3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3....
Transcript of 3. Double Quantum Dots 4. Kondo Effect 5. Open Dot …...1. Introduction 2. Few Electron Dots 3....
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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
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Few Electron Quantum Dots: Vertical
Kouwenhoven, Austing and Tarucha, RPP 64, 701 (2001)
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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)
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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
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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
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2D Periodic Table of Elements
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Excitation Spectra of Circular, Few Electron Dots
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radial
angular momentum
Fock-Darwin Energies
Fock-Darwin States: Single Particle Levels
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Magnetic Field Transitions
“atomic physics” like experiments not accessible in real atoms!!
exact calculation experiment
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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
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Zero to One Electron Transition
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Higher Transitions