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Title: Mixed valent metals

Abstract

Here, we review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer–Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Nozieres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.

Authors:
 [1];  [2]
  1. Temple Univ., Philadelphia, PA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1414146
Alternate Identifier(s):
OSTI ID: 1260062
Report Number(s):
LA-UR-17-22084
Journal ID: ISSN 0034-4885; TRN: US1800669
Grant/Contract Number:  
AC52-06NA25396; FG02-01ER45872
Resource Type:
Accepted Manuscript
Journal Name:
Reports on Progress in Physics
Additional Journal Information:
Journal Volume: 79; Journal Issue: 8; Journal ID: ISSN 0034-4885
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Material Science; single-impurity Anderson model; Luttinger’s theorem; single-impurity Kondo model; Anderson lattice model; Slave-Boson method; Friedel sum rule

Citation Formats

Riseborough, P. S., and Lawrence, Jon M. Mixed valent metals. United States: N. p., 2016. Web. https://doi.org/10.1088/0034-4885/79/8/084501.
Riseborough, P. S., & Lawrence, Jon M. Mixed valent metals. United States. https://doi.org/10.1088/0034-4885/79/8/084501
Riseborough, P. S., and Lawrence, Jon M. Mon . "Mixed valent metals". United States. https://doi.org/10.1088/0034-4885/79/8/084501. https://www.osti.gov/servlets/purl/1414146.
@article{osti_1414146,
title = {Mixed valent metals},
author = {Riseborough, P. S. and Lawrence, Jon M.},
abstractNote = {Here, we review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer–Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Nozieres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.},
doi = {10.1088/0034-4885/79/8/084501},
journal = {Reports on Progress in Physics},
number = 8,
volume = 79,
place = {United States},
year = {2016},
month = {7}
}

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Cited by: 3 works
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Relation between the Anderson and Kondo Hamiltonians
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Interaction Between the d Shells in the Transition Metals
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Bound State Due to the s d Exchange Interaction
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A ?fermi-liquid? description of the Kondo problem at low temperatures
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Coherence Scale of the Kondo Lattice
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Magnetic instability of a highly degenerate Kondo lattice
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Band-filling effects on Kondo-lattice properties
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Correlated Lattice Fermions in d = Dimensions
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Magnetic phase diagram of the Hubbard model in three dimensions:The second-order local approximation
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Mixed valence as an almost broken symmetry
journal, April 1987


New approach to the mixed-valence problem
journal, March 1984


Large-orbital-degeneracy expansion for the lattice Anderson model
journal, March 1987


Slow crossover in Yb X Cu 4 ( X =Ag, Cd, In, Mg, Tl, Zn) intermediate-valence compounds
journal, January 2001


Two Energy Scales and Slow Crossover in YbAl 3
journal, March 2002


Intermediate Valence Metals
journal, May 2008


Universal Scaling in the Dynamical Conductivity of Heavy Fermion Ce and Yb Compounds
journal, February 2007

  • Okamura, Hidekazu; Watanabe, Tatsuya; Matsunami, Masaharu
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  • DOI: 10.1143/JPSJ.76.023703

Observation of an Energy- and Temperature-Dependent Carrier Mass for Mixed-Valence Ce Pd 3
journal, October 1986


Pseudogap Formation and Heavy-Carrier Dynamics in Intermediate-Valence YbAl 3
journal, August 2004

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  • DOI: 10.1143/JPSJ.73.2045

Heavy Fermions in YbAl 3 Studied by the de Haas-van Alphen Effect
journal, March 2000

  • Ebihara, Takao; Inada, Yoshihiko; Murakawa, Masao
  • Journal of the Physical Society of Japan, Vol. 69, Issue 3
  • DOI: 10.1143/JPSJ.69.895

Localized Excitation in the Hybridization Gap in YbAl 3
journal, March 2006


How Bad Metals Turn Good: Spectroscopic Signatures of Resilient Quasiparticles
journal, February 2013


Dynamic susceptibility of intermediate-valence compounds: a random-phase-approximation study of the anderson lattice
journal, June 1980


Self-Consistent Approximations in Many-Body Systems
journal, August 1962


Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach
journal, July 1989


Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model
journal, February 1989


Conserving approximations for strongly fluctuating electron systems. II. Numerical results and parquet extension
journal, April 1991


Formation of a coherent heavy electron state in the Anderson lattice model
journal, July 1993


Pseudogap formation in the symmetric Anderson lattice model
journal, September 1994


Dynamical Cluster Approximation for the Periodic Anderson Model: Competition between Local and Non-local Correlations
journal, April 2002

  • Shimizu, Yukihiro
  • Journal of the Physical Society of Japan, Vol. 71, Issue 4
  • DOI: 10.1143/JPSJ.71.1166

Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems
journal, May 2000


Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
journal, October 2001


Inhomogeneous Electron Gas
journal, November 1964


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Monte Carlo Method for Magnetic Impurities in Metals
journal, June 1986


Spin-liquid ground state of the half-filled Kondo lattice in one dimension
journal, August 1992

  • Tsunetsugu, Hirokazu; Hatsugai, Yasuhiro; Ueda, Kazuo
  • Physical Review B, Vol. 46, Issue 5
  • DOI: 10.1103/PhysRevB.46.3175

One-dimensional symmetric Kondo lattice: A quantum Monte Carlo study
journal, December 1990


Density matrix formulation for quantum renormalization groups
journal, November 1992


The density-matrix renormalization group
journal, April 2005


Numerical renormalization group study of the one-dimensional Kondo insulator
journal, December 1993


The one-dimensional Kondo lattice model studied by the density matrix renormalization group method
journal, January 1999


Localized spin ordering in Kondo lattice models
journal, January 2002


Polaron Problem by Diagrammatic Quantum Monte Carlo
journal, September 1998


A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions
journal, June 1998


Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011

  • Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
  • Reviews of Modern Physics, Vol. 83, Issue 2
  • DOI: 10.1103/RevModPhys.83.349

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