Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys
{"title":"Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys","authors":"Yoshimichi Teratani, Kazuhiko Tsutsumi, Kaiji Motoyama, Rui Sakano, Akira Oguri","doi":"10.1103/physrevb.110.035308","DOIUrl":null,"url":null,"abstract":"We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math> discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> and bias voltage <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>e</mi><mi>V</mi></mrow></math>. The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>N</mi><mi>d</mi><mrow></mrow></msubsup></math> of impurity electrons. We apply this formulation to the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> symmetric QD and MA, and calculate the correlation functions for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math> and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><mo>≲</mo><msubsup><mi>N</mi><mi>d</mi><mrow></mrow></msubsup><mo>≲</mo><mi>N</mi><mo>−</mo><mn>1</mn></mrow></math> for strong Coulomb interactions <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>U</mi></math>, and they also exhibit the plateau structures due to the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> Kondo effects at integer values of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>N</mi><mi>d</mi><mrow></mrow></msubsup></math>. We find that the Lorenz number <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>L</mi><mo>=</mo><mi>κ</mi><mo>/</mo><mo>(</mo><mi>T</mi><mi>σ</mi><mo>)</mo></mrow></math> for QD and MA, defined as the ratio of the thermal conductivity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>κ</mi></math> to the electrical conductivity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>σ</mi></math>, deviates from the universal Wiedemann-Franz value <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mi>π</mi><mn>2</mn></msup><mo>/</mo><mrow><mo>(</mo><mn>3</mn><msup><mi>e</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> as the temperature increases from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></math>, showing the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>T</mi><mn>2</mn></msup></math> dependence, the coefficient for which depends on the three-body correlations away from half filling. Furthermore, we find that the current noise for the SU(4) quantum dots and that for SU(6) show a pronounced difference at the quarter <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msubsup><mi>N</mi><mi>d</mi><mrow></mrow></msubsup><mo>/</mo><mi>N</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>4</mn></mrow></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></math> fillings. In particular, the linear noise for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math> exhibits a flat peak while the peak for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>=</mo><mn>6</mn></mrow></math> shows a round shape, reflecting the fact that, at these filling points, the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> Kondo effects occur for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>≡</mo><mn>0</mn></mrow></math> (mod 4), whereas the intermediate-valence fluctuations occur for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>≡</mo><mn>2</mn></mrow></math> (mod 4). We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.035308","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature and bias voltage . The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number of impurity electrons. We apply this formulation to the symmetric QD and MA, and calculate the correlation functions for and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings for strong Coulomb interactions , and they also exhibit the plateau structures due to the Kondo effects at integer values of . We find that the Lorenz number for QD and MA, defined as the ratio of the thermal conductivity to the electrical conductivity , deviates from the universal Wiedemann-Franz value as the temperature increases from , showing the dependence, the coefficient for which depends on the three-body correlations away from half filling. Furthermore, we find that the current noise for the SU(4) quantum dots and that for SU(6) show a pronounced difference at the quarter and fillings. In particular, the linear noise for exhibits a flat peak while the peak for shows a round shape, reflecting the fact that, at these filling points, the Kondo effects occur for (mod 4), whereas the intermediate-valence fluctuations occur for (mod 4). We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.
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