Localisation of excited states

Solid state spectroscopy usually revolves around the determination of properties characteristic of a solid, such as the density of states in the conduction band, the position of the Fermi energy, etc. These can be probed by X-ray photoabsorption or more directly by photoemission (either angle-resolved [593] or inverse [594]) spectroscopies, in which case the initial quasiatomic state is reasonably well known since it is close to the wavefunction of a free atom, while the final state is the continuum characteristic of the solid, so that the dispersion of the wavevector k can be determined. 

However, solids do not always behave according to the idealised band model. When photoabsorption spectra are studied in the X-ray range, it can happen that the observations reveal quasiatomic properties only slightly modified by solid state effects. These atomic effects in solids must be distinguished from purely solid state properties, but are also of intrinsic interest once properly understood, they provide an alternative route to the study of atoms in condensed matter. 

There are two reasons for which X-rays are ideal probes for condensed matter. First, they can traverse thin films or penetrate a finite depth into bulk solids. Second, they excite deep core holes, whose properties are quasiatomic these are readily related to the atomic constituents, while at the same time revealing, through subtle changes in the spectra, properties characteristic of the solid. 

In the spectroscopy of solids, questions of localisation or delocalisation of particles with respect to each other or else with respect to individual sites play a crucial role. Thus, for example, one distinguishes between two types of luminescence, viz. excitonic type and electron-hole type, depending on whether the electron and hole are bound together to form an exciton, or whether they are essentially independent. In the former case, the yield increases with incident energy, while in the latter it is essentially constant. 

In many situations, X-ray absorption spectroscopy is site specific, i.e. it provides information local to the atom whose X-ray edge is being probed. The questions arising are then how well localised are the excited states in the vicinity of these particular atoms and to what extent do their properties differ from those of free atoms  

---