Quantum transport in the Kondo correlated quantum dot

다국어 초록 (Multilingual Abstract)

In this thesis, the charge relaxation in an interacting multilevel quantum dot with
the spin exchange coupling and the thermoelectric response of an interacting quan
tum dot coupled with an Majorana bound state (MBS) are investigated. Wilson’s
numerical renormalization group (NRG) method is used for non-perturbative study
of many-body interaction.
The charge relaxation resistance of a multilevel quantum dot is examined for
three regimes: ferromagnetic, antiferromagnetic, and two-stage Kondo regimes. Each
regime has distinctive spin binding energy resulting from the Coulomb interaction
and the spin exchange coupling. By the external voltage source or finite Zeeman
splitting, one can break this spin binding. Then the particle-hole generation accom
panying spin flip is stimulated and the charge relaxation resistance greatly increases.
The thermoelectric conductance of the Kondo dot coupled with a MBS shows
different features according to the Majorana-dot coupling, the Kondo temperature,
and the Majorana overlap. For an ideal infinitely long wire, the thermoelectric con
ductance in the weak-coupling regime has a peak caused by asymmetric anti-Fano
resonance between the Kondo resonance and zero-energy Majorana modes. On the
other hand, the Majorana-dot coupling induces the Zeeman splitting in the strong
coupling regime. For an finite wire, destructive interference between two Majorana
modes occurs, the Kondo peak is restored. An additional peak arises due to the
asymmetry of the restored peak. In strong-coupling regime, the restored peak ex
hibits a non-monotonic behavior with respect to the dot gate.
The outcomes of the Kondo correlation in the quantum transport gives a definite
method to control the charge relaxation resistance drastically and also provide a way
to find the nature of the Majorana physics.

목차 (Table of Contents)

• Contents
• Abstract
• Contents i
• List of Figures v
• 1 Introduction 1
• 2 A brief review of the Kondo effect 9
• 2.1 Kondo effect 9
• 2.2 From the Anderson model to the Kondo model: Kondo effect in a quantum dot 12
• 2.3 The Kondo physics of the double Kondo impurity with the exchange iunteraction 15
• 3 Mesoscopic charge relaxation in a multilevel quantum dot with spin exchange coupling 17
• 3.1 Introduction 17
• 3.2 Model 19
• 3.3 The zero-frequency limit of the charge relaxation resistance without Zeeman splitting ∆Z = 0 26
• 3.4 Finite-frequency relaxation resistance without Zeeman splitting ∆Z = 0. 27
• 3.5 Effect of non-zero Zeeman splitting: ferromagnetic and two-stage Kondo
• regimes 34
• 3.6 Asymmetric enhancement of the relaxation resistance in the antiferro
• magnetic regime 37
• 4 Introduction to Majorana fermions 41
• 4.1 Majorana quasiparticle 41
• 4.2 One-dimensional Kitaev model 43
• 4.3 Realization of effective spinless p-wave superconducting nanowire 46
• 5 Thermoelectric effect in the Kondo dot coupled with a Majorana mode 49
• 5.1 Introduction 49
• 5.2 Model 51
• 5.3 Topological superconducting nanowire without the overlap between two Majorana modes 54
• 5.4 Short topological superconducting nanowire 59
• 5.5 Gate dependence of the thermoelectrical conductance
• 63
• 6 Conclusion 67
• Appendices 69
• A The induced Zeeman splitting by Schrieffer Wolf transformation 71
• B Numerical Renormalization Group 75
• B.1 Continuous representation and logarithmic discretization 76
• B.2 Mapping to a semi-infinite chain and Renormalization group transformation 80
• B.3 Iterative diagonalization and symmetry 84
• B.4 The initial impurity matrices for the numerical calculation 85
• B.4.1 Comparision of the impurity part between Majorana and Dirac case in chapter 5 87
• B.4.2 Matrix representation for ∆Z = 0 case in chapter 3 92
• B.4.3 Matrix representation for ∆Z ̸= 0 case in chapter 3 94
• Bibliography 99
• Acowledgement