Thesis High-Resolution Photoemission Study of Kondo Insulators ...

Chapter 2
Photoemission Spectroscopy
In this Chapter we present general principles and experimental technique of photoemission
spectroscopy. In the section of the general principles, we express a formulation of
photoemission spectrum and then show how to deduce spectral density of states (DOS)
from measured photoemission spectra. In the section of the technique, we give some
remarks on a pumping system for photoemission spectroscopy with a He discharge lamp
and then explain a background correction for the photoemission spectra taken with a
He lamp.
2.1 General Principles
2.1.1 Formulation of Photoemission Spectrum
First we present the formulation of photoemission spectrum following Gunnarsson and
Schönhammer [2.1]. We assume a transition from the initial ground state |E0(N) > to
the final states ψ †
k |En(N − 1) >, where the emitted electron |k >has no interaction
with the remaining (N − 1) electrons1 . The golden rule gives the number of emitted
electrons with the energy of ɛout as
P < (ɛout) = � �
k
where τ = �
ki
n
| | 2 δ(ɛout−ɛk)δ(ɛout+En(N−1)−hν−E0(N))
(2.1)
τkiψ †
k ψi represents the transition induced by photons with a matrix ele-
ment τki between the one-electron states |i >and |k >. With a further assumption of
1 This approximation becomes more accurate as the kinetic energy of the emitted electron increases.
17