Transcript Experimental Techniques and New Materials - Nano

Experimental Techniques and New Materials
F. J. Himpsel
Angle-resolved photoemission
( and inverse photoemission )
“Smoking Gun”
(P.W. Anderson)
measure all quantum numbers
of an electron in a solid
E , kx,y kz , point group , spin
Ekin , ,, h, polarization, spin
Electron
Spectrometer
Synchrotron
Radiation
Mott
Detector
E(k) from Angle-Resolved Photoemission
(eV)
E
4
Ni
2
EF
0
-2
0.7
0.9
1.1
(Å-1)
E, k multidetection: Energy bands on TV
-4
-6
-8
States within kBT of the Fermi level EF
-10

K
X
k
determine transport, superconductivity,
magnetism, electronic phase transitions…
Spectrometer with E, x - Multidetection
50 x 50 = 2500 Spectra in One Scan !
Lens
Lens
S
x - Multidetection
Angle Resolved Mode
Lens focused to 
The Next Generation:
3D, with E,, - Multidetection
( 2D + Time of Flight for E )
Energy
Filter
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)
Im() : E = ħ/ , p = ħ/ℓ ,
Length
 = Lifetime , ℓ = Scattering
Fe doped
Altmann et al.,
PRL 87, 137201 (2001)
Magnetic doping of Ni with Fe
suppresses ℓ via large Im() .
Spin-Dependent Lifetimes, Calculated from First Principles
Realistic solids are
complicated !
No simple approximations.
Zhukov et al.,
PRL 93, 096401 (2004)
*
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
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)
Si(111)7x7
USi/Si(111)  10-1 eV
USi/SiC(111)  100 eV
Hexagonal
(eclipsed)
fcc (diamond)
(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)
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
???
n(z)
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
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)
Fermi Surface of a Superlattice
Si(111)21x21
ky
1 ML Ag +
1/7 ML Au
kx
Model using
G21x21
Crain et al., PR B 66, 205302 (2002)
One-Dimensional Electrons at Surfaces
Atom Chains via
Step Decoration"
Clean
Triple step + 7x7 facet
With Gold
1/5 monolayer
Si chain
Si dopant
x-Derivative of the topography (illuminated from the left)
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 from 10:1 to > 70:1 via the step spacing
kx
Graphitic ribbon
(honeycomb chain)
drives the surface
one-dimensional
Au
Tune chain coupling
via chain spacing
Fermi Surface
Band Filling
Band Dispersion
Crain et al.,
PRL 90, 176805 (2003)
Total filling is fractional
8/3 e- per chain atom (spins paired)
5/3 e- per chain atom (spin split)
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
2D,3D
• Electrons avoid each other
1D
• Only collective excitations
• Spin-charge separation
Giamarchi,
Quantum Physics in One Dimension
Photoelectron
EF
Hole  Holon + Spinon
Two Views of Spin Charge Separation
Delocalized e-
Localized e-
Tomonaga-Luttinger Model
Hubbard, t-J Models
Hole
E
EF
Spinon
Holon
k
Holon
• Different velocities for spin and charge
• Holon and spinon bands cross at EF
Spinon
Calculation of Spin - Charge Separation
vSpinon  vF
vHolon  vF /g
g<1
EF =
Spinon
Holon
Crossing at EF
Zacher, Arrigoni, Hanke, Schrieffer,
PRB 57, 6370 (1998)
Needs energy scale
Challenge: Calculate correlations for realistic solids ab initio
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)
Spin-Charge Separation in a Cuprate Insulator
Kim et al.,
Nature Physics 2, 397 (2006)
Is there Spin-Charge Separation in Semiconductors ?
Si(557) - Au
Proposed by
Segovia et al., Nature 402, 504 (1999)
h = 34 eV
Bands remain split at EF
 Not Spinon + Holon
E [eV]
EF
Losio et al., PRL 86, 4632 (2001)
Why two half-filled bands ?
~ two half-filled orbitals
~ two broken bonds
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 Orbitals: Broken Au-Si Backbonds
Graphitic
Honeycomb Au
Chain
Si Adatoms
Si(557) - Au
Is it Spin–Splitting ?
HRashba ~ (ez x k) · 
k  -k ,   -
Spin-orbit splitting: k
Other splittings: E
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)
Spin Split Fermi Surfaces
2D
1D
Au(111)
Au Chains on Si
ky

kx
Extra Level of Complexity: Nanoscale Phase Separation
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:
1 Erwin,
50/50 filled/empty (5x4) sections
PRL 91, 206101 (2003)
2 McChesney
et al., Phys. Rev. B 70, 195430 (2004)
On-going
Developments
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)
0.0
• Specific mode at 70meV (from EELS)
• Electron and phonon both at the adatom
• Coupling strength  as the only parameter
-0.5
Two-photon photoemission
Filled  Empty
Static  Dynamic
Rügheimer et al., PRB 75, 121401(R) (2007)
Micro-Spectroscopy
Overcoming the
size distribution
of quantum dots
Gammon et al.,
Appl. Phys. Lett. 67,
2391 (1995)
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)
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 ?
From k to r : Reconstructing a Wavefunction
from the Intensity Distribution in k-Space
(r)
Phase from Iterated Fourier
Transform with (r) confined
|(k)|2
Mugarza et al., PR B 67, 0814014(R) (2003)
Challenges:
• Tunable solids  Complex solids
 Need realistic calculations
• Is it possible to combine realistic calculations
with strong correlations ?
(Without adjustable parameters U, t, J, …)