Tunneling processes involving superconductors

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Table of contents

1 Introduction 
1.1 Artificial Atoms and Molecules
1.2 EPR-experiments in solid state
2 Basics 
2.1 Single-Walled Carbon Nanotubes
2.1.1 Band structure
2.1.2 Electron transport in Single-Walled Nanotubes
2.2 Quantum dots and Coulomb blockade
2.2.1 Coulomb blockade at zero bias
2.2.2 Coulomb blockade at finite bias
2.3 Double Quantum dots
2.3.1 Capacitive coupling: The electrostatic model
2.3.2 High interdot tunnel coupling: The molecular state
2.4 BCS-theory and the spin singlet state
2.4.1 The BCS ground state
2.4.2 Quasiparticles and the density of states
2.4.3 Tunneling processes involving superconductors
2.5 Injecting superconducting correlations in a normal conductor: Andreev Reflection
2.5.1 Andreev Reflection at an NS interface
2.5.2 Crossed Andreev Reflection
2.6 Putting the puzzle together: Theoretical description of the beamsplitter
2.6.1 Qualitative Theory and Splitting argument
2.6.2 Methods to obtain the Γ’s
3 Sample preparation and Measurement environment 
3.1 CVD growth
3.2 Lithographical patterning
3.3 Evaporation
3.3.1 Shadow Evaporation
3.3.2 Two-step Process
3.4 Measurement setup
3.4.1 Electronics
3.4.2 Cryogenics
4 Transport in a double quantum dot connected to a superconducting lead 
4.1 Spectroscopy of the double dot
4.1.1 Stability diagram of the sample
4.1.2 Extraction of electrostatic parameters
4.1.3 Testing the NS-junction
4.2 Evidence for splitting Cooper pairs
4.2.1 Measurements along the axis of detuning at zero and finite magnetic field
4.2.2 Unbalanced Anticrossings
4.2.3 Quantitative comparison of theory and experiment
4.3 Nonlinear transport at triple points
5 Discussion and Outlook 
6 Conclusion 
A CVD growth of Single-Walled Carbon Nanotubes 
A.1 Catalyst recipe for Single-Walled Carbon Nanotubes
A.2 Growth process – Paris
A.3 Growth process – Regensburg
B Printed-Circuit-Bord 
C Finding the working point of the beamsplitter 
D Determination of the current going to the superconductor in the side-injection setup