Fermi-liquid instabilities at magnetic quantum phase transitions

2006/06/30 by H. v. Löhneysen, Hilbert v. Löhneysen, Achim Rosch +3 · 80 citations
Materials Science · Physics and Astronomy · #Condensed matter physics #Electron #Fermi Gamma-ray Space Telescope #Fermi liquid theory #Fermi surface #Iron-based superconductors research #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum critical point #Quantum mechanics #Quantum oscillations #Quantum phase transition #Quantum phases #Rare-earth and actinide compounds #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/revmodphys.79.1015

published as Rev. Mod. Phys. 79, 1015 (2007) · 62 pages, 29 figs, review article for Rev. Mod. Phys; (v2) discussion extended, refs added; (v3) shortened; final version as published

openalex publication_date 2007/08/17 · arxiv created 2007/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part, experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Citations

• Singular corrections to the Fermi-liquid theory
• Heavy-fermion superconductivity in CeCoIn5at 2.3 K
• Possible Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State inCeCoIn5
• Superconductivity of CeRhIn5 under High Pressure
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Continuous Quantum Phase Transitions
• The break-up of heavy electrons at a quantum critical point
• Coexistence of antiferromagnetism and superconductivity inCeRhIn5under high pressure and magnetic field
• Response of the heavy-fermion superconductor CeCoIn5to pressure: roles of dimensionality and proximity to a quantum-critical point
• Quantum critical effects on transition temperature of magnetically mediatedp-wave superconductivity
• Universal relationship of the resistivity and specific heat in heavy-Fermion compounds
• Probing the extended non-Fermi liquid regimes of MnSi and Fe
• Magnetic Field-Induced Superconductivity in the Ferromagnet URhGe
• Continuous Quantum Phase Transition in a Kondo Lattice Model
• Quantum critical behavior of disordered itinerant ferromagnets
• Electronic liquid-crystal phases of a doped Mott insulator
• Quantum critical phenomena
• High Resolution Study of Magnetic Ordering at Absolute Zero
• Magnetotransport in nearly antiferromagnetic metals
• Relation between the Anderson and Kondo Hamiltonians
• Topological Approach to Luttinger's Theorem and the Fermi Surface of a Kondo Lattice
• The renormalization group: Critical phenomena and the Kondo problem
• Hall number inYbRh2Si2
• Quantum theory of a nematic Fermi fluid
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Localization-Induced Griffiths Phase of Disordered Anderson Lattices
• Fermi Surface and Antiferromagnetism in the Kondo Lattice: An Asymptotically Exact Solution ind>1Dimensions
• Spatial correlations in dynamical mean-field theory
• Superconductivity inCeCoIn5−xSnx: Veil over an Ordered State or Novel Quantum Critical Point?
• Spin Fluctuation in Heavy FermionCeRu2Si2
• Absence of Conventional Quantum Phase Transitions in Itinerant Systems with Disorder
• Fractionalized Fermi Liquids
• Tricritical Behavior in Itinerant Quantum Ferromagnets
• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Singular or non-Fermi liquids
• Effect of random defects on the critical behaviour of Ising models
• First Order Transitions and Multicritical Points in Weak Itinerant Ferromagnets
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Deconfined Quantum Critical Points
• Dynamics of the dissipative two-state system
• Resistance Minimum in Dilute Magnetic Alloys
• Disorder-driven non-Fermi liquid behaviour of correlated electrons
• Quantum phase transitions
• Quantum Critical Point of Itinerant Antiferromagnet in Heavy Fermion
• Signatures of an electronic nematic phase at the isotropic-nematic phase transition
• Ferromagnetic Quantum Critical Fluctuations inYbRh2(Si0.95Ge0.05)2
• Formation of an electronic nematic phase in interacting fermion systems
• A ?fermi-liquid? description of the Kondo problem at low temperatures

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