Analytical and numerical study of quantum impurity systems in the intermediate and strong coupling regimes

URN to cite this document:: urn:nbn:de:bvb:355-epub-341352
DOI to cite this document:: 10.5283/epub.34135

Mantelli, Davide

Preview

License: Publishing license for publications including print on demand
PDF - Other
(34MB)

Date of publication of this fulltext: 29 Jul 2016 08:49

Details

Item type:	Thesis of the University of Regensburg (PhD)
Open Access Type:	Primary Publication
Date:	29 July 2016
Referee:	Prof. Dr. Milena Grifoni and Prof. Dr. Klaus Riechter and Prof. Dr. Dieter Weiss and Prof. Dr. Vladimir Braun
Date of exam:	21 July 2016
Institutions:	Physics > Institute of Theroretical Physics > Chair Professor Grifoni > Group Milena Grifoni
Keywords:	Kondo effect, Intermediate and strong coupling, quantum dots
Dewey Decimal Classification:	500 Science > 530 Physics
Status:	Published
Refereed:	Yes, this version has been refereed
Created at the University of Regensburg:	Yes
Item ID:	34135

Preview

Export bibliographical data

Abstract (English)

Abstract (English)

In this thesis we deal with the description of quantum impurity systems. In order to achieve such an aim, we exploit in the first part of this work the Reduced Density Matrix (RDM) formalism, in the second one the Density Matrix-Numerical Renormalization Group (DM-NRG) method.
The first half of the thesis deals with the derivation and the application of out-of-equilibrium and non-perturbative approximations for the dynamics of the Single Impurity Anderson Model (SIAM) in the perturbative, intermediate coupling and Kondo cross-over regimes. In this part of the thesis, the main aim is to develop new technical tools useful to extend the RDM formalism from the well established perturbative regime to the intermediate and, in the future, to the strong coupling regimes.
In this part, we analyse the advantages and drawbacks of the so-called Dressed Second Order (DSO), Dressed DSO (DDSO) and the Resonant Tunnelling Approximation (RTA). In the DSO we include processes capable to describe the broadening of the Coulomb blockade peaks but the DSO itself, as the RTA, is not capable to describe the Kondo resonance width properly. In the DDSO we propose a prescription to solve this issue and to describe properly the exponential dependence of the Kondo resonance width. However, in the DDSO the vertex corrections are not included and this yields a spurious conductance peak in the empty orbital regime (Coulomb valley with zero electrons). For this reason we turn our attention to the inclusion of the vertex corrections within the RTA framework.
In the second part, we describe transport and thermodynamic properties of carbon-nanotubes (CNTs) based quantum dots using the DM-NRG method. We present results on the spectral function and the linear conductance in cooperation with Catalin Pascu Moca and Gergely Zarand from the Universities of Oradea and Budapest, respectively. In order to model the CNTs we consider an extended Anderson Hamiltonian. Exploiting such an Hamiltonian we study the crossover from the SU(4) to the SU(2) Kondo effect. We demonstrate numerically and analytically that the Kondo temperature scales inversely with respect to the SU(4)-symmetry breaking parameter $\Delta$ , tending to the Kondo temperature of the SU(2) Kondo effect in the large $\Delta$ limit. Furthermore we study the CNT quantum dot in the presence of a parallel and perpendicular (with respect to the CNT axis) magnetic field. We find necessary conditions to observe the so-called ``Kondo revivals'' for specific values of the magnetic field.
In the final part of this thesis, we model a real world device realised by Jean-Pierre Cleuziou, Ngoc-Viet Nguyen and Wolfgang Wernsdorfer in Grenoble by means of the previously studied Hamiltonian. For this system we search for the best set of parameters to reproduce the experimentally measured linear conductance and we study the underlying Kondo state evaluating the CNT added entropy and specific heat.

Translation of the abstract (German)

In dieser Doktorarbeit beschäftigen wir uns mit der Beschreibung von Quanten Störstellen Systemen. Zu diesem Zweck nutzen wir im ersten Teil dieser Arbeit den Reduced Density Matrix (RDM) Formalismus und im zweiten Teil die Methode der Density Matrix-Numerical Renormalization Group (DM-NRG).

Owner only: item control page

Download Statistics

More literature (via CORE)

Details

Preview

Export bibliographical data

Abstract (English)

Abstract (English)

Translation of the abstract (German)

Download Statistics

Downloads

More literature (via CORE)

University Library