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Title: At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

Abstract

This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. In this study, we extend a recently developed Fermi liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, c A, describing its leading ~ε 2 term, and the transport coefficients c V and c T, describing the leading ~V 2 and ~T 2 terms in the nonlinear differential conductance. A sign change in c A or c V is indicative of amore » change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. In conclusion, we find that the fields B A, B T, and B V at which c A, c T, and c V change sign, respectively, are all of order T K, as expected, with B A = B T = B V = 0.75073T K in the Kondo limit.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [4];  [5]
  1. Freie Universität Berlin (Germany). Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik; University of Geneva (Switzerland). Department of Quantum Matter Physics
  2. Budapest University of Technology and Economics (Hungary). BME-MTA Exotic Quantum Phase Group, Institute of Physics; University of Oradea (Romania). Department of Physics
  3. Brookhaven National Lab. (BNL), Upton, NY (United States). CM PMS Division; Ludwig-Maximilians-Universität München (Germany). Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience
  4. Ludwig-Maximilians-Universität München (Germany). Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience
  5. PSL Research University, CNRS, Université Pierre et Marie Curie, Sorbonne Universités, Université Paris Diderot (France). Laboratoire Pierre Aigrain, École normale supérieure
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1473650
Report Number(s):
BNL-209052-2018-JAAM
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 7; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, and Mora, Christophe. At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.075404.
Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, & Mora, Christophe. At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model. United States. doi:10.1103/PhysRevB.98.075404.
Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, and Mora, Christophe. Mon . "At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model". United States. doi:10.1103/PhysRevB.98.075404. https://www.osti.gov/servlets/purl/1473650.
@article{osti_1473650,
title = {At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model},
author = {Filippone, Michele and Moca, Cătălin Paşcu and Weichselbaum, Andreas and von Delft, Jan and Mora, Christophe},
abstractNote = {This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. In this study, we extend a recently developed Fermi liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, cA, describing its leading ~ε2 term, and the transport coefficients cV and cT, describing the leading ~V2 and ~T2 terms in the nonlinear differential conductance. A sign change in cA or cV is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. In conclusion, we find that the fields BA, BT, and BV at which cA, cT, and cV change sign, respectively, are all of order TK, as expected, with BA = BT = BV = 0.75073TK in the Kondo limit.},
doi = {10.1103/PhysRevB.98.075404},
journal = {Physical Review B},
number = 7,
volume = 98,
place = {United States},
year = {2018},
month = {8}
}

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