ARPES

Angle resolved photoemission spectroscopy (ARPES), also known as ARUPS -angle resolved ultraviolet photoemission spectroscopy-, is a direct experimental technique to observe the distribution of the electrons, or more precisely, the density of single particle electronic excitations in the reciprocal space of solids. ARPES is one of the most direct and used methods of studying the electronic structure of solids. With the extremely high angular and energy resolutions now achievable (see The resolution) , this technique reveals the electronic structure with great precision- information that forms the origin for a comprehensive and better understanding of complex solids physics. Indeed, it merits what has sometimes been called: a microscope for where and how the electrons move^[1]. Nowadays ARPES represent the best technique choice in order to better visualize the energy and momentum phase space of the electrons. 

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The technique

  As a special form of scattering experiments, ARPES provides us valuable information about: the direction, the speed, and the scattering processes of valence electrons in the solids. By measuring the kinetic energy and angular distribution of the electrons photoemitted from a sample illuminated with sufficiently high-energy, one can gain information on both, the energy and momentum, of the electrons propagating inside a material. This is of vital importance in elucidating the connection between electronic, magnetic and chemical structure on solids, in particular, for those complex systems which cannot be appropriately described within the independent-particle picture. ARPES technique is very useful in order to know detailed information on band dispertion and Fermi surface.

The resolution

The technologies development has allowed a great improvement in the technique of the photoelectron spectroscopy. Since the decade of 90’s a dramatic improvement in energy and angular (thus momentum) resolution has been achieved, from typical 200 meV and 2~4 degree to 2~10 meV and 0.1-0.3 degree respectively. This advance was made possible by the development of sophisticated spectrometers and advanced synchrotron beamlines; in 2004, ARPES experiments can achieve 2 meV energy resolution and 0.2 degrees in angular resolution^[3].

Kinematics of photoemission

Under the sudden approximation, ARPES measures the single particle spectral function A(k,w) weighted by the photoionisation cross section and the Fermi-Dirac function. In a more formal language: the spectral function is the imaginary part of the single particle Green's function G(k,w) The goal of the technique is to deduce the electronic dispersion relations, E_k, for the sample, it means, the relation between binding energy, E_B, and momentum, k, for the electron propagating inside the solid. In order to do that one has to exploit the total energy and momentum conservation laws: 

E_f − E_i = hv

k_f − k_i = k_hv

Where the indexes i and f refer to initial and final state, respectively, and kh is the momentum of the incoming photon. We will mainly restrict ourselves to the context of the three-step model and the sudden approximation. Within the non-interacting electron picture, it is particularly straightforward to take advantage of the energy conservation law and relate the kinetic energy of the photoelectron to the binding energy E_B = of the electronic-state inside the solid:

• E_k = energy (kinetic) of the outgoing electron (can be measured)
• incoming photon energy (known from theory)
• φ = electron work function (energy required to remove electron from sample to vacuum) can also be measured
• E_B = binding energy of the solid

Therefore can find out information about E_k (energy of K)

Advantages and limitations

The ARPES technique provides us direct and valuable information about the electronic states of a solid and allows us to compare directly with the theory. One can have high resolution information on both energy and momentum. ARPES is surface probe and many body effects sensitive. Another important advantage is its possible application on very small samples, 100 μm x 100 μm x10 nm. On the other hand the ARPES presents some limitations. It is not bulk sensitive and the technique requires a clean and atomically flat surface on a ultra-high vacuum. As a last limitation, it also important to stress that ARPES method cannot be studied as a function of pressure or magnetic field^[2].

ARPES experiments

  A typical ARPES experiment is carried out on freshly prepared sample surfaces in ultra-high vacuum as the short mean free path of the photoelectrons dictates that only the near surface electrons carry the inherent information without suffering scatterings. The surface sensitivity can be a problem for ARPES experiments. However, the two dimensional nature and the easy cleavage some materials, like cuprate crystals, minimizes the problem although special attention is still required in certain cases.

This technique could very useful detecting bands and Fermi surface, and giving us information about the bulk and surface electronic structure. It also has been used to know more about the superconducting gap of materials; it provides us important results to study the Bogoliubov quasiparticles in high-Tc cuprates. Many experiences have a mean purpose to better understand the Many-body effects in the quasiparticle dispersion. At the same time, concerted efforts will be made to perform high-resolution angle resolved photoemission experiments with spin detection, and to perform experiments with very high spatial resolution that approaches the molecular level.

See also

References

NOTES

OTHERS

• Campuzano J C, Norman M R and Randeria M 2004 Photoemission in the High Tc Superconductors vol II, pp 167–265 (Berlin: Springer)
• Shen, Z.-X. and Dessau, D. S., Phys. Rep. 253, 1 (1995).