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Master's Dissertation
DOI
https://doi.org/10.11606/D.76.2022.tde-31102022-162143
Document
Author
Full name
Ana Luiza Rodrigues Ferreira Ferrari
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2022
Supervisor
Committee
Oliveira, Luiz Nunes de (President)
Continentino, Mucio Amado
Silva, Luis Gregorio Godoy de Vasconcellos Dias da
Title in English
Real-space formulation of the Numerical Renormalization Group method (NRG)
Keywords in English
NRG
Side coupled device
Universality
Abstract in English
The equilibrium transport properties of an elementary nanostructured device with sidecoupled geometry are computed and related to universal functions. The computation relies on a real-space formulation of the numerical renormalization-group (NRG) procedure. The real-space construction, dubbed eNRG, is more straightforward than the NRG discretization and allows more faithful description of the coupling between quantum dots and conduction states. The procedure is applied to an Anderson-model description of a quantum wire side-coupled to a single quantum dot. A gate potential controls the dot occupation. In the Kondo regime, the electrical conductance through this device is known to map linearly onto a universal function of the temperature scaled by the Kondo temperature. Here, the energy moments from which the Seebeck coefficient and the thermal conductance can be computed are shown to map linearly onto universal functions also. The moments and transport properties computed by the eNRG procedure are shown to agree very well with these analytical developments. Algorithms facilitating comparison with experimental results are discussed. As an illustration, one of the algorithms is applied to thermal dependence of the thermopower measured by Köhler in Lu 0.9Yb0.1Rh2Si2, and to resistivity measurements in CeRh6Ge4. 1, 2
Title in Portuguese
Formulação no espaço real do grupo de renormalização numérico (NRG).
Keywords in Portuguese
Dispositivo de acoplamento lateral
NRG
Universalidade
Abstract in Portuguese
As propriedades de transporte no equilíbrio de um dispositivo nanoestruturado elementar, com geometria de acoplamento lateral, são calculadas e relacionadas com funções universais. O cálculo se baseia em uma formulação do Grupo de Renormalização Numérico (NRG) no espaço real. A construção no espaço real, chamada de Grupo de Renormalização Numérico Exponencial (eNRG), é mais direta que a do NRG e permite uma descrição fidedigna do acoplamento entre pontos quânticos e estados de condução. Nós aplicamos o método ao modelo de Anderson, que descreve um ponto quântico lateralmente acoplado a um fio quântico. Um potencial de sítio controla a ocupação eletrônica no ponto quântico. No regime Kondo, a condutância elétrica se mapeia linearmente em uma função universal da temperatura. Aqui, mostramos que os momentos energéticos, a partir dos quais calculamos a condutância térmica e o coeficiente de Seeback, também se mapeiam linearmente em funções universais. Os momentos e propriedades de transportes calculados pelo eNRG concordam muito bem com esses resultados analíticos. Além disso, desenvolvemos algorítimos que facilitam a comparação com resultados experimentais. Dentre eles, está o estudo da dsependência térmica do coeficiente de Seeback, medida por Köhler em Lu 0.9Yb0.1Rh2Si2.1
 
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Publishing Date
2022-11-09
 
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