Cooper Minima in the Photoemission Spectra of Solids S. L. Molodtsov, 1, * S.V. Halilov, 2 V. D. P. Servedio, 3 W. Schneider, 1 S. Danzenbächer, 1 J. J. Hinarejos, 1, † Manuel Richter, 3 and C. Laubschat 1 1 Institut f ür Oberflächenphysik und Mikrostrukturphysik, TU Dresden, D-01062 Dresden, Germany 2 Electron Physics Group, NIST, Gaithersburg, Maryland 20899-8412 and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 3 Department of Theoretical Solid State Physics, IFW Dresden, P.O. Box 270016, D-01171 Dresden, Germany (Received 17 April 2000) Variations of the photoionization cross section of valence states as a function of interatomic distance are studied by means of atomic and solid-state density functional approaches and compared with photo- emission data. In contrast to the free atom case, a series of Cooper minima is found for 4d, 5d, and 5f states in Pd, Ag, Au, and U metals. The discovered fundamental phenomenon is of high importance for the correct interpretation of photoemission data. PACS numbers: 78.70.–g, 79.60.Bm The energy dependence of photoionization cross sec- tions is a tool frequently used to identify contributions from different atomic states to valence-band photoemission (PE) spectra. Particularly useful is the appearance of phenom- ena such as Fano resonances [1] or Cooper minima (CM) [2] providing a strong enhancement or decrease of the PE signal from certain states. While the Fano resonance is a many-body effect caused by coupling of the direct PE channel with photoexcitations into localized intermediate states and subsequent autoionization, the CM represents a simple matrix element effect: Due to a node of the initial- state wave functions the transition matrix element into final states with oscillating free-electron-like wave functions be- comes canceled. The behavior of the cross section around the CM depends strongly on the shape of the initial-state waves. Atomic calculations by Yeh and Lindau [3] (de- noted YL in the following) provide the photoionization cross sections for all elements of the periodic table in a wide range of photon energies. Thereby, not more than one CM is found for any atomic shell considered. In solids, however, valence states reveal much less pro- nounced Cooper minima than the related states in the free atoms [4–9]. Additionally, CM in solids are shifted in energy and broadened as compared to their positions and widths in free atoms. These solid-state phenomena have been discussed primarily in terms of hybridization effects [4–7,9]. Another very important difference between free atoms and solids has been, however, completely ignored in the discussion so far: the different symmetry of atomic and solid-state wave functions. For free atom bound states, the amplitudes of the electron wave functions decay ex- ponentially at large distance to the nucleus, and transi- tion matrix elements are calculated by integration over the whole space. In a solid, periodic Bloch states are formed and for direct transitions all translationally equiva- lent Wigner-Seitz (WS) cells give the same contributions to the integral. This difference should heavily affect the conditions for the appearance of CM. In the present Letter we show that the translational sym- metry may cause a series of Cooper minima in solids in- stead of a single one known to exist in the free atom. We find experimentally the existence of more than one CM for 4d states of Pd and Ag metals and reproduce the phe- nomenon by atomic and solid-state density functional cal- culations. Similar effects are predicted for the 5d bands of Au metal. Particular attention is paid to the 5f states of U metal, where CM effects are found to superimpose the 5d ! 5f Fano resonance. We show that proper con- sideration of solid-state phenomena in PE cross sections is not only crucial for a correct identification of different valence-band contributions but is also important for the un- derstanding of many-body phenomena in PE spectra. The experiments were performed at the PM5 beam line of the Berliner Elektronenspeicherring für Synchrotron- strahlung (BESSY I). In order to avoid band structure or possible photoelectron diffraction effects, polycrystalline samples, which were prepared by in situ thermal deposition of about 500 Å Pd or Ag onto a Cu substrate at a pressure better than 2 3 10 28 Pa, were studied. Since polycrys- talline solids do not have any preferential direction, the angular distribution of the Pd and Ag 4d PE is expected to be governed by Yang’s theorem [10]. The influence of the asymmetry parameter was eliminated by recording spectra close to the so-called “magic” angle of 54.7 ± between the axis of electron detection and polarization vector of the incoming photon beam. The spectra were taken in an angle-integrated mode using a hemispherical electron- energy analyzer with an acceptance angle of 614 ± . The light was at near-normal incidence to the sample, so that reflectivity corrections were negligible. The valence-band PE spectra of Pd and Ag metals were normalized to the total PE signal of the 3d bands of polycrystalline Cu metal measured in the same experimental setup [11]. For the Cu 3d states themselves no distorting CM-like cross-section variations in the photon-energy range of interest are expected from our model calculations.