3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3....

12
1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and Tarucha, RPP 64, 701 (2002) Tarucha et al., PRL77, 3613 (1996) Kouwenhoven et al., Science 278, 1788 (1997) rev 120502, dmz

Transcript of 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3....

Page 1: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

1. Introduction

2. Few Electron Dots

3. Double Quantum Dots

4. Kondo Effect

5. Open Dot Experiments

Kouwenhoven, Austing and Tarucha, RPP 64, 701 (2002)Tarucha et al., PRL77, 3613 (1996)Kouwenhoven et al., Science 278, 1788 (1997)

rev 120502, dmz

Page 2: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Few Electron Quantum Dots: Vertical

Kouwenhoven, Austing and Tarucha, RPP 64, 701 (2001)

Page 3: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Few Electron Quantum Dots: Lateral

Ciorga et al., PRB61, R16315 (2000)

Elzerman et al., PRB67, R161308 (2003)similar design: Marcuslab

Chan et al., Nanotech. 15, 609 (2004)Zumbuhl et al., PRL93, 256801 (2004)

Page 4: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Rotation Symmetry and Angular Momentum

Ciorga et al., PRB61, R16315 (2000)Tarucha et al., PRL77, 3613 (1996)

circular symmetry: 2D shell filling circular symmetry broken

Page 5: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Quantum Harmonic Oscillator

harmonic oscillator Hamiltonian

H =p2x2m∗ +

12m

∗ω2x2 +p2y2m∗ +

12m

∗ω2y2

isotropic, circular symmetry: ωx = ωy

anisotropic, no rotation symmetry: ωx 6= ωy

energy levels:Ep,q =

¡p+ 1

2

¢~ωx +

¡q + 1

2

¢~ωy

B. Schuh, J. Phys A: Math. Gen. 18, 803 (1985)

in magnetic field

Page 6: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

2D Periodic Table of Elements

Page 7: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Excitation Spectra of Circular, Few Electron Dots

Page 8: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

radial

angular momentum

Fock-Darwin Energies

Fock-Darwin States: Single Particle Levels

Page 9: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Magnetic Field Transitions

“atomic physics” like experiments not accessible in real atoms!!

exact calculation experiment

Page 10: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Two Electron States

-eVSD

GS

ES

Coulomb interactionsEsinglet B, C >> ES, T

J = ET – ES ~ 0.15meV

note:J <<ET > ES for N=2, B=0

singlet S 1e orbital states

singlet B singlet C3 triplets, T

noninteractingGS

Page 11: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Zero to One Electron Transition

Page 12: 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot Experiments Kouwenhoven, Austing and

Higher Transitions


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Analysis of the Kondo effect in ferromagnetic atomic-sized contacts · 2012. 9. 17. · Kondo effect is the case of a quantum dot connected in series to two metallic leads3,4: When

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