Photoelectron Spectroscopy: Present and Future
F. J. Himpsel
Photoelectron spectroscopy provides the
complete information about electrons in a solid:
All quantum numbers
“Smoking Gun” (P. W. Anderson)
E
kx,y kz
point group
spin
Eel. ϑ,ϕ Ephoton polarization
spin
Electron
Spectrometer
Synchrotron
Radiation
Mott
Detector
Angle-resolved photoemission
Measure intensity I versus E, kx, ky , kz
Fermi surface:
I(kx, ky)
Energy Band:
I(E, kx)
Fermi Surface of a Superlattice on Silicon
Si(111)√21x√21
ky
1 ML Ag +
1/7 ML Au
kx
Model
Crain et al., PR B 66, 205302 (2002)
Energy bands E(k) from Angle-Resolved Photoemission
(eV)
E
4
Nickel
2
EF
0
-2
0.7
-4
0.9
1.1 (Å−1)
E, k multidetection: Energy bands on TV
-6
-8
States within kBT of the Fermi level EF
-10
Γ
K
X
k
determine transport, superconductivity,
magnetism, electronic phase transitions…
Beyond quantum numbers
From peak positions to line shapes
⇒ lifetimes, scattering lengths,
interactions (dressed vs. bare)
• Self-energy:
Σ
• Spectral function:
˜
Im(G)
The Greens function G(A,B) describes the
propagation of an electron from point A to B
Im(Σ) : Lifetime
τ , Scattering Length ℓ
ΔE = ħ/τ ,
Permalloy
Altmann et al.,
PRL 87, 137201 (2001)
Magnetic doping of Ni with Fe
suppresses ℓ via large Im(Σ) .
Δp = ħ/ℓ
Spin-Dependent Lifetimes, Calculated from First Principles
Realistic solids are
complicated !
No simple approximations.
Need data.
Zhukov et al.,
PRL 93, 096401 (2004)
Dressed vs. Bare Electrons
Silicon Surface
E [eV]
Hi-Tc Superconductor
0
Dressed
Bare
Data
- 0 .5
k
Barke et al., PRL 96, 216801 (2006)
Kaminski et al., PRL 86, 1070 (2001)
Dressed
0.0
Find the boson that couples
Bare
-0.5
0
Model
Obtain the electron-phonon coupling λ .
electrons into pairs.
Phonon in Lo-Tc .
What is it in HiTc ?
Spectrometer with E, θ Multidetection
50 x 50 = 2500 Spectra in One Scan !
Lens
Lens
Sample
θ Multidetection
Angle Resolved Mode
Lens focused to ∞
The Next Generation: E,θ,φ Multidetection
Energy
Filter
Time-of flight for E + Imaging for θ,φ
(Scienta, Martin Wolf’s group. Needs short synchrotron pulses.)
New Materials
• Perovskites (Cuprates, Ruthenates, Cobaltates …)
Towards localized, correlated electrons
• Nanostructures (Nanocrystals, Nanowires, Surfaces, …)
New physics in low dimensions
Want Tailored Materials ⇒
Complex Materials
Band Width W
Correlation U/W
Magnetic Coupling J
Dimensionality W1D/W2D/W3D
Case Study: Self-Assembled Nanostructures
at Silicon 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)
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.
Si(111)7x7
as 2DTemplate
for Aluminum
Clusters
One of the two
7x7 triangles is
more reactive.
Jia et al., APL 80,
3186 (2002)
2D Superlattices of Dopants on Si(111)
1 monolayer Ag is
semiconducting:
√3x√3
Add Au as dopant.
Maximum Au doping
of 1/7 monolayer :
√21x√21
Metallic Surface States in 2D
Fermi Surface
e-/atom: 0.0015
Doping by extra Ag atoms
0.012
0.015
0.022
Band Dispersion
Crain et al., PRB 72, 045312 (2005)
0.086
Two-Dimensional Electrons at Surfaces
V(z)
n(z)
Lattice planes
Inversion Layer
1011 e-/cm2
1017 e-/cm3
MOSFET
Quantum Hall Effect
V(z)
Surface State
1014 e-/cm2
1022 e-/cm3
What will happen in 1D ?
n(z)
Physics in One Dimension
• Elegant and simple
• Lowest dimension with translational motion
• Electrons cannot avoid each other
2D,3D
• Electrons avoid each other
1D
• Only collective excitations
• Spin-charge separation
Giamarchi,
Quantum Physics in One Dimension
Photoelectron
ΕF
Hole → Holon + Spinon
"Decoration" of Steps
⇒ 1D Atomic Chains
Clean
Triple step + 7x7 facet
With Gold
1/5 monolayer
Si chain
Si dopant
x-Derivative of the Topography, “ Illumination from the Left ”
Graphitic
honeycomb chain
drives the surface
one-dimensional
Au
Variable
chain
spacing,
coupling
Fermi Surfaces from 2D to 1D
2D
2D +
superlattice
1D
1D/2D Coupling Ratio
t1/t2 ≈ 40 10
t2
Tight Binding Model
t1
Fermi Surface Data
t1/t2 is variable via the step spacing from 10:1 to > 70:1
kx
Fermi Surface
Band Filling
Band Dispersion
Crain et al.,
PRL 90, 176805 (2003)
Total filling is fractional
5/3 e- per chain atom (with spin splitting)
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)
Calculation Predicts
Spin Splitting
E (eV)
Si-Au Antibonding
No magnetic constituents !
Sanchez-Portal et al.
PRL 93, 146803 (2004)
Spin-split band
is similar to that
in photoemission
0
Adatoms
Step Edge
EF
Si-Au Bonding
Adatoms
0
ZB2x1
kx
ZB1x1
Spin-Split Band
Graphitic
Honeycomb
Au
Chain
Si Adatoms
Si(557) - Au
Is it Spin–Splitting ?
HRashba ~ (ez x k) · σ
k → −k , σ → −σ
Spin-orbit splitting: δk
Other splittings: δE
Evidence for Spin–Splitting
• Avoided crossings located left / right for spin-orbit (Rashba) splitting.
• Would be top / bottom for non-magnetic, (anti-)ferromagnetic splittings.
E [eV]
Si(553) - Au
kx [Å−1]
Barke et al., PRL 97, 226405 (2006)
Current Developments
• Spatially resolved
• Time resolved
• Tailored materials
Micro-ARPES
(see Adam Kaminski’s talk, Eli Rotenberg
and the MAESTRO project at the ALS)
Overcome the
size distribution.
Ideally: Look at a
single nano-object.
Narrower size
distribution in a
small spot gives
sharper features.
Example from laser
spectroscopy of selfassembled quantum dots.
Gammon et al.,
APL 67, 2391 (1995)
Obtain the Wave Functions in a Nano-Object
from the Intensity Distribution in k-Space
ψ(r)
Phase from Iterated
Fourier Transform
|ψ(k)|2
Mugarza et al., PR B 67, 0814014(R) (2003)
Can we actually
measure these
orbitals ?
Puzder,…, Galli,
PRL 88, 097401 (2002)