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

Chapter 7
ARPES study of partially
polycrystalline graphite: HOPG
7.1 Electronic structure of polycrystalline materials measured by
ARPES
The capability to resolve crystal momentum values of single particle excitations in ARPES has been
based entirely on the translational symmetry along the surface of a single crystal and the resulting conservation
of the crystal momentum parallel to the surface (k ‖ ) during the photoemission process. This holds
despite the short photoelectron lifetime 119,120,121 which can severely broaden the resolution of the momentum
perpendicular to the surface (k z ). Indeed, even in the limit of an extreme k z broadening that results in
no resolution of k z , strong ARPES dispersions are expected as a function of k ‖ , since the one dimensional
density of states (1D-DOS) D z (E) ∝ dk z /dE obtained by integrating over k z is dominated by contributions
from van Hove singularities in high symmetry planes 121 . For example, Fig. 7.1 shows the dispersions measured
on LaSe, where the dispersions on the two high symmetry planes at k z = 0 and k z = π/c are clearly
observed 122 .
On the contrary, for those systems characterized by orientationally disordered domains, i.e. polycrystalline
materials, the translational symmetry is preserved only within each domain. As a consequence, the
dispersion measured by ARPES is the average dispersion over different domains, or equivalently azimuthal
angle φ, which in general leads to no dispersion. However, extending the 1D-DOS D z (E) scenario for k z discussed
above further to the plane, there is an interesting possibility that a layered polycrystalline sample,
with a strong azimuthal disorder, can nevertheless give distinct dispersions in the radial direction. This
would happen if the average dispersion is dominated by those along the high symmetry directions due to
van Hove singularities in the angular density of states D φ (E) ∝ dφ/dE. This possibility has not been demonstrated
experimentally and photoemission studies on disordered samples have focused on angle-integrated
features without any momentum information.
Here we demonstrate the possibility of measuring band dispersions in partially polycrystalline highly
oriented pyrolytic graphite - HOPG. HOPG is a synthetic graphite, which is formed by cracking hydrocarbon
at high temperature followed by subsequent annealing. It consists of many crystallites on the order of µm
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