Dirac Fermions in Graphene and Graphite—a view from angle ...

Chapter 2
Experimental techniques
2.1 Angle resolved photoemission spectroscopy (ARPES)
2.1.1 ARPES and the photoelectric effect
Photoemission describes the ejection of electrons from a metal when a beam of light is shine on the
clean surface. It was discovered by Hertz in 1887 and explained by Einstein in 1905. The photoelectric effect
was very puzzling when it was first discovered, with a few mysterious key points. First, the electrons were
emitted immediately. Second, increasing the intensity of the light increases the number of photoelectrons,
but not their maximum kinetic energy. Third, red light will not cause ejection of electrons, no matter how
strong it is. Fourth, a weak violet light will eject only a small amount of electrons, but their maximum
kinetic energies are larger than those ejected by intense light of longer wavelength. These results cannot
be explained without invoking the quantum nature of light, the wave-particle duality. Einstein postulated
that light is quantized and that each quanta photon carried energy hν. The maximum kinetic energy of the
photoelectrons is
E max = hν − φ, (2.1)
where φ (typically 4 to 5 eV for most materials) is the work function of the materials, i.e. the minimum
energy needed to excite an electron into the vacuum. In Einstein’s theory, light is not just a particle and not
just a wave: it can be one or the other, depending on how it is measured. For his explanation of photoelectric
effect, Einstein was awarded the Nobel prize in 1921.
It was later realized that photoelectric effect could provide useful information about the electronic
states inside the materials. As a result of energy conservation, the energy distribution of photoelectrons
can provide information about the density of states in the material studied 14 . Started from 1960’s, it was
realized that momentum dependent band structure could be mapped from the angle and energy dependence
of the photoemission spectra and the first angle resolved photoemission was demonstrated in 1974 15,16 .
This technique, today known as angle resolved photoemission spectroscopy (ARPES) is among the most
powerful spectroscopic techniques as it provides direct information on the electronic binding energy and the
crystal momentum of solids. A schematic drawing of the experimental setup used in ARPES experiment
and typical data set is shown in Fig. 2.1. Information on Fermi surface topology and band structure can be
directly extracted from the peak position of the photoemitted electrons as a function of energy and angle of
emission (momentum). As a result of the uncertainty principle, the width of the ARPES peak can also give
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