1. Kyle Shen Stanford University
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
High-Resolution Photoemission Studies of Many-Body Effects in the Solid State : "The story from Einstein's electrons"
Kyle Shen
Stanford University

2. Angle-Resolved Photoemission at Stanford
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Angle-Resolved Photoemission at Stanford
Professor Zhi-Xun Shen
(Stanford & SSRL)
Dr. Donghui Lu
(SSRL)
Other group members (past & present) : Changyoung Kim, Andrea Damascelli,
N. Peter Armitage, Filip Ronning, Donglai Feng, Nik Ingle, Hiroshi Eisaki,
Weisheng Lee

3. History of Photoemission
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
History of Photoemission
The Photoelectric Effect
First experimental work performed by H. Hertz (1886), W. Hallwachs (1888), von Lenard (1900)
Theoretical explanation by Einstein (1905)
FIRST EXPERIMENTAL EVIDENCE FOR QUANTIZATION OF LIGHT!
photoemission just a glorified version of the photoelectric effect
ultraviolet light striking a clean metal surface will give off electrons
discovered over 100 years ago by Hertz and others
explained by Einstein, his Nobel prize
Was the definitive experiment which showed the quantization of light
Clearly, we learned a great deal from the photoelectric effect, as it helped to form
the underpinnings of the quantum theory - but can we learn more?
Is there anything else we can learn from the photoelectric effect?
Insights into the solid-state!

4. Understanding the Solid State
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Understanding the Solid State
Electrons in Reciprocal Space
100 years ago, we learned about the quantum nature of light by photoelectric effect.
Now, quantum theory of light is well-understood - we can use our knowledge of this now
to study the metal itself (before we didn’t care about the metal)
In a solid, there are two important questions - the first is “where are the atoms”.
This can be pretty easily answered by x-ray diffraction. This is because x-rays interact
with electrons, and for a given atom, the vast majority of the electrons are tightly bound
to the nucleus.
The second is where are the electrons and how do they move? In particular, how do
the most loosely bound (or most energetic) electrons move through the lattice? This
determines the conductivity of the material, i.e. whether it is a metal or insulator, semiconductor, etc...
As is for the case of the atoms, in a periodic crystal, one should think of the electrons moving
in reciprocal space. For electrons moving freely in space, their energy / momentum relationship
is very simple (parabola). Because electrons cannot occupy the same quantum state, we fill up the
occupation states starting from the lowest energy, to the highest energy, called EF. The electrons
occupy a region in space called the Fermi sphere, the surface of this sphere is called the Fermi surface.
1) Crystal Structure?
X-ray diffraction
2) Electronic Structure?
Photoemission

5. “One-Electron” Picture : Band Structure and Fermi Surfaces
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
“One-Electron” Picture : Band Structure and Fermi Surfaces
The interactions between the electrons and the lattice potential
Ignore interactions between electrons (correlations)
Consider a single electron travelling through a periodic potential
Fermi surfaces determined primarily by size and shape of Brillouin zone and number of electrons
Basis for modern calculations of electronic structure of solids
Fermi Surfaces of Metals
The simplest way to consider electrons in a solid is to ignore the direct interactions between electrons and other excitations in the solid.
In this picture, we calculate the behavior of a single electron moving in the periodic lattice. We can do this, as shown above, as
small perturbations starting from the “free electron” parabola, which cause the bands to “split” and “gaps” to form.
This is a one dimensional case here, and for a three dimensional case shown on the right (Ashcroft). The Fermi surface
Some examples of this “one electron picture” are shown below as the calculated Fermi surfaces. In Na, it is not
too far away from the perfect sphere shown in the last slide. The size and shape of the Brillouin zone and the number of loosely
bound valence electrons primarily determine the shape of the FS’s.
Using the BZ and electron counting, we can typically determine if the solid is metallic, semiconducting, or insulating for many systems.
This “non-interacting” picture has been extremely successful, and forms the basis for modern solid state.

6. Photoemission as a Probe of the Solid State
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Photoemission as a Probe of the Solid State
This is a geometrical schematic of the photoemission process. We measure the outgoing angles and kinetic energy
of photoemitted electrons by an electron analyzer. From momentum and energy conservation laws, we can
back out the momentum and energy states of the electron inside the crystal from the information of the free
electron.
Given that the surface is a well-defined crystal plane, what we essentially do is to pick a point (or number of
points) and fire an electron out of that point in momentum space. This way, we can look at electrons
(or many-body effects) as a function of momentum.
Measured Quantities
Ekin, q, f
Desired Quantities EB, k||
Energy Conservation
EB= hn - Ekin - F
Momentum Conservation
K|| = k||+ G||

7. A “Simple” Example : Metal Surfaces (Cu and Ag)
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
A “Simple” Example : Metal Surfaces (Cu and Ag)
Copper
F. Baumberger et al., PRB 64, (2001)
F. Reinert et al., PRB 63, (2001)
Silver

8. Interaction effects between electrons : “Many-body Physics”
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Interaction effects between electrons : “Many-body Physics”
The interactions between the electrons and each other, or with
excitations inside the crystal :
1) A “many-body” problem : intrinsically hard to calculate and understand
2) Responsible for many surprising phenomena :
Superconductivity, Magnetism, Density Waves, ....
Non-Interacting
Interacting
However, the noninteracting band picture is not always successful and fails to many phenomena in the solid state.
This happens when one can no longer ignore the interactions between the electrons and other excitations in the solid.
These interactions can, in fact, often be very strong, causing the noninteracting picture to break down. The interesting
effects which arise due to these interactions gives rise to many of the most interesting phenomena in solid state.
Two very famous phenomena that you may be familiar with are SC and magnetism.
Non interacting picture - electrons buzzing around, without paying much attention to each other (like a gas)
Interacting - electrons coupled strongly to each other, as well as possibly to the lattice (shown in red).
How can we learn about these interactions? We can “rip” an electron out of the material, so quickly that
it still retains information about the interactions that it had when it was in the solid!

9. Observing “Many Body” Effects by Photoemission
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Observing “Many Body” Effects by Photoemission
Photoemission intensity: I(k,w)=I0 |M(k,w)|2f(w) A(k,w)
There in fact exists precise mathematical formalisms for expressing how one can observe
many-body effects in photoemission. The photoemission intensity can, in general, be shown
to be directly proportional to a quantity known as the “single-particle spectral function”. This
“spectral function” contains a term known as the “self-energy” which directly encapsulates
the effects of interactions. This self-energy is directly calculable by theoretical methods in
certain limited cases, so one can make a precise comparison between theory and
experiment (not just qualitative!)
Single-particle spectral function
S(k,w) : the “self-energy” - captures the effects of interactions

10. State-of-the-art Photoemission
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
State-of-the-art Photoemission
0.2°
2-10
now 2°
20-40
past Dq
DE (meV)
Improved energy resolution
Improved momentum resolution
Improved data-acquisition efficiency
Parallel multi-angle recording
Shown is a typical modern photoemission setup. Light comes in off a synchrotron undulator, where
it passes through beamline optics and off a monochromator and then directed on the sample.
The emitted photoelectrons are then detected, and the momentum and energy read off by the analyzer.
The progress achieved in improving the resolution over the decades is illustrated in the bottom right. This
improvement shows about 2 orders of magnitude of improvement, to the point where we are now, the
width is limited intriniscally by the many-body interactions in the solid itself, and not the instrumental
resolution or surface quality.
Not only has the energy resolution improved dramatically, but the momentum resolution has likewise
improved, along with the data acqusition efficiency.
F. Reinert et al., PRB 63 (2001)

11. SSRL Beamline 5-4 : NIM / Scienta System
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
SSRL Beamline 5-4 : NIM / Scienta System
NIM / SCIENTA System
This is SSRL Beamline 5-4 where we perform our ARPES experiments. The beam comes in off the undulator
and is diffracted off of our normal incidence monochromator with an energy resolution of typically 1 meV.
The light is guided onto the sample, which can be as small as 100 microns in a side. The ejected photoelectrons are
detected by the scienta ses-200 analyzer, shown in green. We can achieve a total energy resolution, including
beamline, analyzer resolution, and thermal broadening of about 5 meV in our experiments.

12. SSRL Beamline 5-4 : NIM / Scienta System
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
SSRL Beamline 5-4 : NIM / Scienta System
Here is another view of our chamber, with Donghui Lu working on the chamber. You can clearly see the
electron analyzer in this picture, and the electrons will take a path through its concentric hemispheres
before being detected. Some of the necessary or featured capabilities of the system are as follows :
Low base temperature (~ 10 K)
Ultra-high vacuum (~ torr)
High angular precision (+/- 0.1o)
Wide temperature range ( K)
Variable photon energies (12-30 eV)
Multiple light sources (Plasma discharge)
Sample surface preparation & cleaning
Single crystal cleaving
Low-Energy Electron Diffraction (LEED)

13. SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Superconductivity

14. The BCS Theory of Superconductivity
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
The BCS Theory of Superconductivity
Bardeen, Cooper, and Schrieffer
(1957) -k k
Cooper Pair

15. “Classic Low-temperature” Superconductors
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
“Classic Low-temperature” Superconductors Pb
Metallic Density of States
Superconducting Density of States
Conventional “low” temperature superconductors
Superconductivity can only be seen on low energy scales and needs high resolution!
V3Si Nb
F. Reinert et al., PRL 85 (2000), A. Chainani et al., PRL 85 (2000)

16. “Exotic” Superconductors : Insights from Photoemission
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
“Exotic” Superconductors : Insights from Photoemission
1. Sr2RuO4 : A “Spin-Triplet” Superconductor
Layered
perovskite
compounds
Discovered by Y. Maeno in 1994
Highly unconventional, low-Tc ( ~ 1 K) superconductor
Electrons “pair” together with PARALLEL spins
Strange interplay between superconductivity and magnetism
2. The High-Tc Cuprate Superconductors
Discovered by J.G. Bednorz and K.A. Muller in 1986
Very high maximum Tc’s (current record is 167 K)
Many potential applications
Strong electronic correlations cause the cuprates to insulate at low doping levels
RuO2,
CuO2

17. Fermi Surface of Sr2RuO4 ARPES : circa 1996 ARPES : present day
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Fermi Surface of Sr2RuO4
D.J. Singh, PRB 52, 1358 (1995)
ARPES : circa 1996
A. Damascelli et al., PRL 85, 5194 (2000)
K.M. Shen et al., PRB 64, R (2001)
ARPES : present day

18. High-Temperature Superconductors
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
High-Temperature Superconductors
Half-Filled Metal
Mott Insulator
Increase inter-electron
Coulomb repulsion
(U)

19. High-Temperature Superconductors
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
High-Temperature Superconductors
ARPES Spectra of Insulating
Ca2CuO2Cl2 along (0,0)-(p,p)

20. High-Temperature Superconductors
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
High-Temperature Superconductors
“s-wave”
“d-wave”

21. High-Temperature Superconductors : Fermi Surfaces
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
High-Temperature Superconductors : Fermi Surfaces
Bi2Sr2CaCu2O8+d
YBa2Cu3O7-d
Nd2-xCexCuO4
Bi2Sr2Ca2Cu3O10+d
Ca2-xNaxCuO2Cl2

22. Advantages and Limitations of ARPES
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Advantages and Limitations of ARPES
Advantages
Limitations
Direct information about electronic states!
Straightforward comparison with theory - little or no modelling.
High-resolution information about BOTH energy and momentum
Surface-sensitive probe
Sensitive to “many-body” effects
Can be applied to small samples (100 mm x 100 mm x 10 nm)
Not bulk sensitive
Requires clean, atomically flat surfaces in ultra-high vacuum
Cannot be studied as a function of pressure or magnetic field

23. Advancing the State-of-the-Art
SSRL 2002 : X-ray Imaging and Spectro-microscopy Workshop
Advancing the State-of-the-Art
1. Higher Brightness = Smaller Single Crystals!
On the materials end, appears to be fundamental issues on the achievable maximum single crystal size. Current “optimal” size on SSRL BL5-4 is ~ 1 mm x 1 mm
Electronic states of fabricated nanostructures?
2. New Insertion Devices
Circularly polarized light (EPU) should allow for novel ARPES studies of the solid state, especially in systems exhibiting dichroism (magnetism)
May be combined with spin-resolved photoemission to gain new insight into spin / orbital physics in the solid state
3. Ultrafast Pulses
Time-resolved Photoemission has been demonstrated using femtosecond lasers. An ultrafast light source (SPPS / LCLS) would provide unprecedented information into the dynamics of electrons in the solid state!