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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 ) - PowerPoint PPT Presentation
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Angle-resolved
photoemission
( and inverse
photoemission )
measure all quantum
numbers
of an electron in a solid
“Smoking Gun”(P.W. Anderson)
E , kx,y kz , point group , spin
Ekin , ,, h, polarization, spin
Electron Spectromete
r
Synchrotron Radiation
Mott Detector
E(k) from Angle-Resolved Photoemission
States within kBT of the Fermi level EF
determine transport,
superconductivity, magnetism,
electronic phase transitions…
-10
-8
-6
-4
-2
0
2
4
XK
Ni
0.7 0.9 1.1 Å
E
k
EF
(eV)
E, k multidetection: Energy bands on TV
Angle Resolved Mode
Transmission Mode
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, 137201 (2001)
Spin-Dependent Lifetimes, Calculated from First
Principles
*
Realistic solids are
complicated !No simple approximations.
Zhukov et al., PRL 93, 096401 (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 t1D/t2D/t3D
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 EF 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 )
USi/Si(111) 101 eV
USi/SiC(111) 100 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
1011 e-/cm2
1017 e-/cm3
Surface State 1014 e-/cm2
1022 e-/cm3
V(z)
n(z)
n(z)
MOSFETQuantum Hall Effect
???
V(z)
Metallic Surface States in 2D
Doping by extra Ag atomsFermi Surface
Band Dispersion
e-/atom: 0.0015 0.012 0.015 0.022 0.086
Crain et al., PRB 72, 045312 (2005)
2D Superlattices of Dopants on Si(111)
1 monolayer Ag is
semiconducting:
3x3
Add 1/7 monolayer
Au on top (dopant):
21x21
(simplified)
kx
Si(111)21x21
1 ML Ag + 1/7 ML Au
Fermi Surface of a Superlattice
ky
Model using
G21x21
Crain et al., PR B 66, 205302 (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
t1/t2 40 10
kx
1D/2D Coupling Ratio
Tight Binding Model
Fermi Surface Data
t1/t2 is variable from 10:1 to > 70:1 via the step
spacing
t2
t1
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, 176805 (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, 076801 (2006)
Physics in One Dimension
• Elegant and simple
• Lowest dimension with translational motion
• Electrons cannot avoid each other
Hole Holon + Spinon
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
EF
Two Views of Spin Charge Separation
Holon
Hole
Spinon
EF
k
E
Spinon
Holon
Calculation of Spin - Charge Separation
Zacher, Arrigoni, Hanke, Schrieffer, PRB 57, 6370 (1998)
Spinon
Holon
EF =
Crossing at EF
Challenge: Calculate correlations for realistic solids ab initio
vSpinon vF
vHolon vF /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, 096402 (2002), PRB 68, 125111 (2003)
Is there Spin-Charge Separation in Semiconductors ?
Bands remain split at EF
Not Spinon + Holon
Losio et al., PRL 86, 4632 (2001)
Why two half-filled
bands ?
~ two half-filled orbitals
~ two broken bonds
EF
Proposed by
Segovia et al., Nature 402, 504 (1999)
Si(557) - Au
h= 34 eV
E [eV]
Sanchez-Portal et al. PRL 93, 146803 (2004)
Calculation Predicts
Spin Splitting
No magnetic constituents !
Adatoms
Step Edge
Si-Au AntibondingE (eV)
0 ZB1x1
Adatoms
ZB2x1
kx
EF
0 Si-Au Bonding
Spin-split band is similar to that in photoemission
Evidence for Spin–Splitting
E [eV]
kx [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, 226405 (2006)
Si(553) - Au
Extra Level of Complexity: Nanoscale Phase Separation
1 Erwin, PRL 91, 206101 (2003) 2 McChesney et al., Phys. Rev. B 70, 195430 (2004)
Si(111)5x2 -
Au
• 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
Beyond Quantum Numbers:Electron-Phonon Coupling at the Si(111)7x7 Surface
Analogy between Silicon and Hi-Tc Superconductors
En
erg
y [eV]
- 0.5
- 1.0
0
Momentum
77 77K77K
En
erg
y [eV]
- 0.5
- 1.0
0
Momentum
77 77K77K
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
10
0
80
60
40
20 0
550
500
450
400
350
300
250
200
150
100
50
0
0.0
-0.5
Dressed
Bare
Barke et al., PRL 96, 216801 (2006)
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 EF
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, 0814014(R) (2003)
Phase from Iterated FourierTransform with (r) confined
From k to r : Reconstructing a
Wavefunction
from the Intensity Distribution in k-Space(r) |(k)|2