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Orbital Stark Shift of donor-interface states

ε. Oxide-Si-impurity. Orbital Stark Shift of donor-interface states. ε=0. Oxide-Si-impurity. Donor-interface system Smit et al. PRB 68 (2003) Martins et al. PRB 69 (2004) Calderon et al. PRL 96 (2006). Lansbergen, Rahman, GK, LH, SR, Nature Physics, 4, 656 (2008).

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Orbital Stark Shift of donor-interface states

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  1. ε Oxide-Si-impurity Orbital Stark Shift of donor-interface states ε=0 Oxide-Si-impurity Donor-interface system Smit et al. PRB 68 (2003) Martins et al. PRB 69 (2004) Calderon et al. PRL 96 (2006) Lansbergen, Rahman, GK, LH, SR, Nature Physics, 4, 656 (2008)

  2. Orbital Stark Shift of donor-interface states Exp. Measurements Energies w.r.t. ground state (below CB) Transport through donor states • Energies different from a bulk donor (21, 23, 44) • Donor states – depth & field dependent

  3. Orbital Stark Shift of donor-interface states Si:As (Depth 7a0) Si:P (Bulk) • Features found • 3 regimes • Interface effects • anti-crossing • p-manifold • valley-orbit A B C Friesen, PRL 94 (2005) A (Coulomb bound) B (Hybridized) C (Surface bound) Rahman, Lansbergen, GK, LH, SR (Orbital Stark effect theory paper, to be submitted)

  4. Stark Effect in donor-interface well Exp data with TB simulations Where are the exp. points? • Interpretation of Exp. • Indirect observation of symmetry transition • P vs As Donor distinction Lansbergen, Rahman, GK, LH, SR, Nature Physics (2008), IEDM (2008)

  5. Stark Shift of Hyperfine Interaction e Contact HF: ET A(ε) |(ε, r0)|2 n ES => Nuclear spin site => Impurity site oxide Donor D BMB TB ∆A(ε)/A(0) = 2ε2 (bulk) ∆A(ε)/A(0) = (2ε2 + 1ε) (interface) Exp: Bradbury et al., PRL 97, 176404 (2006) Theory: Rahman et al. PRL. 99, 036403 (2007)

  6. Stark Shift of Hyperfine Interaction How good are the theories? Quadratic Stark Coefficients EMT: Friesen, PRL 94, 186403 (2005) Why linear Stark Effect near interfaces? Asymmetry in wf Large Depth: 1st order PT: Even symmetry broken Small Depth: Oxide-Si-impurity Rahman et al. PRL. 99, 036403 (2007)

  7. Hyperfine Map of Donor Wave-functions Usefulness of HF – an example Observables in QM: Hyperfine: ESR Experiments can measure A => Direct measure of WF Si isotopes: 28Si (S=0) 29Si (S=1/2) Application: Experimentally mapping WF deformations (idea: L. Hollenberg) Park, Rahman, Klimeck, Hollenberg (submitted)

  8. Stark Shift of the donor g-factor Zeeman effect: B-field response => g-factor Spin-orbit (LS) interaction: very important in QC g-factor Stark shift: Indirect measure of SO Anisotropic Zeeman Effect ε [010] Si:P

  9. Stark Shift of the donor g-factor Quadratic Stark Shift (bulk): ∆g(ε)/g(0) = 2ε2 Multi-valley g to single-valley g transition in Si (g||-g|_=8e-3) • Conclusions • SO strength • valley-structure • anisotropic Zeeman • single-valley anisotropy • Exp. Magnitude verified Rahman, Park, GK, LH (Gate induced g-factor control, to be submitted)

  10. Vs1 Vb1 Vb2 Vs2 15 nm P P+ P+ 15 nm V=0 V>0 Electrostatic gating of single donors Nano-TCAD+TB E2 E2 E2 E2 E2 E1 E1 E1 E1 E1 Vs1=0.05V Vs1=0.1V Vs1=0.4V Vs1=0.0V Vs1=0.3V

  11. Coherent Tunneling Adiabatic Passage (CTAP) • Purpose (NEMO-CTAP): • Relax assumptions • Real solid-state system: bands, interfaces, excited states, gate-cross talk, realistic donor models • Does the adiabatic path exist ? Quantum Info Transport Hollenberg et al., PRB 74 (2006) • Solid-state analogue of STIRAP (Quantum Optics), Greentree et al., PRB 70 (2004) • Molecular states: no middle donor occupation • Pathways in Eigen-space connecting end states • Spin state transport • Many-donor chain: Less gating, more robust

  12. Atomistic simulations of CTAP3 |Ψ2|2 at various voltages Left localized No population at center donor any time Barrier gate modulation Middle stage Right localized Anti-crossing gap => tunneling times Rahman, Park, GK, LH (Atomistic simulations of CTAP, in prep.)

  13. B S P+ P0 Donor Based Charge Qubits Molecular States TCAD Gate Sensitivity to impurity positioning • Molecular states of P2+ encode info • Proposal: Hollenberg • EMT work: X. Hu, B. Koiller, Das Sarma • Tunnel Coupling: 12 = E2 - E1 • Excited states ignored so far: 23 = E3 – E2 TB result similar to EMT

  14. Control of Charge Qubits Molecular Spectrum • Goal: • Establish limiting conditions for operation • Characterize gate control • Explore design parameter space Surface Gate Control • Some Findings • R > 8 nm • Smooth Control • Surface Ionization • Saturated regime • 12 = 23

  15. Surface Gate Control of Charge Qubits Wf 1 Wf 2 Saturation V=0 Ionization V=0.2 Linear Bonding V=-0.2 Wf 1 Wf 2 V=-0.5 V=0.5

  16. e e Many-body Interactions in Donor Qubits • Kane Qubit: Two qubit interaction • Exchange coupling J between donors • Modify WF overlap by gate voltage 2e Hamiltonian Koiller, Hu, Das Sarma, PRL 88, No 2 (2002) P+ P+ R=|R2-R1| • Known facts: • J oscillates with R (Koiller) • SiGe strain can reduce oscillations (conditionally) (Koiller) • Gate control smooth (mostly) – Wellard, Hollenberg • A BMB (Wellard) work showed reduced oscillatons. • Goal: • TB wfs, extended band structure, VO interaction • Beyond Heitler-London (CI) • Effect of strain, interfaces, gates • Other systems: spin-measurement

  17. Vb Vb Vb P 2P P L Dot 2 electron system R Dot Exchange Interaction in Heitler-London Formalism HL valid for “large” donor separations Basis: Many-body wfs must be anti-symmetric w.r.t. interchange of r and s Singlet: Triplet: Voltage Controllability Problem. TB Similar result in EMT: Wellard et al., J. Phys.: Condens. Matter 16 5697–5704 (2004).

  18. Conf. 1 Conf. 2 Conf. 3 Conf. 4 Conf. 5 Conf. 6 Exchange Interaction in FCI Formalism (on-going) • Example: 4 states • 4 choose 2 Many Body configurations • 6 x 6 CI Hamiltonian • Possible Future Work with CI • P-P Molecular Spectrum • D- State of P: Charging Energy • Donor-Interface 2e problem (spin read-out prop. by Kane) New goal: Refine HL by including spin, HM states (TCI)

  19. Objective: Study Stark Shift of hyperfine coupling Compare with experiment, BMB & EMT Investigate interface effects Establish the physics of quadratic and linear Stark coefficients Approach: Use 3.5 M atomistic domain P impurity under E-fields TB approach optimized for P donors Vary impurity depth from interface Solve the 20 band spin Hamiltonian by parallel Lanczos algorithm Results / Impact: Quadratic Stark coefficient from TB, BMB & experiment agree well EMT estimate differs by an order of magnitude Proximity of impurity to interface produces significant linear Stark effect Hyperfine Stark Effect of P-Impurities wavefunction change with E field Hyperfine coupling in E field / depths Quadratic Stark Coefficients Rahman et al. PRL. 99, 036403 (2007)

  20. Hyperfine maps of donor wave functions • Challenge / Objective: • Can a single impurity donor wavefunction(wf) be experimentally mapped? • Approach: • Indirectly probe wfs by measuring Hyperfine tensors (idea: L. Hollenberg). • Use Si-29 as a single probe atom or a sample of probe atoms • Calculate donor wfs in realistic geometries and electric fields • Propose experiment:Distort wf by electric fields and interfaces => distort HF => measure HF based on lattice symmetries=> map the wavefunction • Results / Impact: • Probe local values of WF instead of global expectation values • Demonstrated distortion of the WF through its hyperfine map • Verified feasibility of detecting such distortions. 28Si host, 29Si probe Fermi term Dipolar term Park, Rahman, GK, LH, Rogge (paper submitted)

  21. Gate control of donor g-factors and dimensional isotropy transition Objective: Investigate Stark Shift of the donor g-factor. g-factor shift for interface-donor system. Probes spin-orbit effects with E-fields and symmetry transition. Relative orientations of B and E field. Approach: The 20 band nearest neighbor sp3d5s* spin model captures SO interaction of the host. Same atom p-orbital SO correction g-factor obtained from L and S operators. Donor wfs with E-field are obtained from NEMO Results / Impact: Quadratic trend with E-field for bulk donors. Stark parameter larger in Ge and GaAs Anisotropic Zeeman effect – E and B field Dimensional transition- multi-valley to single valley g-factors. Exp. Quadratic coef. matches in magnitude. Si:P Rahman, Park, GK, LH (to be submitted)

  22. Coherent Tunneling Adiabatic Passage (CTAP) Objective: Investigate CTAP in realistic setting. Include Si full band-structure, TCAD gates, interfaces, excited states, cross-talk. Verify that adiabatic path exists: 3 donor device. Approach: TCAD gates coupled with a 3 donor TB. Hamiltonian: obtain molecular states in the solid state. Simulate 3-4 M atoms for a realistic device. Compute time of 4-5 hours on 40 procs. Fine tune gate voltages to explore the CTAP. regime. Results / Impact: Demonstrated that the CTAP regime exists for a 3 donor test device. Verification of results (under relaxed assumptions) CTAP despite noisy solid-state environment. Developed the framework to guide future CTAP expt. Rahman, Park, GK, LH ( to be submitted)

  23. Objective: Control & design issues: donor depths, separation, gate placement. Feasible S and B gate regimes. Effect of excited states: charge state superposition. Approach: S and B gates - TCAD potentials Empirical Donor model + TB+ TCAD: bound molecular states. Lanczos + Block Lanczos solver Results: Smooth voltage control excited states at higher bias mingle with operation. Placement of S and B gates important relative to donors. Comparison with EMT RR, SHP, GK, LH (to be submitted) Charge qubit control Molecular Spectrum + Tunnel barriers Surface gate response of tunnel barriers

  24. D- Modeling for As/P Donor Objective: Obtain 2e binding energy of donors with E-fields and donor depths: important in spin-dependent tunneling and measurement. D- ground and excited states : Analyze measured Coulomb diamonds from Transport Spectroscopy measurements. Approach: 1st approximation: SCF Hartree method. Use a domain of 1.4 M atoms with 1 donor. SCF: 1. Obtain wf from NEMO 2. Calculate electron density and Coulomb repulsion potential 3. Repeat NEMO with the new potential. 4. Stop when D- energy has converged. On-going: D- from configuration interaction Results: D- energy for a bulk donor within 2 meV from measured value. D- vs. Depth & field calculations. Explains charging energy of some samples Screening likely to play a role. D-, D0 vs E D0 D7a0 -45.6 D- D- vs charging energy -4 Ec comparison Rahman, Arjan, Park, GK, LH, Rogge (in prep)

  25. Objective: Investigate gate control of exchange(vs EMT) Reconfirm controllability issues (from BMB) Treatment of interfaces & strain From Heitler London to Full CI Approach: atomistic basis for exchange calculations orbital interactions for short distances Interpolate TCAD potential on atomistic lattice Heitler-London scaled and tested for 4 M atoms removing previous computational bottlenecks. FCI is still a computational challenge Results / Impact: Similar exchange trends obtained as BMB Controllability issues at some specific angular separations verified Magnitude an order less from EMT Basis functions for short range interactions? Control of exchange for adjacent qubits J(V) for various impurity separations along [100] Sensitivity of J(V) to donor placement

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