One-step Model Of Photoemission Research Articles

Soft X-ray Fermi surface tomography of palladium and rhodium via momentum microscopy

Fermi surfaces of transition metals, which describe all thermodynamical and transport quantities of solids, often fail to be modeled by one-electron mean-field theory due to strong correlations among the valence electrons. In addition, relativistic spin–orbit coupling pronounced in heavier elements lifts the degeneracy of the energy bands and further modifies the Fermi surface. Palladium and rhodium, two 4d metals attributed to show significant spin–orbit coupling and electron correlations, are ideal for a systematic and fundamental study of the two fundamental physical phenomena and their interplay in the electronic structure. In this study, we explored the Fermi surface of the 4d noble metals palladium and rhodium obtained via high-resolution constant initial state momentum microscopy. The complete 3D-Fermi surfaces of palladium and rhodium were tomographically mapped using soft X-ray photon energies from 34 eV up to 660 eV. To fully capture the orbital angular momentum of states across the Fermi surface, the Fermi surface tomography was performed using p- and s- polarized light. Applicability and limitations of the nearly-free electron final state model in photoemission are discussed using a complex band structure model supported by experimental evidence. The significance of spin–orbit coupling and electron correlations across the Fermi surfaces will be discussed within the context of the photoemission results. State-of-the-art fully relativistic Korringa–Kohn–Rostoker (KKR) calculations within the one-step model of photoemission are used to support the experimental results.

Observation and theory of strong circular dichroism in angle-revolved photoemission from graphite

Experimental angle-resolved photoemission spectra (ARPES) and its circular dichroism (CD) from a graphite surface are reported together with calculations in the one-step model of photoemission. For photoelectrons emitted with surface parallel momentum k∥ perpendicular to the incoming light, a strong and complex CD signal is observed and analyzed along the Γ-K and Γ-M lines of the Brillouin zone. Calculations using real-space multiple scattering theory agree well with the data both for the total ARPES and the CD intensity maps. In the independent atomic approximation, i.e. when photoelectron scattering is neglected, the total ARPES intensity map is still well described, but not the CD. We find that photoelectron scattering makes a large contribution to the CD signal and may change its sign. Moreover, the CD of the bands depends strongly on photon energy, while this is much less the case for the total ARPES intensity. The present findings show that an accurate description of the photoemission final state, including photoelectron scattering effects, is crucial for understanding the CD in ARPES from surfaces and two-dimensional materials.

Revealing Hidden Orbital Pseudospin Texture with Time-Reversal Dichroism in Photoelectron Angular Distributions.

We performed angle-resolved photoemission spectroscopy (ARPES) of bulk 2H-WSe_{2} for different crystal orientations linked to each other by time-reversal symmetry. We introduce a new observable called time-reversal dichroism in photoelectron angular distributions (TRDAD), which quantifies the modulation of the photoemission intensity upon effective time-reversal operation. We demonstrate that the hidden orbital pseudospin texture leaves its imprint on TRDAD, due to multiple orbital interference effects in photoemission. Our experimental results are in quantitative agreement with both the tight-binding model and state-of-the-art fully relativistic calculations performed using the one-step model of photoemission. While spin-resolved ARPES probes the spin component of entangled spin-orbital texture in multiorbital systems, we unambiguously demonstrate that TRDAD reveals its orbital pseudospin texture counterpart.

One-step model of photoemission at finite temperatures: Spin fluctuations of Fe(001)

Various technical developments extended the potential of angle-resolved photoemission (ARPES) tremendously during the last twenty years. In particular improved momentum, energy and spin resolution as well as the use of photon energies from few eV up to several keV makes ARPES a rather unique tool to investigate the electronic properties of solids and surfaces. With our work we present a generalization of the state of the art description of the photoemission process, the so called one-step model that describes excitation, transport to the surface and escape into the vacuum in a coherent way. In particular, we present a theoretical description of temperature-dependent ARPES with a special emphasis on spin fluctuations. Finite temperature effects are included within the so called alloy analogy model which is based on the coherent potential approximation and this way allows to describe uncorrelated lattice vibrations in combination with spin fluctuations quantitatively on the same level of accuracy. To demonstrate the applicability of our approach a corresponding numerical analysis has been applied to spin- and angle-resolved photoemission of Fe(100) at finite temperatures.

Bi ultra-thin crystalline films on InAs(1 1 1)A and B substrates: a combined core-level and valence-band angle-resolved and dichroic photoemission study

The growth of Bi on both the In-terminated (A) face and the As-terminated (B) face of InAs(1 1 1) has been investigated by low-energy electron diffraction, scanning tunnelling microscopy, and photoelectron spectroscopy using synchrotron radiation. The changes upon Bi deposition of the In 4d and Bi 5d5/2 photoelectron signals allow to get a comprehensive picture of the Bi/InAs(1 1 1) interface. From the early stage the Bi growth on the A face is epitaxial, contrary to that on the B face that proceeds via the formation of islands. Angle-resolved photoelectron spectra show that the electronic structure of a Bi deposit of ≈10 bi-layers on the A face is identical to that of bulk Bi, while more than ≈30 bi-layers are needed for the B face. Both bulk and surface electronic states observed are well accounted for by fully relativistic ab initio calculations performed using the one-step model of photoemission. These calculations are used to analyse the dichroic photoemission data recorded in the vicinity of the Fermi level around the point of the Brillouin zone.

One-step model of photoemission from single-crystal surfaces

In this paper, we present a 3-D one step photoemission model that can be used to calculate the quantum efficiency and momentum distributions of electrons photoemitted from ordered single crystal surfaces close to the photoemission threshold. Using Ag(111) as an example, we show that the model can not only calculate the quantum efficiency from the surface state accurately without using any ad hoc parameters, but also provides a theoretical quantitative explanation of the vectorial photoelectric effect. This model in conjunction with other band structure and wave function calculation techniques can be effectively used to screen single crystal photoemitters for use as electron sources for particle accelerator and ultrafast electron diffraction applications.

Recent developments in the theory of HARPES

Various technical developments extended the potential of angle-resolved photo emission spectroscopy tremendously during the last one or two decades. In particular improved momentum and energy resolution as well as the use of photon energies from few eV up to several keV makes this experimental technique a rather unique tool to investigate the electronic properties of solids and surfaces. Obviously, this rises the need for a corresponding theoretical formalism that allows to accompany experimental hard X-ray angle-resolved photo emission (HARPES) studies in an adequate way. This could be achieved by various recent developments on the basis of the one-step model of photo emission: all spin–orbit effects are accounted for by a fully relativistic description. Calculating phonon properties allows a direct comparison with features in the HARPES spectra caused by temperature induced disorder. The same holds for the influence of electronic correlation effects. These are accounted for by means of the dynamical mean field theory that removes the most serious short comings of standard calculations based on the conventional local spin-density approximation. Finally, accounting for the photon momentum and going beyond the single scatterer approximation for the final state allows to deal quantitatively with HARPES.

Correlation effects in magnetic materials: An ab initio investigation on electronic structure and spectroscopy

Various technical developments enlarged the potential of angle-resolved photoemission spectroscopy (ARPES) tremendously during the last two decades. In particular improved momentum and energy resolution in combination with spin-resolution as well as the use of photon energies from few eV up to several keV makes ARPES a rather unique tool to investigate the electronic properties of solids and surfaces. Obviously, this rises the need for a corresponding theoretical formalism that allows to accompany experimental ARPES studies in an adequate way. As will be demonstrated by several examples this goal could be achieved by various recent developments on the basis of density functional theory (DFT) in combination with dynamical mean field theory (DMFT) and with the one-step model of photoemission (1SM). A concrete realization of electronic structure calculations in the framework of multiple scattering theory further more provides direct access to the spectral function of the initial states via the one-electron Green function. Based on this bare spectral function matrix-element and final-state effects as well as surface related features may be calculated in addition using the one-step formalism that offers the possibility to analyse corresponding angle-resolved photoemission experiments in a quantitative sense. The impact of chemical disorder can be handled by means of the coherent potential approximation (CPA) alloy theory, in the electronic structure calculation as well as in the photoemission analyses. The same holds for the influence of electronic correlation effects. These are accounted for by means of the DMFT that removes the most serious short comings of calculations based on the standard local spin density approximation (LSDA). The self-consistent combination of this approach with the CPA allows, for example, the investigation of correlated transition metal alloys. Finally, accounting for the photon momentum and going beyond the single scatterer approximation for the final state allows to deal quantitatively with ARPES in the high-energy regime (HAXPES) that reduces the influence of the surface on the spectra and therefore probes primarily the bulk electronic structure this way.

Hard x-ray photoemission study of near-Heusler FexSi1−xalloys

The structural and electronic properties of epitaxial and amorphous Fe${}_{x}$Si${}_{1\ensuremath{-}x}$ alloys with $x$ $=$ 0.72 and 0.67 near the binary Heusler composition of $x$ $=$ 0.75 were determined using hard x-ray photoelectron spectroscopy (HXPS). By performing the measurements at a photon energy of 5950.3 eV, the bulk-sensitivity of the measurement is enhanced by a factor of 4--7 compared to conventional soft x-ray photoelectron spectroscopy at about 1000 keV. HXPS probes, on average, as far as 76 \AA{} into the Fe${}_{x}$Si${}_{1\ensuremath{-}x}$ samples. Via core-level spectra, it is found in the amorphous alloy that, in spite of the disordered structure that could lead to a broad distribution of chemical environments, the Si environment is mostly unique. Valence-band spectra reveal a clear distinction between the contributions of the two inequivalent Fe sites of the most highly ordered ($x$ $=$ 0.72, $D$0${}_{3}$) epitaxial sample. The valence-band spectra are compared to results of fully relativistic coherent potential approximation calculations performed in the framework of the one-step model of photoemission, which reveal details of the atomic-orbital makeup of various features, and generally exhibit good agreement with experiment.

Surface electronic structure of fcc Co films: a combined spin-resolved one- and two-photon-photoemission study

The surface electronic structure of face-centred-cubic cobalt films on Cu(0 0 1) was studied by spin-resolved one- and two-photon photoemission. A minority surface state in a Δ1-symmetry gap of the minority band-structure was identified at about 0.45 eV below the Fermi energy. This state causes a resonance-like enhancement in the population of the minority image-potential surface state in the two-photon-photoemission experiment excited by p-polarized light. Additionally, it appears as a surface-sensitive spectral feature in normal photoemission (PE) and its existence is confirmed by calculations within the one-step model of PE. The majority counterpart of the surface state is theoretically expected at a binding energy of about 1.95 eV. Due to lifetime broadening and bulk transitions in this energy range, the majority state does not appear as a pronounced feature in the spectra. Bulk-derived states close to the Fermi level exhibit shifts to higher binding energy with increasing film thickness, while the minority surface state does not change its energy as a function of Co coverage. These results provide a basis for the interpretation of time-resolved measurements concerning ultrafast magnetization dynamics, which rely on a detailed knowledge of the surface electronic structure of ultrathin films.

Identification of the conduction-band photoemission in time-resolved two-photon photoemission spectroscopy of Si surfaces

We study photoemissions from $\mathrm{Si}(111)\text{\ensuremath{-}}(7\ifmmode\times\else\texttimes\fi{}7)$ and $\mathrm{Si}(001)\text{\ensuremath{-}}(2\ifmmode\times\else\texttimes\fi{}1)$ surfaces by means of time-resolved two-photon photoemission spectroscopy. The peak from the conduction-band minimum (CBM) of bulk Si electronic states has been identified unambiguously in the photoemission spectra for both surfaces, together with peaks from their intrinsic surface states. The CBM photoemission is excited selectively by $p$-polarized probe light with photon energy of around $5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. In terms of the one-step model of photoemission, we conclude that the CBM photoemission results from the transition to evanescent final states induced by the surface photoelectric effect.

Role of final states in photoemission from Al(1 1 1)

Enhancement of surface state peaks in angle resolved ultraviolet photoelectron spectra (ARUPS) from the Al(1 1 1) surface is studied experimentally and theoretically within the one-step model of photoemission. The resonant enhancement of the surface state emission is explained by the crucial role of elastic scattering of the outgoing electron. Dipole transitions to evanescent states in the final bands of the crystal are shown to determine photoemission at the resonant photon energy. The band structure based explanation is confirmed by the measurements of electron reflectivity and of the fine structure of valence band spectra. The surface sensitivity of ARUPS is shown to depend strongly on the complex band structure of the crystal and to be finely tunable by the choice of photoemitted electron energy.

Surfaces and interfaces in short-period GaAs/AlAs superlattices

Photoelectron spectroscopy, in particular the angular resolved photoemission excited by ultraviolet radiation (ARUPS), provides the most direct experimental information about the electron structure of crystals, both of the bulk and of the low-index surfaces. The sensitivity of the method, as well as its difficulties, when applied to GaAs/AlAs superlattices are described. The new periodicity of these man-made crystals in the direction of their growth (e.g., in the layer-by-layer growth in molecular beam epitaxy), is responsible for opening of the new energy gaps (so-called minigaps) in the electron energy bands of crystals forming the superlattice. In addition to the well-known confinement of electrons at the valence and conduction band edges in long-period superlattices, the electron confinement to the interfaces has also been found in the vicinity of minigaps in short-period superlattices. The role of this confinement in the intensities of electrons photoemitted from superlattice surfaces is discussed. Superlattices with different thicknesses in the topmost layers represent systems with a simple change of the surface atomic structure. The predictions of one-dimensional models about a change of the surface-state energy within the band gap with a change of crystal potential termination are tested for the ideally terminated (1 0 0) surface of a very thin superlattice (GaAs) 2 (AlAs) 2 . The results of the energy distributions of photoemitted electrons, calculated in the one-step model of photoemission, show that the ARUPS experimental observation of surface-state shifts should be possible, at least in larger minigaps. The results indicate the possibility of a straightforward tuning of the electronic structure of the superlattice surface by geometrical means.

Surfaces and interfaces in short-period GaAs/AlAs superlattices

Photoelectron spectroscopy, in particular the angular resolved photoemission excited by ultraviolet radiation (ARUPS), provides the most direct experimental information about the electron structure of crystals, both of the bulk and of the low-index surfaces. The sensitivity of the method, as well as its difficulties, when applied to GaAs/AlAs superlattices are described. The new periodicity of these man-made crystals in the direction of their growth (e.g., in the layer-by-layer growth in molecular beam epitaxy), is responsible for opening of the new energy gaps (so-called minigaps) in the electron energy bands of crystals forming the superlattice. In addition to the well-known confinement of electrons at the valence and conduction band edges in long-period superlattices, the electron confinement to the interfaces has also been found in the vicinity of minigaps in short-period superlattices. The role of this confinement in the intensities of electrons photoemitted from superlattice surfaces is discussed. Superlattices with different thicknesses in the topmost layers represent systems with a simple change of the surface atomic structure. The predictions of one-dimensional models about a change of the surface-state energy within the band gap with a change of crystal potential termination are tested for the ideally terminated (1 0 0) surface of a very thin superlattice (GaAs) 2(AlAs) 2. The results of the energy distributions of photoemitted electrons, calculated in the one-step model of photoemission, show that the ARUPS experimental observation of surface-state shifts should be possible, at least in larger minigaps. The results indicate the possibility of a straightforward tuning of the electronic structure of the superlattice surface by geometrical means.

Theoretical description of the Fano-effect in the angle-integrated valence-band photoemission of paramagnetic solids

A theoretical description of the Fano-effect in the angle-integrated valence-band photoemission (VB XPS) of paramagnetic solids is presented that is based on the one-step model of photoemission and relativistic multiple scattering theory. Applications to fcc-Cu and fcc-Ag led to a very satisfying agreement with recent experimental data that show the Fano-effect, i.e., a finite spin polarisation of the photoelectrons is found for excitation with circularly polarised radiation. As can be demonstrated by model calculations, this finding is caused by the presence of spin-orbit coupling. To allow for a more detailed discussion of the spectra, a simplified description of the Fano-effect is presented that treats spin-orbit coupling as a perturbation.

Inelastic inverse lifetimes of medium-energy electrons: photoemission analysis of s,p-band direct transitions at Cu( [formula omitted]) and Cu( [formula omitted

We investigate the inelastic lifetime of electrons in copper at excitation energies E f between 7 and 20 eV above the Fermi level. High-resolution photoemission experiments allow to determine the inelastic inverse lifetime of final state electrons precisely by measuring the line widths of s,p-band direct transitions. Energy coincidence measurements on Cu(1 0 0) and Cu(1 1 0) show dramatically different line widths which can be quantitatively explained by calculations within the one-step model of photoemission as well as by numerical line shape calculations. Our analysis shows that the distinct line widths on the differently oriented surfaces do not result from lifetime effects but from the influence of the band structure. All observations are in good agreement with a linearly increasing lifetime width Γ e= a( E f− E F), with a=(0.13±0.01) in the energy range mentioned above.

Wave-vector-dependent symmetry analysis of a photoemission matrix element: The quasi-one-dimensional model systemCu(110)(2×1)O

We derive orbital symmetry character from the study of peak intensities in angle-resolved photoemission spectra taken at different incidence angles of p-polarized light. Our method of analysis is tested at the oxygen-derived antibonding band on the $\mathrm{Cu}(110)(2\ifmmode\times\else\texttimes\fi{}1)\mathrm{O}$ surface. This band has an initial state energy ${E}_{i}=\ensuremath{-}1.37\mathrm{eV}$ $(T=300\mathrm{K})$ at the $\overline{Y}$ point and shows even symmetry with respect to the $\ensuremath{\Gamma}\mathrm{LUX}$ mirror plane (along $\overline{\ensuremath{\Gamma}Y}).$ The intensity analysis reveals that orbitals both of z-like (along surface normal) and y-like symmetry (y along the Cu-O chains) are mixed into this band. This interpretation is supported by several calculations. The ground-state symmetry character was studied by a full-potential linearized augmented plane-wave method using a seven-layer supercell geometry. For a direct comparison with the experimental intensities, photoemission spectra at the $\overline{Y}$ point were calculated using the one-step model of photoemission. Our results contribute to a long-standing discussion about the orbital character of the even antibonding band. In particular we demonstrate that this kind of intensity analysis can supply valuable information about symmetry properties.

Theoretical description of the Fano effect in the angle-integrated valence-band photoemission of paramagnetic solids

A theoretical description of the Fano effect in the angle-integrated valence-band photoemission of paramagnetic solids is presented that is based on the one-step model of photoemission and relativistic multiple-scattering theory. Applications to fcc-Cu led to a very satisfying agreement with recent experimental data that show the Fano effect, i.e., a finite spin-polarization for the spectra is found for excitation with circularly polarized radiation. As can be demonstrated by model calculations, this finding is caused by the presence of spin-orbit coupling. To allow for a more detailed discussion of the spectra a simplified description of the Fano effect is presented that treats spin-orbit coupling as a perturbation.

Valence-band photoemission fromGaAs(100)−c(4×4)

The energy distributions of photoelectrons emitted from the $c(4\ifmmode\times\else\texttimes\fi{}4)$ reconstructed GaAs(100) surface are carefully analyzed within the one-step model of photoemission, thus demonstrating that such calculations work for large unit cells. It is used for detailed interpretation of published and new angular resolved $\mathrm{He}I$ experimental data. Surface-related features are found and their localization and symmetry are determined. Backfolding of the electron energy bands and its splitting at the reduced Brillouin zone's boundaries lead to smaller energy dispersion of electron surface states and resonances. The experimentally observed longer period of a surface resonance than that corresponding to the translation symmetry of the reconstructed surface is confirmed and explained. The existence of two surface states near the upper valence-band edge is verified. One major difference between the theory and the experiment is found that cannot be explained by means of the one-step model for a perfectly reconstructed surface.

Quantum-size effects in photoemission from ultra-thin films:

Abstract We report on detailed calculations of quantum-size effects on the electronic structure of the valence-band regime and their manifestation in photoemission. Model calculations reveal the basic features of photoemission from quantum-well states (QWS). First, emission from QWS shows intensity variations with photon energy which is similar to that of semi-infinite systems, despite the discrete binding energies of the QWS. Second, conservation of the wave-vector component normal to the surface is directly related to the film thickness. Numerical calculations within the relativistic one-step model of photoemission show that these effects should be observable in ‘real’ systems. This is demonstrated to be the case for Cu films on fcc-Co(001).