Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions

Abstract

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the heavy fermion metals, in which antiferromagnetic quantum critical points have been explicitly observed. Here, I address two types of antiferromagnetic quantum critical points. In addition to the standard description based on the fluctuations of the antiferromagnetic order, a local quantum critical point is also considered. It contains inherently quantum modes that are associated with a critical breakdown of the Kondo effect. Across such a quantum critical point, there is a sudden collapse of a large Fermi surface to a small one. I also consider the proximate antiferromagnetic and paramagnetic phases, and these considerations lead to a global phase diagram. Finally, I discuss the pertinent experiments on the antiferromagnetic heavy fermions, briefly address the case of ferromagnetic heavy fermions, and outline some directions for future studies.

(v2) reference added, and typos corrected; (v1) 10 pages, 2 figures, based on a plenary talk given at the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden)

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Cited by in corpus (80)

• Holographic quantum matter
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Quantum phases driven by strong correlations
• Frustration and the Kondo effect in heavy fermion materials
• Destruction of Kondo effect in cubic heavy fermion compound Ce3Pd20Si6
• Frustration and quantum criticality
• Quantum-critical phase out of frustrated magnetism in a strongly correlated metal
• Multiple quantum phase transitions in a heavy fermion antiferromagnet
• Emulating heavy fermions in twisted trilayer graphene
• Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn${}_5$
• Quantum phase transitions in heavy fermion metals and Kondo insulators
• Magnetic field tuned quantum criticality of heavy fermion system YbPtBi
• Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
• Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions
• Grüneisen parameter studies on heavy fermion quantum criticality
• Itinerant vs Localized Heavy-Electron Magnetism
• Antiferromagnetism and Superconductivity in Cerium based Heavy Fermion Compounds
• Weyl-Kondo semimetals in nonsymmorphic systems
• Multiple regions of quantum criticality in YbAgGe
• Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy Fermion Metals
• Large and Small Fermi-Surface Spin Density Waves in the Kondo Lattice Model
• Holographic impurities and Kondo effect
• Another dimension: investigations of molecular magnetism using muon-spin relaxation
• muSR and inelastic neutron scattering investigations of the caged type Kondo semimetals: CeT2Al10 (T=Fe, Ru and Os)
• Hall effect in heavy-fermion metals
• Fermi Surface Properties, Metamgnetic Transition and Quantum Phase Transition of CeRu${}_2$Si${}_2$ and Its Alloys Probed by the dHvA Effect--Fermi Surface Studies on the Itinerant and Localized Dichotomy of $f$ Electron Nature
• The two-dimensional metallic triangular lattice antiferromagnet CeCd3P3
• Weak ferromagnetism with the Kondo screening effect in the Kondo lattice systems
• Magnetic property and crystalline electric field effect in ThCr${}_2$Si${}_2$-type CeNi${}_2$As${}_2$
• Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
• Triangular Kondo lattice in $\mathrm{Yb}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$ and its quantum critical behaviors in magnetic field
• Quantum critical scaling and fluctuations in Kondo lattice materials
• Strong coupling theory of heavy fermion criticality II
• Lifshitz Transition and Metamagnetism: Thermoelectric Studies of CeRu${}_2$Si${}_2$
• Fragile antiferromagnetism in the heavy-fermion compound YbBiPt
• Quasi-two-dimensional Fermi surfaces of the heavy-fermion superconductor Ce${}_2$PdIn${}_8$
• Ordered Phases and Quantum Criticality in Cubic Heavy Fermion Compounds
• Kondo destruction in a quantum paramagnet with magnetic frustration
• Field-induced long-range magnetic order in the spin-singlet ground state system YbAl3C3: Neutron diffraction study
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Inhomogeneous Kondo-lattice in geometrically frustrated Pr${}_2$Ir${}_2$O${}_7$
• Multiple superconducting phases in heavy-fermion metals
• Semimetallic Kondo lattice behavior in YbPdAs with a distorted kagome structure
• Kondo effect and its destruction in hetero-bilayer transition metal dichalcogenides
• Magnetization plateau and anisotropic magnetoresistance in the frustrated Kondo-lattice compound Ce3ScBi5
• Classification of materials with divergent magnetic Grüneisen parameter
• Long-range magnetic order in the anisotropic triangular lattice system CeCd3As3
• Quantum critical metals and loss of quasiparticles
• Quantum critical spin-liquid-like behavior in S = 1/2 quasikagome lattice CeRh1-xPdxSn investigated using muon spin relaxation and neutron scattering
• Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
• Incommensurate spin-density-wave antiferromagnetism in CeRu${}_2$Al${}_2$B
• Global Phase Diagram and Momentum Distribution of Single-Particle Excitations in Kondo insulators
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Effects of Berry phase and instantons in one dimensional Kondo-Heisenberg model
• Break up of heavy fermions at an antiferromagnetic instability
• Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice
• Filling-enforced Kondo semimetals in two-dimensional non-symmorphic crystals
• Dimer-induced heavy-fermion superconductivity in the Shastry-Sutherland Kondo lattice model
• Quantum Criticality and Novel Phases: Summary and Outlook
• Ring-exchange periodic Anderson model for 3He bilayers
• An emerging global picture of heavy fermion physics
• Coexisting Kondo hybridization and itinerant f-electron ferromagnetism in UGe2
• Frustration-induced quantum criticality in Ni-doped CePdAl as revealed by the $\mu$SR technique
• Asymmetry effects on the phases of RKKY-coupled two-impurity Kondo systems
• Evidence for charge delocalization crossover in the quantum critical superconductor CeRhIn${}_5$
• The Future of the Correlated Electron Problem
• Inexorable Edge Kondo Breakdown in Topological Kondo Insulators
• Spins, electrons and broken symmetries: realizations of two channel Kondo physics
• Magnon Bose-Einstein Condensation and Superconductivity in a Frustrated Kondo Lattice
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Global phase diagram of a spin-orbit-coupled Kondo lattice model on the honeycomb lattice
• Converse effect of pressure on quadrupolar and magnetic transition in Ce${}_3$Pd${}_{20}$Si${}_6$
• Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides
• Rich unconventional Hall effects in a single quasi-kagome Kondo Weyl semimetal candidate Ce${}_3$TiSb${}_5$
• Two-band model and RVB-type states: application to Kondo lattices, pyrochlores and Mn-based systems
• Quasi-two-dimensional Fermi surfaces with localized $f$ electrons in the layered heavy-fermion compound CePt${}_2$In${}_7$
• Spin nematic order and superconductivity in $J_1$-$J_2$ Kondo lattice model on square lattice
• Anomalous Hall effect and quantum criticality in geometrically frustrated heavy fermion metals
• A Holographic Two-Impurity Kondo Model
• Emergent Chiral Metal near a Kondo Breakdown Quantum Phase Transition