The Materials Computation Center, University of IllinoisDuane Johnson and Richard Martin (PIs), NSF DMR-03-25939 •  www.mcc.uiuc.edu

Spintronics in Coupled Quantum Dots

aJihan Kim, aDmitriy Melnikov, aJ.-P. Leburton,bRichard Martin, and cGuy Austing

University of Illinois at Urbana-Champaign,Departments of aElectrical and Computer Engineering, bDept. of Physics, and

cInstitute for Microstructural Sciences National Research Council of Canada

This work is supported by the Materials Computation Center (UIUC) NSF DMR 03-25939 and ARO Grant No. DAAD 19-01-1-0659 under the DARPA-QUIST program.

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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Triple Quantum Dots: Experimental (w/ G. Austing)

SEM Image of Triple Quantum Dots, G. Austing

• Coupled quantum dots: promising systems for realizing a CNOT gate (quantum computing)

• Entanglement between spin-qubits can be manipulated by external fields: tunable exchange

• Triple quantum dots (TQD) – natural extension from coupled double quantum dots

– Possible applications: solid-state entangler, triple quantum dot charge rectifier, quantum gates

Detector Dot

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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Numerical Approaches

Accuracy is dependent on initial, trial wavefunctions (Error bars)

Result is independent of initial, trial wavefunctions

Requires small amount of memory ( < 1MB)Requires large amount of memory (~500MB – 1G)

No meshDiscretized Mesh (Finite Element Method)

Stochastic simulationDeterministic simulation

Fixed potentialSelf-consistent potential

With magnetic fieldWith magnetic field

Solve Many-body Schrödinger Equation (potential is fixed)*

Solve coupled Poisson and Kohn-Sham equations (EMA)

Variational Monte CarloDensity Functional Theory

*D. Das, L. Zhang, J.P. Leburton, R. Martin previously reported

Drawbacks: convergence (numerical), wrong ground state at weak coupling (physical)

Towards hybrid DFT-VMC approach

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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1-D Potential Energy Profile

x(Ǻ)-1 -0.5 0 0.5 1

x104

me

V0

40

80

120

Barrier Height

eVDensity Functional Theory: Real Potential

Landscape

2-D Potential Energy Profile

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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Triple Quantum Dot Electronic Properties

N = 1N = 2N = 3N = 4

EF = 0 eV

Charging Points

x 10-3

X (μm)0-0.25-0.5 0.50.25

0

Y (

μm

)

-0.1

0.1

Ground-state Electron Densities

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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• Hamiltonian for N electrons

N

i

N

ji ji

iext

i

rr

erV

m

Ace

iH

1

22

)(*2

)(

• General form for Slater-Jastrow wavefunction for N electrons

– Slater Determinants– Jastrow two-body correlation factors

• Trial wavefunction for two electrons

)( 1221122211 rJT 21122211

21122211 Singlet :

Triplet :

N

jiijrJDD )(

VMC Model for Quantum Dots

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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2222222 )(,,)(min*2

1),( iiiiiioiiext yaxyxyaxmyxV

Parabolic Potential Profiles ( a = 20nm, )

x(nm)y(nm)

Ene

rgy(

meV

)VMC - Model Potential for Triple QDs

x(nm), y=0nmE

nerg

y(m

eV)

meV30

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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VMC – Exchange Interaction (Triple Dot, 2 Electrons)

B(T)

J(m

eV

)

Distance(nm)

elec

tron

den

sity

(cm

-3)

Triplet

Distance(nm)

elec

tron

den

sity

(cm

-3)

Distance(nm)

elec

tron

den

sity

(cm

-3)

Distance(nm)

SingletmeV30

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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VMC – Tunable Exchange (Center Dot)

B(T)

sepa

ratio

n(n

m) Tripletse

para

tion(

nm

)

B(T)

Singlet

220

22222 )(,,)(min*2

1),( iiiiiioiiext yaxVyxyaxmyxV

J(m

eV

)

B(T)x(nm), y=0nm

Ene

rgy(

meV

)

Materials Computation Center, NSF DMR-03-25939J.Kim,D.Melnikov,J.-P.Leburton,R.Martin,and G.Austing

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Conclusions

• Quantum dots as artificial molecules: Many-body laboratory

• Computational tools for quantum materials– DFT approach : solve for potentials and electron wavefunction self-

consistently (collaboration w/ Prof. Richard Martin)– VMC approach: solve many-body Schrödinger equation for fixed potential– Next step: VMC → Diffusion Monte Carlo (DMC) w/ Dr. Jeongnim Kim

• Experimental collaboration with Dr. Guy Austing (NRC, Ottawa) (design tools, interpretation of experiments)

• Outreach: Dr. de Sousa (Brazil) Electronic properties of Si nanocrystals (self-consistent DFT solver)