High-Resolution Photoemission Studies of Many-Body Effects in the Solid State : "The story from Einstein's electrons" Kyle ShenStanford University

Angle-Resolved Photoemission at StanfordProfessor 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

History of Photoemission 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!The Photoelectric EffectIs there anything else we can learn from the photoelectric effect?Insights into the solid-state!

Understanding the Solid State1) Crystal Structure?X-ray diffraction

2) Electronic Structure?PhotoemissionElectrons in Reciprocal Space

One-Electron Picture : Band Structure and Fermi SurfacesThe interactions between the electrons and the lattice potentialFermi Surfaces of Metals 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

Photoemission as a Probe of the Solid StateMeasured Quantities Ekin, q, f

Desired Quantities EB, k||

A Simple Example : Metal Surfaces (Cu and Ag)

Interaction effects between electrons : Many-body PhysicsThe interactions between the electrons and each other, or with excitations inside the crystal :

1) A many-body problem : intrinsically hard to calculate and understand2) Responsible for many surprising phenomena :Superconductivity, Magnetism, Density Waves, ....Non-InteractingInteracting

Observing Many Body Effects by Photoemission Photoemission intensity: I(k,w)=I0 |M(k,w)|2f(w) A(k,w) S(k,w) : the self-energy - captures the effects of interactions

State-of-the-art PhotoemissionF. Reinert et al., PRB 63 (2001)

SSRL Beamline 5-4 : NIM / Scienta System

SSRL Beamline 5-4 : NIM / Scienta System Low base temperature (~ 10 K) Ultra-high vacuum (~ 10-11 torr) High angular precision (+/- 0.1o) Wide temperature range (10 - 350 K) Variable photon energies (12-30 eV) Multiple light sources (Plasma discharge) Sample surface preparation & cleaning Single crystal cleaving Low-Energy Electron Diffraction (LEED)

Superconductivity

The BCS Theory of SuperconductivityBardeen, Cooper, and Schrieffer(1957)

Classic Low-temperature SuperconductorsV3SiPbNbF. Reinert et al., PRL 85 (2000), A. Chainani et al., PRL 85 (2000) Conventional low temperature superconductors

Superconductivity can only be seen on low energy scales and needs high resolution!

Exotic Superconductors : Insights from Photoemission1. Sr2RuO4 : A Spin-Triplet Superconductor2. The High-Tc Cuprate SuperconductorsLayeredperovskitecompounds 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 Discovered by J.G. Bednorz and K.A. Muller in 1986 Very high maximum Tcs (current record is 167 K) Many potential applications Strong electronic correlations cause the cuprates to insulate at low doping levelsRuO2,CuO2

Fermi Surface of Sr2RuO4ARPES : circa 1996

High-Temperature SuperconductorsHalf-Filled MetalMott InsulatorIncrease inter-electronCoulomb repulsion (U)

High-Temperature SuperconductorsARPES Spectra of InsulatingCa2CuO2Cl2 along (0,0)-(p,p)

High-Temperature Superconductorss-waved-wave

High-Temperature Superconductors : Fermi SurfacesNd2-xCexCuO4YBa2Cu3O7-dBi2Sr2CaCu2O8+dBi2Sr2Ca2Cu3O10+dCa2-xNaxCuO2Cl2

Advantages and Limitations of ARPESAdvantagesLimitations 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

Advancing the State-of-the-Art1. 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 state3. 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!

photoemission just a glorified version of the photoelectric effectultraviolet light striking a clean metal surface will give off electronsdiscovered over 100 years ago by Hertz and othersexplained by Einstein, his Nobel prizeWas 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? 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 nowto study the metal itself (before we didnt 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 interactwith electrons, and for a given atom, the vast majority of the electrons are tightly boundto 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? Thisdetermines 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 movingin reciprocal space. For electrons moving freely in space, their energy / momentum relationshipis 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 electronsoccupy a region in space called the Fermi sphere, the surface of this sphere is called the Fermi surface.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, assmall 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 surfaceSome examples of this one electron picture are shown below as the calculated Fermi surfaces. In Na, it is nottoo 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 FSs.

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.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 freeelectron.

Given that the surface is a well-defined crystal plane, what we essentially do is to pick a point (or number ofpoints) 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.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 thatit still retains information about the interactions that it had when it was in the solid!

There in fact exists precise mathematical formalisms for expressing how one can observemany-body effects in photoemission. The photoemission intensity can, in general, be shownto be directly proportional to a quantity known as the single-particle spectral function. Thisspectral function contains a term known as the self-energy which directly encapsulatesthe effects of interactions. This self-energy is directly calculable by theoretical methods incertain limited cases, so one can make a precise comparison between theory andexperiment (not just qualitative!)Shown is a typical modern photoemission setup. Light comes in off a synchrotron undulator, whereit 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. Thisimprovement shows about 2 orders of magnitude of improvement, to the point where we are now, thewidth is limited intriniscally by the many-body interactions in the solid itself, and not the instrumentalresolution or surface quality.

Not only has the energy resolution improved dramatically, but the momentum resolution has likewiseimproved, along with the data acqusition efficiency.

This is SSRL Beamline 5-4 where we perform our ARPES experiments. The beam comes in off the undulatorand 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.Here is another view of our chamber, with Donghui Lu working on the chamber. You can clearly see theelectron 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 :