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 , 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

Spectrometer with E, x -

Multidetection

50 x 50 = 2500 Spectra in One Scan !

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

2D

Fermi Surfaces from 2D to 1D

2D + super

-lattic

e

1D

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)

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 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

Si

AdatomsAu

GraphiticHoneycom

b Chain

Spin-Split Orbitals: Broken Au-Si Backbonds

Si(557) - Au

Is it Spin–Splitting ?

Spin-orbit splitting: k

Other splittings: E

HRashba ~ (ez x k) ·

k k ,

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

2D Au Chains on SiAu(111)

Spin Split Fermi

Surfaces

1D

ky

kx

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

On-going

Developments

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)

Rügheimer et al., PRB 75, 121401(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 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

• Tunable solids Complex solids

Need realistic calculations

• Is it possible to combine realistic calculations

with strong correlations ?

(Without adjustable parameters U, t, J, …)

Challenges: