Multi-orbital Kondo effect in vertical quantum dot system

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Multi-orbital Kondo effectin vertical quantum
dot system

• Sakano, Rui
• Kawakami, Norio
• Osaka University

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Back ground of my talk
Kondo effect a typical example of electron
correlations
Originally
ltDilute magnetic alloysgt
Resistivity minimum
Less tunable parameters
Recently
ltArtificial systems quantum dot (QD)gt
A lot of tunable parameters
Systematic study- Electron correlations
Kondo effect in QD
D. Goldhaber-Gordon, et al., Nature 391 156 (1998)
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Outline of my talk
1.Brief introduction
Quantum dot
Typical Kondo effect spin Kondo effect
2.Multi-orbital Kondo effect
interplay
orbital
spin
Orbital in quantum dot
2-orbital case
carbon nanotube dot
P. J.-H. Herrero, et al, Nature 434, 484 (2005)
Transport properties
3-orbital case
vertical quantum dot
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Quantum Dot

• introduction

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Quantum dot
Quantum Dot (QD) small lump of semiconductor
ltcharacteristic propertiesgt
Electron confinement to small area
Discrete energy levels
Atom-like properties of QD
Electron correlation phenomena
in QD systems
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Typical Set Up of QDto observe transport
properties
tunneling
lead
Electrons move by tunneling between QD and leads.
gate electrode
To control energy levels in the quantum dot
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Scanning electron microscope image
confinement
electrode
Schottky effect
Quantum dot
GaAs basis
Gate electrode
Lead
D. Goldhaber-Gordon, et al., Nature 391 156 (1998)
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Transport properties
Coulomb Blockade
Schematic energy state
No flow
Coulomb repulsion
Controlling gate
One-Body effect
Many-body effect (Kondo effect)
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Kondo Effect

• introduction

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Spin Kondo effect
Coulomb blockade regime (one-body effect)
Many-body effect
At low temperatures
Spin degrees of freedom
Resonance peak
Remarkable phenomenon -Kondo Effect-
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The experimental results
D. Goldhaber-Gordon, et al., Phys. Rev. Lett. 81,
52255228 (1998)
ltdata pointsgt Experimental data
Coulomb blockade suppresses G.
conductance
At low temperatures
Kondo Effect enhances G.
temperature
The characteristic temperature
Kondo temperatur TK 40mK
very low!
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Magnetic field
Spin degrees of freedom
Spin Kondo effect
Sensitive to Magnetic Fields
experimental
The Conductance monotonically decreases with B.
conductance
Magnetic fields
suppress!
Spin Kondo effect
D. Goldhaber-Gordon, et al., Nature 391 156 (1998)
Bias voltage
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Summary of spin Kondo effect
-important points-
1. Electron Correlations
due to spin degrees of freedom
2. Low temperature phenomena
Kondo temperature in QD 40mK
3. Sensitive to magnetic fields
Magnetic fields suppress conductance.
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Orbital Kondo effect
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Motivation orbital Kondo effect
Recent advance in nano fabrication
to control orbitals in QD!
High
Kondo temperature for Multi-orbital systems
easy to access experimentally!
stimulate
Experimental study
Orbital Kondo effect
Theoretical study
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Orbital Kondo effect
Orbital
New type of Kondo effect
interplay
Spin
Question
What is the essential nature of this Kondo
effect? Is it similar to spin Kondo effect or
different?
Transport properties
System with 2 orbitals - SU(4) Kondo effect
System with 3 orbitals SU(6) Kondo effect
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What is orbital in QD? -vertical quantum dot-
Electron microscope image
Schematic picture
Symmetric shape
characteristic orbitals
S. Tarucha, et al., PRL 77, 3613 (1996)
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Energy state in vertical QD
Fock-Darwin state
Hamiltonian of an electron in QD
Eigen energy
2D harmonic potential
Magnetic field
orbital
Each line
Orbital Kondo effect
Rectangular well
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Orbital -carbon nanotube QD
Special band structure
Symmetrical shape
Degenerate 2 orbitals
spin
2-orbital Kondo effect
C. T. WHITE, et al,. Nature, 393,240 (1998)
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2-orbital Kondo effect
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Theoretical analysis2-orbital Kondo effect
Landauer formula
Tfinite
conductance
T0
conductance
Remarkable!
Kondo temperature
Tfinite
decrease
decrease
Suppression of Kondo effect
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Experimental results2-orbital Kondo effect
Conductance decreases.
conductance
agreement
Kondo temperature
TK7.7K
High!
Magnetic field
Spin Kondo effect
TK40mK
P. J.-H. Herrero, et al, Nature 434, 484 (2005)
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3-orbital Kondo effect
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Energy state in vertical QD
Fock-Darwin state
3 fold orbital state
spin
3 orbital Kondo effect
experimentally
Tarucha group
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3-orbital Kondo effect
T0
Tfinite
conductance
Conductance increase
Conductance maximum
Magnetic field
Tfinite
Suppression of Kondo effect
Our prediction
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Conductance-Finite temperatures-
Self consistent diagram approximation
Conductance Maximum
conductance
Low
High
Magnetic field
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Comparison of the Kondo effects
Spin Kondo effect 2-orbital Kondo effect 3-orbital Kondo effect
Energy splitting Zeeman splitting Orbital splitting Orbital splitting
Conductance T0
Conductance Tfinite decrease decrease
Constant 2e2/h
decrease
increase
maximum
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Summary
Orbital Kondo effect
Interplay
orbital
spin
Experimentally
spin Kondo effect
2-orbital Kondo effect
In the future
Conductance maximum
3-orbital Kondo effect