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Spintronics in Coupled Quantum Dots

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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.

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

SEM Image of Triple Quantum Dots, G. Austing

Numerical Approaches

Density Functional Theory

Variational Monte Carlo

Solve coupled Poisson and Kohn-Sham equations (EMA)

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

With magnetic field

With magnetic field

Self-consistent potential

Fixed potential

Deterministic simulation

Stochastic simulation

Discretized Mesh (Finite Element Method)

No mesh

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

Requires small amount of memory ( < 1MB)

Result is independent of initial, trial wavefunctions

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

Drawbacks: convergence (numerical),

wrong ground state at weak coupling (physical)

Towards hybrid DFT-VMC approach

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

Density Functional Theory: Real Potential Landscape

1-D Potential

Energy Profile

2-D Potential

Energy Profile

120

eV

80

meV

40

0

Barrier Height

-1

-0.5

0

0.5

1

x(Ǻ)

x104

Triple Quantum Dot Electronic Properties

Ground-state Electron

Densities

x 10-3

EF = 0 eV

N = 1

0.1

N = 2

Y (μm)

N = 3

0

N = 4

-0.1

-0.5

0.25

0.5

0

-0.25

Charging Points

X (μm)

VMC Model for Quantum Dots

- Hamiltonian for N electrons

- General form for Slater-Jastrow wavefunction for N electrons
- Slater Determinants
- Jastrow two-body correlation factors

- Trial wavefunction for two electrons

Singlet :

Triplet :

Parabolic Potential Profiles ( a = 20nm, )

VMC - Model Potential for Triple QDs

Energy(meV)

Energy(meV)

y(nm)

x(nm)

x(nm), y=0nm

Singlet

Triplet

J(meV)

electron density(cm-3)

Distance(nm)

B(T)

Distance(nm)

electron density(cm-3)

electron density(cm-3)

Distance(nm)

Distance(nm)

Energy(meV)

J(meV)

x(nm), y=0nm

B(T)

separation(nm)

separation(nm)

Singlet

Triplet

B(T)

B(T)

- 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)