There are a hundred billion trillion electrons in a typical solid, and every one of them interacts with every other. Luckily, understanding a solid's electronic structure doesn't require precise quantum-state solutions for the whole kit and kaboodle.
Instead of coping with 10-to-the-23rd entangled electrons (not to mention oppositely charged atomic nuclei), solid-state physicists base their calculations on quasielectrons, entities with the same spin and charge as electrons but with fictitious masses and finite lifetimes, properties that allow realistic approximations of their local interactions as they move through a crystal. Quasiparticle theory, which dates from the 1950s, is unsurpassed at modeling a host of materials.
Among other things, quasiparticle theory modifies the straightforward energy-versus-momentum relation that applies to free particles by taking into account interactions of electrons with other nearby electrons, with the ion cores of atoms, and with phonons, which are quantized vibrations of the crystal lattice. A key parameter is the Fermi surface, giving the momentum values of all electrons at the Fermi energy, which separates occupied electronic levels from unoccupied ones.
"ARPES is a good way to look at these features with extreme sensitivity and very high resolution," says Yi-De Chuang, "especially using the improved HERS endstation and the extremely bright monochromatic beam available at the Advanced Light Source's new undulator beamline 10."
When a sample is struck by the beam's energetic photons it emits photoelectrons, which are collected by HERS, the High Resolution Energy Spectrometer. The Fermi surface, energy versus momentum relations, and other features can be reconstructed by measuring the precise angles and energies of the photoelectrons; from ARPES data gathered by HERS, the energies and lifetimes of the material's quasielectrons can be derived.