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Spintronics in Coupled Quantum Dots

Spintronics in Coupled Quantum Dots a Jihan Kim, a Dmitriy Melnikov, a J.-P. Leburton, b Richard Martin, and c Guy Austing University of Illinois at Urbana-Champaign, Departments of a Electrical and Computer Engineering, b Dept. of Physics, and

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Spintronics in Coupled Quantum Dots

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  1. 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.

  2. 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 Triple Quantum Dots: Experimental (w/ G. Austing) Detector Dot SEM Image of Triple Quantum Dots, G. Austing

  3. 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

  4. 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

  5. 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)

  6. 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 :

  7. Parabolic Potential Profiles ( a = 20nm, ) VMC - Model Potential for Triple QDs Energy(meV) Energy(meV) y(nm) x(nm) x(nm), y=0nm

  8. VMC – Exchange Interaction (Triple Dot, 2 Electrons) 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)

  9. VMC – Tunable Exchange (Center Dot) Energy(meV) J(meV) x(nm), y=0nm B(T) separation(nm) separation(nm) Singlet Triplet B(T) B(T)

  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)

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