Experimental and theoretical graphite valence-band photoelectron angular distributions are presented and compared. We observe a zone-selection eAect, wherein interference between photoelectron amplitudes from the two atoms in each graphene unit cell cause both o. and~states to appear with diferent intensity in otherwise equivalent Brillouin zones. To simulate the experimental graphite valence-band photoelectron angular distributions, our simple model includes eA'ects of (1) valence-band wave functions and (2) the relative emission path-length diA'erence, from the atoms in each unit cell to one s detector (which is determined by the experimental geometry).
I. INTRQDUCTI(3NSince the earliest studies of solids by angle-resolved, photoelectron spectroscopy (ARPES), ' graphite has served as a useful material in demonstrating the e%cacy of this technique.In principle, photoelectron spectroscopy enables one to probe the wave functions and energies of occupied electron states in a material. Electrons originating from near a surface are observed with the greatest intensity, because of the finite mean free paths of photoelectrons in solids. If one has a periodic, singlecrystal sample, with a high-quality, simple surface termination, the energy-dependent, photoelectron angular distribution (PAD) may be used to map the valence-band structure.Photons typically have momenta small compared with Brillouin-zone dimensions. Thus, a photoelectron's vacuum momentum may be related directly to the momentum of the particle's initial state. The Inomentum of an electron parallel to the surface is preserved during photoemission, modulo surface reciprocal-lattice vectors, due to translational periodicity parallel to the surface. Because of the solid's surface termination, meanwhile, the electron's momentum perpendicular to the surface cannot be a good quantum number. Nonetheless, due to the nearly-free-electron-like dispersion of moderately energetic photoelectrons -say, those excited by photons with energy hv) 50 eV -a photoelectron's momentum perpendicular to the surface is often restricted to a narrow range of values.Certain issues concerning an electron's momentum are simplified in graphite, due to the layered structure of this material. In many instances, including the present work, graphite may be treated as an essentially two-dimensional solid. In graphite, the interactions between the graphene sheets of carbon atoms are fairly weak. Consequently, interlayer banding effects lead to band dispersion, in the direction perpendicular to the sheets, on the order of only a few percent of the occupied, valence bandwidth. ' Analyzing a PAD is usually somewhat complicated, for the problem of isoenergetic photoelectrons leaving a solid in various directions, because all three components of the initial-state momentum vary with the direction of exit.Meanwhile, the (practically) two-dimensional quality of the graphite valence bands minimizes the need to identify the initial-state momentum perpendicular to the layers. ' (The sheets lie parallel ...