fermi surface instability at the hidden-order transition of URu2Si2
• Electron Cotunneling into a Kondo Lattice
• Interplay between SDW and induced local moments in URu2Si2
• The modulated spin liquid: a new paradigm for URu${}_2$Si${}_2$
• Antiferromagnetic critical pressure in URu2Si2 under hydrostatic conditions
• Evolution of critical scaling behavior near a ferromagnetic quantum phase transition
• Competition between hidden order and antiferromagnetism in URu_2Si_2 under uniaxial stress studied by neutron scattering
• Mesoscopic Phase Coherence in a Quantum Spin Fluid
• Competing Ordered Phases in URu2Si2: Hydrostatic Pressure and Re-substitution
• Determination of the Antiferroquadrupolar Order Parameters in UPd3
• Possible Phase Transition Deep Inside the Hidden Order Phase of Ultraclean URu2Si2
• Details of Sample Dependence and Transport Properties of URu2Si2
• The degree of 5f electron localization in URu2Si2: electron energy-loss spectroscopy and spin-orbit sum rule analysis
• First-Principles Theory of Multipolar Order in Neptunium Dioxide
• The Fano effect in the point contact spectroscopy of heavy electron materials
• Electrical Resistivity and Thermal Expansion Measurements of URu2Si2 under Pressure
• Flux Line Lattice Melting and the Formation of a Coherent Quasiparticle Bloch State in the Ultraclean URu${}_2$Si${}_2$ Superconductor
• Pressure dependence of the magnetization of URu2Si2
• On the destruction of the hidden order in URu${}_2$Si${}_2$ by a strong magnetic field
• Itinerancy and Hidden Order in $UR{u}_{2}S{i}_2$
• Magnetization, Maxwell's Relations and the Local Physics of the Dilute System Th_{1-x}U_{x}Ru_{2}Si_{2}
• Pressure dependence of magnetism in URu2Si2

Cited by in corpus (216)

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• Unconventional Superconductivity
• HORACE: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments
• Odd-frequency superconductivity
• Nernst effect in metals and superconductors: a review of concepts and experiments
• Topological surface states in nodal superconductors
• Emergent Rank-5 'Nematic' Order in URu2Si2
• A review of two-band superconductivity: materials and effects on the thermodynamic and reversible mixed-state properties
• Hastatic Order in URu2Si2
• Evidence for broken time-reversal symmetry in the superconducting phase of URu${}_2$Si${}_2$
• Chirality density wave of the 'hidden order' phase in URu${}_2$Si${}_2$
• Excitonic condensation in systems of strongly correlated electrons
• Single-component superconducting state in UTe2 at 2 K
• Hidden Order Behaviour in URu2Si2 (A Critical Review of the Status of Hidden Order in 2014)
• First-principles theory of magnetic multipoles in condensed matter systems
• Detection of multipolar orders in the spin-orbit-entangled 5d Mott insulator Ba2MgReO6
• Observation of the hybridization gap and Fano resonance in the Kondo lattice URu2Si2
• Probing hidden spin order with interpretable machine learning
• Intertwined dipolar and multipolar order in the triangular-lattice magnet TmMgGaO${}_4$
• Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu${}_2$Si${}_2$
• Multipolar phases and magnetically hidden order: Review of the heavy-fermion compound Ce(1-x)La(x)B6
• Photoemission Imaging of 3D Fermi Surface Pairing at the Hidden Order Transition in URu2Si2
• Unconventional Magnetic Ground State in Yb${}_2$Ti${}_2$O${}_7$
• Emergent states in heavy electron materials
• Heavy fermions in high magnetic field
• Evidence for a nematic component to the Hidden Order parameter in URu2Si2 from differential elastoresistance measurements
• Colossal thermomagnetic response in the exotic superconductor URu2Si2
• Resonant magnetic exciton mode in the heavy-fermion antiferromagnet CeB6
• Excitonic condensation of strongly correlated electrons: the case of Pr${}_{0.5}$Ca${}_{0.5}$CoO${}_3$
• Microscopic theory of the insulating electronic ground states of actinide dioxides AnO2 (An=U, Np, Pu, Am, and Cm)
• Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2
• Intense low-energy ferromagnetic fluctuations in the antiferromagnetic heavy-fermion metal CeB6
• Long range order and two-fluid behavior in heavy electron materials
• Cyclotron Resonance in the Hidden-Order Phase of URu2Si2
• Hidden and antiferromagnetic order as a rank-5 superspin in URu2Si2
• Resonant x-ray spectroscopy of uranium intermetallics at the U $M_{4,5}$ edges
• Spin and orbital hybridization at specifically nested Fermi surfaces in URu${}_2$Si${}_2$
• Momentum-resolved evolution of the Kondo lattice into 'hidden-order' in URu2Si2
• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
• Formation of the coherent heavy fermion liquid at the 'hidden order' transition in URu2Si2
• One-Component Order Parameter in URu${}_2$Si${}_2$ Uncovered by Resonant Ultrasound Spectroscopy and Machine Learning
• Competition between the Pseudogap and Superconducting States of Bi${}_2$Sr${}_2$Ca${}_{0.92}$Y${}_{0.08}$Cu${}_2$O${}_{8+\delta }$ Single Crystals Revealed by Ultrafast Broadband Optical Reflectivity
• Measurements of the NMR Knight shift tensor and nonlinear magnetization in URu${}_2$Si${}_2$
• Dual nature of 5$f$ electrons in the isostructural UM${}_2$Si${}_2$ family: from antiferro- to Pauli paramagnetism via hidden order
• Field-induced spin-density wave beyond hidden order in URu2Si2
• Evidence for chiral d-wave superconductivity in URu2Si2 from the field-angle variation of its specific heat
• Direct bulk sensitive probe of 5f symmetry in URu2Si2
• Spin-orbit density wave induced hidden topological order in URu2Si2
• Selection rules for Cooper pairing in two-dimensional interfaces and sheets
• The Superfluid Glass Phase of 3He-A
• Direct experimental observation of the molecular Jeff=3/2 ground state in the lacunar spinel GaTa4Se8
• Chemical pressure tuning of URu${}_2$Si${}_2$ via isoelectronic substitution of Ru with Fe
• Probing 5f-state configurations in URu2Si2 with U L3-edge resonant x-ray emission spectroscopy
• Synchrotron Radiation Techniques and their Application to Actinide Materials
• Interplay of magnetism, Fermi surface reconstructions, and hidden-order in the heavy-fermion material URu${}_2$Si${}_2$
• Resolution of Entropy $\ln \sqrt{2}$ by Ordering in Two-Channel Kondo Lattice
• Symmetry of the Excitations in the Hidden Order State of URu2Si2
• Analogy between the "Hidden Order" and the Orbital Antiferromagnetism in URu${}_{2-x}$Fe${}_x$Si${}_2$
• Sequential localization of a complex electron fluid
• Simulating the Haldane Phase in Trapped Ion Spins Using Optical Fields
• Two-site fluctuations and multipolar superexchange interactions in strongly correlated systems
• Lifshitz transition from valence fluctuations in YbAl3
• Order Fractionalization in a Kitaev-Kondo model
• Neutron scattering studies on URu2Si2
• Heat capacity double transitions in time-reversal symmetry broken superconductors
• Hastatic Order in URu2Si2 : Hybridization with a Twist
• The Tricritical Point of the f-electron Antiferromagnet USb2 Driven by High Magnetic Fields
• Unfolding the physics of URu2Si2 through Si -> P substitution
• Phase diagram and thermal expansion measurements on the system of URu_{2-x}Fe_xSi_2
• Universal Knight shift anomaly in the Periodic Anderson model
• Understanding Magnetic Properties of Actinide-Based Compounds from Machine Learning
• Spontaneous Spatial Inversion Symmetry Breaking and Spin Hall Effect in a Spin-ice Double-exchange Model on a Pyrochlore Lattice
• Revealing the nature of antiferro-quadrupolar ordering in Cerium Hexaboride: CeB${}_6$
• Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory
• Hidden order and multipolar exchange striction in a correlated f-electron system
• Thermodynamic approach to electric quadrupole moments
• Charge density wave with anomalous temperature dependence in UPt2Si2
• Antiferromagnetism and Hidden Order in Isoelectronic Doping of URu${}_2$Si${}_2$
• Fragile antiferromagnetism in the heavy-fermion compound YbBiPt
• Absence of a static in-plane magnetic moment in the "hidden-order" phase of URu${}_2$Si${}_2$
• Fermi Surface Nesting with Heavy Quasiparticles in the Locally Noncentrosymmetric Superconductor CeRh${}_2$As${}_2$
• Effective Coulomb interaction in actinides from linear response approach
• Critical theory of non-Fermi liquid fixed point in multipolar Kondo problem
• Pressure-Induced Rotational Symmetry Breaking in URu${}_2$Si${}_2$
• Modelling Magnetic Multipolar Phases in Density Functional Theory
• Strict limit on in-plane ordered magnetic dipole moment in URu2Si2
• Lattice dynamics of the heavy fermion compound URu${}_2$Si${}_2$
• Pressure-Tuned Point-Contact Spectroscopy of URu2Si2 from Hidden Order to Antiferromagnetic States: Similarity of the Fermi Surface Gapping
• Unusual Nonmagnetic Ordered State in CeCoSi Revealed by ${}^{59}$Co-NMR and NQR Measurements
• Anomalous Hall effect in heavy electron materials
• The dual nature of magnetism in a uranium heavy fermion system
• High-magnetic field lattice length changes in URu2Si2
• Singlet magnetism in intermetallic UGa${}_2$ unveiled by inelastic x-ray scattering
• Isoelectronic perturbations to $f$-$d$-electron hybridization and the enhancement of hidden order in URu${}_2$Si${}_2$
• Hidden orders in spin-orbit entangled correlated insulators
• Spin current and chirality degrees of freedom inherent in localized electron orbitals
• Observation of Multiple-Gap Structure in Hidden Order State of URu2Si2 from Optical Conductivity
• Hybridization gap versus hidden order gap in URu${}_2$Si${}_2$ as revealed by optical spectroscopy
• Multipole order and global/site symmetry in the hidden order phase of URu2Si2
• Magnetic Exciton Mediated Superconductivity in the Hidden-Order Phase of URu2Si2
• Charge-$2e$ Skyrmion condensate in a hidden order state
• Incommensurate short-range multipolar order parameter of phase II in Ce3Pd20Si6
• Distinct magnetic spectra in the hidden order and antiferromagnetic phases in URu2-xFexSi2
• Electronic nematicity in URu2Si2 revisited
• Local observation of linear-$T$ superfluid density and anomalous vortex dynamics in URu${}_2$Si${}_2$
• Emergent non-Fermi-liquid phenomena in multipolar quantum impurity systems
• Exactly Solvable Kondo Lattice Model in Anisotropic Limit
• Nuclear magnetic resonance studies of pseudospin fluctuations in URu${}_2$Si${}_2$
• Optical conductivity of URu${}_2$Si${}_2$ in the Kondo Liquid and Hidden-Order Phases
• Cyclotron resonance study of quasiparticle mass and scattering rate in the hidden-order and superconducting phases of URu2Si2
• Field induced Lifshitz transition in UPt${}_2$Si${}_2$: Fermi surface under extreme conditions
• Structure of the normal state and origin of Schottky anomaly in the correlated heavy fermion superconductor UTe2
• Imprints of spin-orbit density wave in the hidden order state of URu2Si2
• ARPES/STM study of the surface terminations and 5$f$-electron character in URu${}_2$Si${}_2$
• Signatures of hidden octupolar order from nonlinear Hall effects
• Search for Multipolar Instability in URu${}_2$Si${}_2$ Studied by Ultrasonic Measurements under Pulsed Magnetic Field
• Structure of vortex-bound states in spin-singlet chiral superconductors
• Nature of the unconventional heavy fermion Kondo state in monolayer CeSiI
• Weak-coupling superconductivity in an anisotropic three-dimensional repulsive Hubbard model
• Relation between $c$-$f$ hybridization and magnetic ordering in CeRu${}_2$Al${}_{10}$: An optical conductivity study of Ce(Ru${}_{1-x}$Rh${}_x$)${}_2$Al${}_{10}$ ($x\le 0.05$)
• 3D Modulated Spin Liquid model applied to URu${}_2$Si${}_2$
• Detailed optical spectroscopy of the hybridization gap and the hidden order transition in high quality URu${}_2$Si${}_2$ single crystals
• On the possibility to detect multipolar order in URu${}_2$Si${}_2$ by the electric quadrupolar transition of resonant elastic X-ray scattering
• Magnetic field-Temperature Phase Diagram of CeCoSi Constructed by Specific Heat, Magnetoresistivity, and Magnetization Measurements for a Single Crystal
• Superconducting phase within the hidden-order state of the heavy-fermion material $\mathrm{UR}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$
• Hidden Charge Order in an Iron Oxide Square-Lattice Compound
• Interplay of superexchange and vibronic effects in the hidden order of Ba${}_2$MgReO${}_6$ from first principles
• Hidden Order Signatures in the Antiferromagnetic Phase of U(Ru${}_{1-x}$Fe${}_x$)${}_2$Si${}_2$
• From local moment to mixed-valence regime in Ce(1-x)Yb(x)CoIn5 alloys
• Fermi surface in the hidden-order state of URu${}_2$Si${}_2$ under intense pulsed magnetic fields up to 81~T
• Electronic structure of ThRu2Si2 studied by angle-resolved photoelectron spectroscopy: Elucidating the contribution of U 5f states in URu2Si2
• Electronic properties of a heavy-fermion U(Ru0.92Rh0.08)2Si2 single crystal
• Fermi-Surface Selective Determination of the $\mathbf{g}$-Factor Anisotropy in URu${}_2$Si${}_2$
• Unconventional Superconductivity arising from Multipolar Kondo Interactions
• Thermodynamic Measurement of Angular Anisotropy at the Hidden Order Transition of URu${}_2$Si${}_2$
• Strong Correlation between Anomalous Quasiparticle Scattering and Unconventional Superconductivity in Hidden Order Phase of URu${}_2$Si${}_2$
• Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition of URu${}_2$Si${}_2$
• Novel critical behavior of magnetization in URhSi:Similarities to uranium ferromagnetic superconductors UGe${}_2$ and URhGe
• Thermodynamic evidence for broken fourfold rotational symmetry in the hidden-order phase of URu2Si2
• Hybridization gap in the heavy-fermion compound UPd${}_2$Al${}_3$ via quasiparticle scattering spectroscopy
• A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn${}_3$
• Exceptional Ising Magnetic Behavior of Itinerant Spin-polarized Carriers in URu2Si2
• Basal-Plane Nonlinear Susceptibility: A Direct Probe of the Single-Ion Physics in URu2Si2
• Inelastic x-ray scattering measurements on URu2Si2
• Composite Orders and Lifshitz Transition of Heavy Electrons
• Observation of Electronic Structure Modification in the Hidden Order Phase of CeCoSi
• Hidden and Hastatic Orders in URu2Si2
• A "hidden" transition in heavy fermion compound CeB${}_6$ at $T\sim$ 20 K?
• Modulated Spin Liquid and Magnetic Order from a Kondo-Heisenberg model applied to $UR{u}_{2}S{i}_2$
• Simulating heavy fermion physics in optical lattice: Periodic Anderson model with harmonic trapping potential
• Magnetic structure in U(Ru0.92Rh0.08)2Si2 single crystal studied by neutron diffraction in static magnetic fields up to 24 T
• Magnetoelastic phenomena in antiferromagnetic uranium intermetallics: the $\mathrm{UA}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$ case
• Angular Dependence of the High-Magnetic-Field Phase Diagram of URu2Si2
• From hidden-order to antiferromagnetism: electronic structure changes in Fe-doped URu${}_2$Si${}_2$
• Tunneling spectroscopy of the superconducting state of URu2Si2
• Electronic correlations of element cerium under high pressure
• Theory Perspective: SCES 2016
• Quantum Phase Transition in a Clean Two-Dimensional Electron System
• Evolution of the propagation vector of antiferroquadrupolar phases in Ce3Pd20Si6 with magnetic field
• NMR Investigation of antiferromagnetism and coherence in URu${}_2$Si${}_{2-x}$P${}_x$
• Origin of gap-like behaviors in URu${}_2$Si${}_2$: Combined study via quasiparticle scattering spectroscopy and resistivity measurements
• Global perspectives of the bulk electronic structure of URu${}_2$Si${}_2$ from angle-resolved photoemission
• An emerging global picture of heavy fermion physics
• Cascade of magnetic-field-driven quantum phase transitions in Ce3Pd20Si6
• Spin liquid versus long range magnetic order in the frustrated body-centered tetragonal lattice
• Hidden order symmetry and superconductivity in URu2Si2 investigated by quasiparticle interference
• Collective spin resonance excitation in the gapped itinerant multipole hidden order phase of URu2Si2
• In-plane anisotropic response to the uniaxial pressure in the hidden order state of URu${}_2$Si${}_2$
• Fe substitution in URu${}_2$Si${}_2$: singlet magnetism in an extended Doniach phase diagram
• Skyrmions in a density wave state: a mechanism for chiral superconductivity
• Spin liquid versus long range magnetic order in the frustrated body-centered tetragonal lattice
• Unfolding of antiferromagnetic phases and multicritical points in a two-orbital model for Uranium compounds under pressure and magnetic field
• Efficient Method for Prediction of Meta-stable/Ground Multipolar Ordered States and its Application in Monolayer $\alpha$-\ce{RuX3} (X=Cl,I)
• Anisotropic Kondo pseudo-gap in URu2Si2
• Non-collinear magnetism engendered by a hidden another order
• Analysis of Magnetoacoustic Quadrupole Resonance and Application to Probe Quadrupole Degrees of Freedom in Quantum Magnets
• Molecular orbital polarization in Na2Ti2Sb2O: microscopic route to metal-metal transition without spontaneous symmetry breaking
• Quasiparticle Relaxation Dynamics in URu${}_{2-x}$Fe${}_x$Si${}_2$ Single Crystals
• Recent Progress of Point Contact Spectroscopy as a Probe of Correlated Electron States
• The Fermi volume as a probe of hidden order
• Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid
• Nonlinear Transport Signatures of Hidden Symmetry Breaking in a Weyl Altermagnet
• 29Si nuclear magnetic resonance study of URu2Si2 under pressure
• Textured Superconductivity in the Presence of a Coexisting Order: Ce115s and Other Heavy-Fermion Compounds
• Raman Active High Energy Excitations in URu${}_2$Si${}_2$
• The role of band filling in tuning the high field phases of URu2Si2
• URu${}_2$Si${}_2$ under intense magnetic fields: from hidden order to spin-density wave
• Correlation and disorder-enhanced nematic spin response in superconductors with weakly broken rotational symmetry
• Spins, electrons and broken symmetries: realizations of two channel Kondo physics
• Hidden spin-orbital hexagonal ordering induced by strong correlations in LiVS${}_2$
• Implications of the Measured Angular Anisotropy at the Hidden Order Transition of URu2Si2
• Universal behavior in the Nernst effect of heavy fermion materials
• The hidden order in URu2Si2: Symmetry-induced anti-toroidal vortices
• Chiral superconductivity in nematic states
• A Model for Metastable Magnetism in the Hidden-Order Phase of URu2Si2
• Novel universality class for the ferromagnetic transition in the low carrier concentration systems UTeS and USeS exhibiting large negative magnetoresistance
• Origin of the Large Anisotropy in the χ_3 Anomaly in URu_2Si_2
• Study of the hidden-order of URu2Si2 by point contact tunnel junctions
• One-dimensional moire charge density wave in the hidden order state of URu2Si2 induced by fracture
• Hidden Anderson Localization in Disorder-Free Ising-Kondo Lattice
• Field-induced phases in a heavy-fermion U(Ru${}_{0.92}$Rh${}_{0.08}$)${}_2$Si${}_2$ single crystal
• Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach
• f-electron charge densities probed using core level non-resonant inelastic x-ray scattering
• Collinear antiferromagnetic order in URu${}_2$Si${}_{2-x}$P${}_x$ revealed by neutron diffraction
• Ungapped magnetic excitations beyond Hidden Order in URu${}_{2-x}$Re${}_x$Si${}_2$
• Emergence of quadrupolar order under magnetic field in $5d^2$ double perovskites
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Large Kohn anomaly and phonon collapse induced by charge density wave in UPt${}_2$Si${}_2$
• Unified Theory of Hastatic order and Antiferromagnetism in URu${}_2$Si${}_2$
• Multiple localized-itinerant dualities in magnetism of 5f electron systems. The case of UPt${}_2$Si${}_2$
• Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal
• Evolution of magnetic bubble domains in the uniaxial ferromagnet CeRu${}_2$Ga${}_2$B inferred from the Hall effect and ac magnetic susceptibility
• Two-orbital model for CeB${}_6$
• Magnetic transitions induced by pressure and magnetic field in a two-orbital $5f$-electron model in cubic and tetragonal lattices
• Pseudo-chiral phonon splitting from octupolar magnetic order