Experimental Techniques and New Materials F. J. Himpsel

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

E(k) from Angle-Resolved Photoemission States within k B T of the Fermi level E F determine transport, superconductivity, magnetism, electronic phase transitions… Ni  Å   E k EFEF (eV) E, k multidetection: Energy bands on TV

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

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

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

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

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

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 t 1D /t 2D /t 3D New Materials

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 E F de-coupled (in the gap) Atoms locked to the substrate (by covalent bonds) Self-Assembled Nanostructures at Si Surfaces

Most stable silicon surface; >100 atoms are rearranged to minimize broken bonds. Si(111)7x7 Hexagonal fcc (diamond) (eclipsed)(staggered) Adatom (heals 3 broken bonds, adds 1 ) U Si/Si(111)  10  1 eV U Si/SiC(111)  10 0 eV

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

Two-Dimensional Electrons at Surfaces Lattice planes Inversion Layer e - /cm e - /cm 3 Surface State e - /cm e - /cm 3 V(z) n(z) MOSFET Quantum Hall Effect ??? V(z)

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

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)

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

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

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

t 1 /t 2  kxkx 1D/2D Coupling Ratio Tight Binding Model Fermi Surface Data t 1 /t 2 is variable from 10:1 to > 70:1 via the step spacing t2t2 t1t1

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

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

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, (2006)

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

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

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

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

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

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

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

Sanchez-Portal et al. PRL 93, (2004) Calculation Predicts Spin Splitting No magnetic constituents ! Adatoms Step Edge Si-Au Antibonding E (eV) 0 ZB 1x1 Adatoms ZB 2x1 kxkx EFEF 0 Si-Au Bonding Spin-split band is similar to that in photoemission

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

Is it Spin–Splitting ? Spin-orbit splitting:  k Other splittings:  E H Rashba ~ (e z x k) ·  k   k,   

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

 2D Au Chains on Si Au(111) Spin Split Fermi Surfaces 1D kyky kxkx

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

On-going Developments

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

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

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

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

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 ?

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

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