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Experimental Techniques and New Materials F. J. Himpsel

Experimental Techniques and New Materials F. J. Himpsel. E , k x,y k z , point group , spin E kin ,  ,  , h  , polarization, spin. Electron Spectrometer. Synchrotron Radiation. Mott Detector. Angle-resolved photoemission ( and inverse photoemission )

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Experimental Techniques and New Materials F. J. Himpsel

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  1. Experimental Techniques and NewMaterials F. J. Himpsel

  2. E , kx,y kz , point group, spin Ekin , ,,h, polarization,spin Electron Spectrometer Synchrotron Radiation Mott Detector Angle-resolved photoemission (and inverse photoemission) measure all quantum numbers of an electron in a solid “Smoking Gun” (P.W. Anderson)

  3. E(k) from Angle-Resolved Photoemission (eV) E Ni EF (Å-1) 0.7 0.9 1.1 E,kmultidetection: Energy bands on TV States withinkBTof the Fermi levelEFdetermine transport, superconductivity, magnetism, electronic phase transitions… k

  4. Spectrometer with E,x-Multidetection 50x50 = 2500 Spectra in One Scan !

  5. Lens focused to  Energy Filter x-Multidetection The Next Generation: 3D, with E,, - Multidetection (2D + Time of Flight for E)

  6. Self-energy:  • Spectral function: Im(G) • Greens function G • (e propagator in real space) Beyond quantum numbers: From peak positions to line shapes  lifetimes, scattering lengths, …

  7. Im(): E=ħ/, p=ħ/ℓ , =Lifetime , ℓ =Scattering Length Fe doped Magnetic doping of Ni with Fe suppresses ℓvia large Im(). Altmann et al., PRL 87, 137201 (2001)

  8. Spin-Dependent Lifetimes, Calculated from First Principles Realistic solids are complicated! No simple approximations. Zhukov et al., PRL 93, 096401 (2004) *

  9. New Materials • Perovskites (Cuprates, Ruthenates, Cobaltates …) • Towards localized, correlated electrons • Nanostructures (Nanocrystals, Nanowires, Surfaces, …) • New physics in low dimensions • Want Tunability  Complex Materials • Correlation U/W • Magnetic Coupling J • Dimensionality t1D/t2D/t3D

  10. Self-Assembled Nanostructures at Si Surfaces • Atomic precision • Achieved by self-assembly (<10 nm) • Reconstructed surface as template • Si(111)7x7 rearranges >100 atoms (to heal broken bonds) • Steps produce 1D atom chains (the ultimate nanowires) • Eliminate coupling to the bulk • Electrons at EF de-coupled (in the gap) • Atoms locked to the substrate (by covalent bonds)

  11. Si(111)7x7 USi/Si(111) 101 eV USi/SiC(111) 100 eV Hexagonal fcc (diamond) (eclipsed) (staggered) Adatom (heals 3 broken bonds, adds 1) Most stable silicon surface; >100 atoms are rearranged to minimize broken bonds.

  12. Si(111)7x7 as 2DTemplate for Aluminum Clusters One of the two 7x7 triangles is more reactive. Jia et al., APL 80, 3186 (2002)

  13. Two-Dimensional Electrons at Surfaces Lattice planes V(z) Inversion Layer 1011 e-/cm2 1017 e-/cm3 n(z) MOSFET Quantum Hall Effect V(z) Surface State 1014 e-/cm2 1022 e-/cm3 ??? n(z)

  14. Metallic Surface States in 2D Doping by extra Ag atoms Fermi Surface e-/atom: 0.0015 0.012 0.015 0.022 0.086 Band Dispersion Crain et al., PRB 72, 045312 (2005)

  15. 2D Superlattices of Dopants on Si(111) 1 monolayer Ag is semiconducting: 3x3 Add 1/7 monolayer Au on top (dopant): 21x21 (simplified)

  16. Fermi Surface of a Superlattice Si(111)21x21 1 ML Ag + 1/7 ML Au ky kx Model using G21x21 Crain et al., PR B 66, 205302 (2002)

  17. Si chain Si dopant One-Dimensional Electrons at Surfaces Atom Chains via Step Decoration" Clean Triple step + 7x7 facet With Gold 1/5 monolayer x-Derivative of the topography (illuminated from the left)

  18. Fermi Surfaces from 2D to 1D 2D 2D + super-lattice 1D

  19. kx 1D/2D Coupling Ratio t2 t1/t2  40 10 t1 Tight Binding Model Fermi Surface Data t1/t2is variable from10:1to>70:1 via the step spacing

  20. Graphitic ribbon (honeycomb chain) drives the surface one-dimensional Au Tune chain coupling via chain spacing

  21. Band Filling Fermi Surface Band Dispersion Total filling isfractional 8/3 e-per chain atom (spins paired) 5/3 e-per chain atom (spin split) Crain et al., PRL 90, 176805 (2003)

  22. Fractional Charge at a 3x1 Phase Slip (End of a Chain Segment) Seen for 2x1 (polyacetylene): Su, Schrieffer, Heeger PR B 22, 2099 (1980) Predicted for 3x1: Su, Schrieffer PRL 46, 738 (1981) Suggested for Si(553)3x1-Au: Snijders et al. PRL 96, 076801 (2006)

  23. Physics in One Dimension • Elegant and simple • Lowest dimension with translational motion • Electrons cannot avoid each other

  24. 2D,3D • Electrons avoid each other • 1D • Only collective excitations • Spin-charge separation Giamarchi, Quantum Physics in One Dimension Photo- electron EF HoleHolon+Spinon

  25. Hole E EF Spinon Holon k Holon Spinon Two Views of Spin Charge Separation Delocalized e- Localized e- Tomonaga-Luttinger Model Hubbard, t-J Models • Different velocities for spin and charge • Holon and spinon bands cross at EF

  26. EF = Crossing at EF Spinon Holon Zacher, Arrigoni, Hanke, Schrieffer, PRB 57, 6370 (1998) Calculation of Spin - Charge Separation vSpinon vF vHolon vF /g g<1 Needs energy scale Challenge: Calculate correlations for realistic solids ab initio

  27. Spin-Charge Separation in TTF-TCNQ (1D Organic) Localized, highly correlated electrons enhance spinon/holon splitting Claessen et al., PRL 88, 096402 (2002), PRB 68, 125111 (2003)

  28. Spin-Charge Separation in a Cuprate Insulator Kim et al., Nature Physics 2, 397 (2006)

  29. EF Is there Spin-Charge Separation in Semiconductors ? Si(557)-Au Proposed by Segovia et al., Nature 402, 504 (1999) h=34eV Bands remain split at EF  Not Spinon + Holon E[eV] Losio et al., PRL 86, 4632 (2001) Why two half-filled bands? ~ two half-filled orbitals ~ two broken bonds

  30. Calculation Predicts Spin Splitting No magnetic constituents! E(eV) Si-Au Antibonding Adatoms Sanchez-Portal et al. PRL 93, 146803 (2004) Spin-split band is similar to that in photoemission Step Edge EF Si-Au Bonding 0 Adatoms kx 0 ZB2x1 ZB1x1

  31. Graphitic Honeycomb Chain Si Adatoms Au Spin-Split Orbitals: Broken Au-Si Backbonds Si(557)-Au

  32. Is it Spin–Splitting ? HRashba ~ (ez x k) ·  kk ,  Spin-orbit splitting:k Other splittings:E

  33. Evidence for Spin–Splitting • Avoided crossings located left/right for spin-orbit (Rashba) splitting. • Would betop/bottom for non-magnetic, (anti-)ferromagnetic splittings. E [eV] Si(553)-Au kx [Å−1] Barke et al., PRL 97, 226405 (2006)

  34. Spin Split Fermi Surfaces 2D Au(111) 1D Au Chains on Si ky  kx

  35. Doped and undoped segments (1D version of“stripes”) • gap! metallic • Competition between optimum doping1 (5x8) and Fermi surface nesting2 (5x4) • Compromise: 50/50 filled/empty (5x4) sections Extra Level of Complexity: Nanoscale Phase Separation Si(111)5x2-Au 1 Erwin, PRL 91, 206101 (2003) 2 McChesney et al., Phys. Rev. B 70, 195430 (2004)

  36. On-going Developments

  37. 0.0 -0.5 Beyond Quantum Numbers: Electron-Phonon Coupling at the Si(111)7x7 Surface Analogy between Silicon and Hi-Tc Superconductors Dressed Bare Barke et al., PRL 96, 216801 (2006) Kaminski et al, PRL 86, 1070 (2001) • Specific mode at 70meV (from EELS) • Electron and phonon both at theadatom • Coupling strength  as the only parameter

  38. Two-photon photoemission Filled  Empty Static  Dynamic Rügheimer et al., PRB 75, 121401(R) (2007)

  39. Micro-Spectroscopy Overcoming the size distribution of quantum dots Gammon et al., Appl. Phys. Lett. 67, 2391 (1995)

  40. Fourier Transform from Real Space to k-Space Nanostructures demand high k-resolution (small BZ). Easier to work in real space via STS. dI/dV at EF Real space |(r)|2 Fermi surface k- space |(k)|2 Philip Hofmann (Bi surface) Seamus Davis (Cuprates)

  41. Are Photoemission and Scanning Tunneling Spectroscopy Measuring the Same Quantity? • Photoemission essentially measures the Greens function G. • Fourier transform STS involves G and T, which describes • back-reflection from a defect. Defects are needed to see • standing waves. • How does the Bardeen tunneling formula relate to photoemission?

  42. From k to r: Reconstructing a Wavefunction from the Intensity Distribution in k-Space (r) |(k)|2 Phase from Iterated Fourier Transform with (r) confined Mugarza et al., PR B 67, 0814014(R) (2003)

  43. Challenges: • Tunable solids  Complex solids •  Need realistic calculations • Is it possible to combine realistic calculations • with strong correlations? • (Without adjustable parameters U, t, J, …)

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