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  1. Transport theory and simulations in hybrid structures: the need for a bottom-up approach in new semiconductor spintronic systems JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Joerg Wünderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, Karel Vyborny, et al Hamburg University Jan Jacob, Bodo Krause-Kyora, et al International Symposium High Performance Computing in Nano-Spintronics Hamburg, November 30th, 2011 Research fueled by:

  2. Transport theory and simulations in hybrid structures:the need for a bottom-up approach in new spintronic systems • Introduction: using the dual personality of the electron • Internal coupling of charge and spin: origin and present use • Spintronic devices and the need to understand them microscopically • Spin injection Hall effect FET: a new paradigm in exploiting SO coupling • Spin based FET: old and new paradigm in charge-spin transport • II. Spin filters in InAs nano-wires • III. A bottom to top approach: from mesoscopic to microscopic • Why is it important to approach the problem from the mesoscopic regime • V. Theoretical tools of the mesoscopic world: • Landauer-Büttiker (coherent regime) • Non-Equilibrium Green’s Function approach: quantum Boltzmann Eq. • Beyond coherent transport: the basic master equation of the non-equilibrium density matrix • VI. Computational Challenges of NEGF approach Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  3. CHARGE Easy to manipulate: Coulomb interaction “Classical” external manipulation of charge & spin SPIN 1/2 Makes the electron antisocial: a fermion = + quantum mechanics E=p2/2m E→ iħ d/dt p→ -iħ d/dr special relativity E2/c2=p2+m2c2 (E=mc2 for p=0) particles/antiparticles & spin Dirac equation The electron: the key character with dual personalities Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  4. Using charge to create a field effect transistor: work horse of information processing >0 Using spin: Pauli exclusion principle and Coulomb repulsion →ferromagnetism work horse of information storage gate Vg substrate insulator D S semiconductor e- What about the internal communication between charge & spin? (spintronics) total wf antisymmetric = orbital wf antisymmetric × spin wf symmetric (aligned) • Robust(can be as strong as bonding in solids) • Strong coupling to magnetic field • (weak fields = anisotropy fields needed • only to reorient macroscopic moment) Using charge and spin in information technology HIGH tunablity of electronic transport properties the key to FET success in processing technology Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  5. Internal communication between spin and charge:spin-orbit coupling interaction This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) p In the rest frame of an electron the electric field generates an effective magnetic field Produces an electric field s • “Impurity” potential V(r) e- • Motion of an electron ∇V Beff (one of the few echoes of relativistic physics in the solid state) Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  6. Internal communication between spin and charge:spin-orbit coupling interaction This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) p s In the rest frame of an electron the electric field generates an effective magnetic field Produces an electric field • “Impurity” potential V(r) e- ∇V • Motion of an electron Beff (one of the few echoes of relativistic physics in the solid state) Consequence #1 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  7. Internal communication between spin and charge:spin-orbit coupling interaction This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) p s In the rest frame of an electron the electric field generates an effective magnetic field Produces an electric field • “Impurity” potential V(r) e- ∇V • Motion of an electron Beff (one of the few echoes of relativistic physics in the solid state) Consequence #2 Mott scattering Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  8. Giant magnetoresistance (GMR) read head - 1997 1992 - dawn of (metallic) spintronics e- e- • Anisotropic magnetoresistance (AMR): In ferromagnets the current is sensitive to the relative direction of magnetization and current direction Fert, Grünberg et al. 1998 × Nobel Price 2007 Fert and Grünberg magnetization High sensitivity, very large effect 30-100% ↑↑ and ↑↓ are almost on and off states: “1” and “0” & magnetic → memory bit current Appreciable sensitivity, simple design, cheap BUT only a 2-8 % effect How spintronics has impacted your life: Metallic spintronics Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  9. What next? The need for basic research Industry has been successful in doubling of transistor numbers on a chip approximately every 18 months (Moore’s law). Although expected to continue for several decades several major challenges will need to be faced. Circuit heat generation is one key limiting factor for scaling device speed Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  10. Transport theory and simulations in hybrid structures:the need for a bottom-up approach in new spintronic systems • Introduction: using the dual personality of the electron • Internal coupling of charge and spin: origin and present use • Spintronic devices and the need to understand them microscopically • Spin injection Hall effect FET: a new paradigm in exploiting SO coupling • Spin based FET: old and new paradigm in charge-spin transport • II. Spin filters in InAs nano-wires • III. A bottom to top approach: from mesoscopic to microscopic • Why is it important to approach the problem from the mesoscopic regime • V. Theoretical tools of the mesoscopic world: • Landauer-Büttiker (coherent regime) • Non-Equilibrium Green’s Function approach: quantum Boltzmann Eq. • Beyond coherent transport: the basic master equation of the non-equilibrium density matrix • VI. Computational Challenges of NEGF approach Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  11. Unfortunately it has not worked : • no reliable detection of spin-polarization in a diagonal transport configuration • No long spin-coherence in a Rashba spin-orbit coupled system (Dyakonov-Perel mechanism) Towards a realistic spin-based non-magnetic FET device Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system? Long standing paradigm: Datta-Das FET Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  12. Use the persistent spin-Helix state and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wunderlich et al 09, 10) Use AHE to measure injected current polarization at the nano-scale electrically (Wunderlich, et al 09, 04) New paradigm using SO coupling: SO not so bad for dephasing Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism). • Can we use SO coupling to manipulate spin AND increase spin-coherence? • Can we detect the spin in a non-destructive way electrically? Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  13. _ _ ky [010] ky [010] α > 0, β = 0 [110] [110] α = 0, β < 0 [110] [110] kx [100] kx [100] Dresselhauss: from the broken inversion symmetry of the material, a bulk property Rashba: from the asymmetry of the confinement in the z-direction Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling • Can we use SO coupling to manipulate spin AND increase spin-coherence? a 2DEG is well described by the effective Hamiltonian: Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  14. _ _ _ ky [010] ky [010] ky [010] α = -β α = 0, β < 0 [110] [110] α > 0, β = 0 [110] [110] [110] [110] kx [100] kx [100] kx [100] Effects of Rashba and Dresselhaus SO coupling Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  15. _ _ [110] [110] Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling For the same distance traveled along [1-10], the spin precesses by exactly the same angle. [110] Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  16. Spin-helix state when α ≠ β In addition we performed MC Boltzmann transport calculations incorporating spin physics For Rashba or Dresselhaus by themselves NO oscillations are present; only and over damped solution exists; i.e. the spin-orbit coupling destroys the phase coherence. There must be TWO competing spin-orbit interactions for the spin to survive!!! Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  17. majority _ _ _ FSO _ FSO I minority InMnAs V “Local” magnetization measurement through the Anomalous Hall Effect Spin dependent “force” deflectslike-spin particles M⊥ ρH=R0B ┴ +4π RsM┴ AHE is does NOT originate from any internal magnetic field created by M⊥; the field would have to be of the order of 100T!!! Simple electrical measurement of out of plane magnetization (or spin polarization ~ n↑-n↓) Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  18. Skew scattering independent of impurity density Vimp(r) (Δso>ħ/τ)or ∝ λ*∇Vimp(r) (Δso<ħ/τ) A ~σ~1/ni Intrinsic deflection B B Side jump scattering E Vimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ) Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure) Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering. independent of impurity density Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. SO coupled quasiparticles Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling. Cartoon of the mechanisms contributing to AHE Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  19. AHE contribution to Spin-injection Hall effect in a 2D gas • Two types of contributions: • S.O. from band structure interacting with the field (external and internal) • Bloch electrons interacting with S.O. part of the disorder Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii) Crepieux et al PRB 01 Nozier et al J. Phys. 79 Lower bound estimate of skew scatt. contribution Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  20. SIHE ↔ Anomalous Hall VL Spin-injection Hall device measurements trans. signal Local Hall voltage changes sign and magnitude along a channel of 6 μm Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  21. T = 250K Further experimental tests of the observed SIHE Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  22. Vb Vg Vb Vg VH x VH I Δx=1μm σ+ SiHE transistor Spin Hall effect transitor: Wunderlich, Irvine, Sinova, Jungwirth, et al, Science 2010 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  23. Vg2 [V] σ- +0.1 0 -0.1 SiHE transistor AND gate σ- 12 6 0 0 3 6 RH2 [Ω] RH1 [Ω] σ- σ- H2 H1 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  24. Next SiHE transistor: all electrical spin FET • Key features: • Spin injection through thin Fe contacts into GaAs • Detection via SHE and Non-Local Hanle effect • Spin current control through charge current bias K. Olejnik, Wunderlich, et al Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  25. Splits an unpolarized current into two oppositely spin-polarized currents A. A. Kiselev and K. W. Kim, Appl. Phys. Lett. 78, 775 (2001); J. Appl. Phys. 94, 4001 (2003). J. I. Ohe, M. Yamamoto, T. Ohtsuki, and J. Nitta, Phys. Rev. B 72, 041308 (2005). M. Yamamoto, T. Ohtsuki, and B. Kramer, Phys. Rev. B 72, 115321 (2005). A. W. Cummings, R. Akis, and D. K. Ferry, Appl. Phys. Lett. 89, 172115 (2006). M. Yamamoto, K. Dittmer, B. Kramer, and T. Ohtsuki, Physica E 32, 462 (2006). Semiconductor spin filters in InAs nanowires Jan Jacob’s group Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg 12

  26. In-plane magnetic fields Detect spin-Hall signal infilter outputs Top-gated spin-filter cascades Single quantum-point contacts Top/Backgate-controlledspin-orbit coupling Ferromagnet-Semiconductor Spin-Valves (together with OSU) Semiconductor spin filters in InAs nanowires Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg 30

  27. Transport theory and simulations in hybrid structures:the need for a bottom-up approach in new spintronic systems • Introduction: using the dual personality of the electron • Internal coupling of charge and spin: origin and present use • Spintronic devices and the need to understand them microscopically • Spin injection Hall effect FET: a new paradigm in exploiting SO coupling • Spin based FET: old and new paradigm in charge-spin transport • II. Spin filters in InAs nano-wires • III. A bottom to top approach: from mesoscopic to microscopic • Why is it important to approach the problem from the mesoscopic regime • V. Theoretical tools of the mesoscopic world: • Landauer-Büttiker (coherent regime) • Non-Equilibrium Green’s Function approach: quantum Boltzmann Eq. • Beyond coherent transport: the basic master equation of the non-equilibrium density matrix • VI. Computational Challenges of NEGF approach Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  28. quantitative modeling of spin-current based devices from bottom up ✓ Semiclassical: Boltzmann-Monte-Carlo (2010) scale ~ 1μ Connection to effective Hamiltonians and boundary conditions of different phenomena Mesoscopic: Non-Equil. Green’s Function (2007) ✓ scale ~ 1nm Microscopic: Ab-initio (tight-binding) Interface effects of spin-injection and bulk spin coherence COMPETING LENGTH SCALES OF THE SAME ORDER Molecular level modeling scale ~ 1Å Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  29. Semiclassical bulk transport theory:Boltzmann “diagonal” transport Electrons are treated as Newtonian pinballs, but having an effective mass and g-factor determined by the band structure and undergo random quantum scattering Dynamics of the occupation number • Very successful for charge transport and micro-device modeling • Key feature: l.h.s. classical – r.h.s. quantum collision term • Main shortcoming: Does not treat systematically inter-band coherence or spin transport • Applicable in the diffusive metallic regime ASSUMES COLLISIONS ARE INSTANTANEOUS AND UNEVENTFUL Sinova 29 International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  30. Semiclassical approach to bulk Hall transport: breakdown of collision assumption Modified Boltzmann Equation: Coordinate shift (Side jump): Golden Rule: Berry curvature: velocity: current: Sinitsyn et al PRB 06 Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  31. E c) Skew scattering b) Side jump scattering a) Intrinsic deflection What is what in the modified Boltzmann treatment Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  32. Quantum mesoscopic transport • When the mean free path is of the same order as the system size then quantum interference effects appear • In the presence of SO coupling bands are mixed: occupation number is not the only thing needed to describe transport • Need to explore the non-equilibrium dynamics of the whole density matrix Nikolic et al 04 NEGF formalism is in a sense the quantum Boltzmann Equation: both the collisions AND dynamics between collisions are treated quantum mechanically Sinova 32 International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  33. WHAT CAN WE ADDRESS FROM THIS MICROSCOPIC (1) What is the effect of the nature of the scattering on the induced spin-currents and spin coherence in general? (2) What is the nature of the spin-current? (3) Can these induced currents lead to strong enough spin-accumulation? (4) Does coherent transport matter? (5) What is the loss of spin-coherence in relation to scattering? (6) Is the effect more readily controlled at the mesoscopic scales? (7) What is the dissipative ratio in spintronic devices analogous to current devices? • Advantages of NEGF approach: • No assumptions on spin-currents • Deals with intrinsic and extrinsic on an equal footing • Multi-band treatment comes out naturally • No assumed length scales • Inelastic processes can be incorporated Limitations: system sizes and extrapolation to the bulk regime Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  34. Uncorrelated electrons injected from left lead. Mesoscopic transport via Landauer-Büttiker Formalism(Coherent limit of the NEGF formalism) Single channel conductance: T transmission probability Sharvin conductance Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  35. Landauer-Büttiker Procedure in a Nutshell (real space) • Calculate the leads self-energies (f-numberelt by the sample): • Compute the sample retarded GF: • Obtain transmission coefficients: Usually known or easily calculable 4. Calculate currents with Büttiker formula: See, e.g., Electronic Transport in Mesos. Systems by Datta Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  36. How to actually compute things: Tight-Binding Approximation Tight-binding lattice Continuous 2DEG Artificial length scale Effective mass Hamiltonian Tight-binding Hamiltonian Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  37. Example: Quantum Point Contact Conductance Conductance of a ballistic 2DEG Experimental evidence of conductance quantization: QPC: Van Wees et al, PRL 60, 848 (1988) Sinova 37 International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  38. Limitations of Landauer-Büttiker • Limited to relatively small systems. • Must rely on finite size scaling to reach bulk values • Limited to coherent transport NEGF formalism advantages • Expresses physical quantities via correlation functions. • Studies non-coherent transport. • Can include the effect of interactions and dissipation gradually • Can make clearer connection to the bulk transport theories However, it still has same size limitation as LB Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  39. Nonequilibrium Green Function Formalism Classical transport: Quantum transport: density matrix distribution function Key correlation function Generalizes the density matrix. Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  40. Electron distribution function Electron correlation function Hole distribution function Hole correlation function Scattering functions Scattering functions Boltzmann vs. NEGF Functions(but not literally; r.h.s. knows about interband coherence) Include phase correlations. Do not take into account phase correlations. Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  41. Connection to semiclassical Boltzmann when looking in real space Using the relation shown and G in real space Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  42. NEGF Algorithm - Interactions 1. Compute self-energies only first iteration 2. Calculate the retarded GF 3. Find the correlation function 4. Calculate interaction self-energy If not 5. Check for convergence 6. Compute physical quantities Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  43. NEGF Algorithm – Molecular Transport 4. Compute the charge density for biased sample: The sample Hamiltonian depends on charge density: 1. Calculate self-energies of the electrodes: 5. Check for convergence: no 2. Calculate the retarded GF: 6. Compute physical quantities: 3. Compute the correlation function: Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  44. eV=0 -eV/2 +eV/2 Nonequilibrium Spin Hall Accumulation in mesoscopic Rashba 2DEG: non-linear transport Spin density (NEGF): PRL 95, 046601 (2005) Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg NEGF Formalism

  45. Transport theory and simulations in hybrid structures:the need for a bottom-up approach in new spintronic systems • Introduction: using the dual personality of the electron • Internal coupling of charge and spin: origin and present use • Spintronic devices and the need to understand them microscopically • Spin injection Hall effect FET: a new paradigm in exploiting SO coupling • Spin based FET: old and new paradigm in charge-spin transport • II. Spin filters in InAs nano-wires • III. A bottom to top approach: from mesoscopic to microscopic • Why is it important to approach the problem from the mesoscopic regime • V. Theoretical tools of the mesoscopic world: • Landauer-Büttiker (coherent regime) • Non-Equilibrium Green’s Function approach: quantum Boltzmann Eq. • Beyond coherent transport: the basic master equation of the non-equilibrium density matrix • VI. Computational Challenges of NEGF approach Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  46. Usuki-transfer matrix method with GPUs (two terminal) Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  47. Key computational challenges The key issue with NEGF for realistic size microscopic calculations is how to best deal with large matrices (both multiplication and inversion) • In order to obtain bulk realistic values one needs to do finite size scaling of more than three small sizes • Can one dynamically deal with sparsity? • Not all eginevectors are created equal - how to select? • 2-terminal vs. multi-terminal? • Conductance (two terminal) vs. G< (much more computationally expensive but contains everything) Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  48. Principal Outside Collaborators Laurens Molenkamp Würzburg Bryan Gallagher U. of Nottingham Gerrit Bauer TU Delft Jan Jacob U. Hamburg Tomas Jungwirth Texas A&M U. Inst. of Phys. ASCR U. of Nottingham Allan MacDonald U of Texas Joerg Wunderlich Cambridge-Hitachi and many others Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  49. Sinova’s group Vivek Amin Texas A&M U. Erin Vehstedt Texas A&M U. H. Gao Texas A&M U. Jacob Gyles Texas A&M U. Oleg Tretiakov (main PI Abanov) Texas A&M U. Xin Liu Texas A&M U. Previous members Liviu Zarbo PD-Texas A&M Univ. Now: PD- ASCR Alexey Kovalev PD-Texas A&M Now: PD-UC Riverside Ewelina Hankiewicz (PD-Texas A&M Univ.) Now: W2-Professor at Würzburg University Nikolai Sinitsyn Texas A&M U. Now: StaffLANL Xiong-Jun Liu Texas A&M U. Now: PD- U. Maryland Mario Borunda Texas A&M Univ. Now: PD-Harvard Univ. Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg

  50. What next? Sinova International Symposium High Performance Computing in Nano-Spintronics, Hamburg