conductance through coupled quantum dots

www-f1.ijs.si/~bonca/work.html Hvar, 2005

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


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


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


Double- and multiple- dot structures

Craig et el., Science 304, 565 (2004)

Holleitner et el., Science 297, 70 (2002)


Quantum Dot (Anderson single impurity problem)

d


Quantum Dot

d d+U

d

d+U/2

U


Quantum Dot

dd+U

d

U


Quantum Dot

d

d+U

d

U


Quantum Dot

d

Meir-Wingreen, PRL 68, 2512 (1992)

d+U

d

d+U/2

U


Quantum Dot

dd+U

d

d+U/2

U


Quantum Dot

d

d+U

d

d+U/2

U


Quantum Dot

d

d+U

d

d+U/2 ~ gate voltage

U

=U>>


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).


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)

~

~


Comparison: CPMC,GS,NRG

• CPMC, • GS-variational,• Hartree-Fock:

• NRG:


U<t;Wide-band


Comparison: CPMC,GS,NRG

• CPMC, • GS-variational,• Hartree-Fock:

• NRG:


U>>t;Narrow-band


Side-coupled Double Quantum Dot


Large td


Large td –

Widths of conductance plateaus:Energies on isolated DQD:

1 2


Large td –

Kondo temperatures:

Estimating TK using Scrieffer-Wolf:


Large td –

Adding FM coupling

ES=1

ES=0

-Jad


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


Small td –

Two-stage Kondo effect

Jeff>TK

Jeff

0.25 0.50


Small td –


Jeff~TK

TK

0.25 0.50

TK0


Small td –


Jeff<TK

TK

0.25 0.50

TK0


Small td –


Jeff<TK~T

TK

0.25 0.50 Experimental evidence

Wiel et al., PRL 88, 126803 (2002).


Large td –

Adding FM coupling

Two-stage Kondo effect?

Voja et al., PRB 65, 140405 (2002), Hofstetter,

Schoeller, PRL 88, 016803 (2002),


Three coupled quantum dots

Using CPMC: NCPMC [100,180] Using GS – variational: NGS [1000,2000]


Three coupled QDs 1 2 3

Oguri, Nisikawa,Hewson, cond-mat/0504771


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

conductance through coupled quantum dots

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