Optically mapping the electronic structure of coupled quantum dots
Spintronics in Coupled Quantum Dots
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Transcript of Spintronics in Coupled Quantum Dots
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
2
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
3
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
5
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
7
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
10
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)