Conductance through coupled quantum dots
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Transcript of Conductance through coupled quantum dots
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J. BončaJ. BončaPhysics Department, FMF, University of Physics Department, FMF, University of
Ljubljana, Ljubljana,
J. Stefan Institute, Ljubljana, SLOVENIAJ. Stefan Institute, Ljubljana, SLOVENIA
Conductance through coupled quantum dots
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Collaborators:
R. Žitko, J. Stefan Inst., Ljubljana, Slovenia
A.Ramšak and T. Rejec, FMF, Physics dept., University of Ljubljana and J. Stefan Inst., Ljubljana, Slovenia
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Experimental motivation
Single QD: using three different methods: NRG, CPMC and GS – accurate results in a wide parameter regime
DQD system: Large td: Kondo regimes for odd DQD occupancy Small td: Two-stage Kondo regime Adding FM coupling
Three QD’s: Good agreement between CPMC and GS. Two regimes
t’’>: three peaks in G() due to 3 molecular levels t’’<: a single peak in G() of width ~ U
Introduction
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Double- and multiple- dot structures
Craig et el., Science 304, 565 (2004)
Holleitner et el., Science 297, 70 (2002)
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Quantum Dot (Anderson single impurity problem)
d
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Quantum Dot
d d+U
d
d+U/2
U
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Quantum Dot
dd+U
d
U
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Quantum Dot
d
d+U
d
U
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Quantum Dot
d
d+U
d
U
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Quantum Dot
d
d+U
d
U
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Quantum Dot
d
d+U
d
U
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Quantum Dot
d
d+U
d
U
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Quantum Dot
d
Meir-Wingreen, PRL 68, 2512 (1992)
d+U
d
d+U/2
U
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Quantum Dot
dd+U
d
d+U/2
U
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Quantum Dot
d
d+U
d
d+U/2
U
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Quantum Dot
d
d+U
d
d+U/2
U
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Quantum Dot
d
d+U
d
d+U/2
U
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Quantum Dot
d
d+U
d
d+U/2
U
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Quantum Dot
d
d+U
d
d+U/2 ~ gate voltage
U
=U>>
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Three alternative methods:
Constrained Path Monte Carlo method (CPMC), Zhang, Carlson and Gubernatis, PRL 74 ,3652 (1995);PRB 59, 12788 (1999).
Projection – variational metod (GS), Schonhammer, Z. Phys. B 21, 389 (1975); PRB 13, 4336 (1976), Gunnarson and Shonhammer, PRB 31, 4185 (1985), Rejec and Ramšak, PRB 68, 035342 (2003).
Numerical Renormalization Group using Reduced Density Matrix (NRG), Krishna-murthy, Wilkins and Wilson, PRB 21, 1003 (1980); Costi, Hewson and Zlatić, J. Phys.: Condens. Matter 6, 2519, (1994); Hofstetter, PRL 85, 1508 (2000).
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How to obtain G from GS properties:
CPMC and GS are zero-temperature methods Ground state energy
Conditions: System is a Fermi liquid
N-(noninteracting) sites, N ∞
G0=2e2/h
Rejec, Ramšak, PRB 68, 035342 (2003)
~
~
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Comparison: CPMC,GS,NRG
• CPMC, • GS-variational,• Hartree-Fock:
• NRG:
Meir-Wingreen, PRL 68, 2512 (1992)
U<t;Wide-band
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Comparison: CPMC,GS,NRG
• CPMC, • GS-variational,• Hartree-Fock:
• NRG:
Meir-Wingreen, PRL 68, 2512 (1992)
U>>t;Narrow-band
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Side-coupled Double Quantum Dot
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Large td
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Large td –
Widths of conductance plateaus:Energies on isolated DQD:
1 2
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Large td –
Kondo temperatures:
Estimating TK using Scrieffer-Wolf:
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Large td –
Kondo temperatures:
Estimating TK using Scrieffer-Wolf:
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Large td –
Adding FM coupling
ES=1
ES=0
-Jad
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Small td – Two-stage Kondo effect
Jeff<TK:Two Kondo temperatures:
TK and TK0
TKTK0
Jeff<TK
Vojta et al., PRB 65, 140405 (2002); Hofstetter, Schoeller, PRL 88, 016803 (2002), Cornaglia and Grempel, PRB 71, 075305 (2005), Wiel et al., PRL 88, 126803 (2002).
Two energy scales: Jeff=4td2/U, TK
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Small td –
Two-stage Kondo effect
Jeff>TK
Jeff
0.25 0.50
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Small td –
Two-stage Kondo effect
Jeff~TK
TK
0.25 0.50
TK0
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Small td –
Two-stage Kondo effect
Jeff<TK
TK
0.25 0.50
TK0
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Small td –
Two-stage Kondo effect
Jeff<TK~T
TK
0.25 0.50 Experimental evidence
Wiel et al., PRL 88, 126803 (2002).
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Large td –
Adding FM coupling
Two-stage Kondo effect?
Voja et al., PRB 65, 140405 (2002), Hofstetter,
Schoeller, PRL 88, 016803 (2002),
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Three coupled quantum dots
Using CPMC: NCPMC [100,180] Using GS – variational: NGS [1000,2000]
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Three coupled QDs 1 2 3
Oguri, Nisikawa,Hewson, cond-mat/0504771
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Using three different methods: NRG, CPMC and GS – accurate results in a wide parameter regime
DQD system: Large td: Kondo regimes for odd DQD occupancy
(analytical expressions for TK and widh G()) Small td: Two-stage Kondo regime (analytical
expressions for TK0)
Three QD’s: Good agreement between CPMC and GS. Two regimes
t’’>: three peaks in G() due to 3 molecular levels t’’<: a single peak in G() of width ~ U
Conclusions