Unoccupied Electronic States Fundamentals for XANES, EELS, IPS and B
In the past two decades our understanding of the occupied electronic states of solides has undergone a revolution, while our knowledge of the unoccupied states has lagged behind. This is now changing, owing to the progress in techniques such as X-ray abso
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The study of strongly correlated electron systems is still at a stage where the search is for the basic principles. Unoccupied state spectroscopies have started to play a significant role in this field, and on more than one occasion breakthroughs occurred after new experimental data became available. However, it is the combination of high-energy spectroscopy for both occupied and unoccupied states which has had the most impact, and therefore we shall consider states below and above the Fermi energy in this chapter. A fundamental property of the electronic state is the single electron Green's function. This Green's function, the starting point for most many-body descriptions of the interacting electron system, is at zero temperature defined as (INo > being the N-particle ground state with energy Eo)
~,(z,k)= No c~+U_Eo ckN0
+
No Ckz
H+Eo (4.1)
The object which we wish to interpret is its imaginary part, the single electron spectral function 1
A ( k , co) = - lim Im {Ga(k, co - i0+)} RO+~O
= ~ I < N s- ICklNo > Is c5(co + EL - Eo) f
+ Z I12c5(co- El+ + Eo),
(4.2)
f
where INS+>andl N J'_ > a r e t h e f t h eigenstates of the system with one electron added or removed, respectively, at energies EI+ and EY_. In other words, this spectral function measures the probability of adding or removing an electron to the system at energy co. When the sudden approximation holds, that is, when the kinetic energy of the outgoing/incoming electron is large, this is exactly the quantity which we measure in (angle-resolved) photoelectron spectroscopy (ARPES) and (angle-resolved) inverse photoemission (ARIPES). This spectral function is the main subject of this chapter. Although they are less direct because they involve a core hole, the spectral functions for core level photoemission (c-XPS) and X-ray absorption spectroscopy (XAS) offer useful information
90
J. Zaanen
t o o - - i n the end it is the combination of all these spectroscopies which makes our interpretations trustworthy. Traditionally, studies of correlated systems concentrated on macroscopic properties, such as transport, susceptibility, specific heat and so on. It was believed that away from. the ground state and the low-lying excitations, the problem was too complicated to be understood in any detail. However, thanks to high-energy data, it became more and more clear that the physics on a scale of ~ 20eV around the Fermi energy is much simpler than expected. In fact, simple models seem to tell us rather precisely what we see in the spectra. This works so well that a belief has emerged that a 'top-to-bottom' approach might work: starting out from the understanding of the physics on short time- and length-scales, one might attempt to deduce the proper model for macroscopic physics. The seminal work in this respect has been the demonstration by Gunnarsson and Schfnhammer that all known high-energy data (core-XPS, XAS, valence band photoemission and inverse photoemission) of Ce intermetallics could be explained with a single underlying (Anderson impurity) model
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