Dichroism In Angular Distribution Of Photoelectrons Research Articles

Probing topological Floquet states in WSe2 using circular dichroism in time- and angle-resolved photoemission spectroscopy

Observing signatures of light-induced topological Floquet states in materials has been shown to be very challenging. Angle-resolved photoemission spectroscopy (ARPES) is well suited for the investigation of Floquet physics, as it allows to directly probe the dressed electronic states of driven solids. Depending on the system, scattering and decoherence can play an important role, hampering the emergence of Floquet states. Another challenge is to disentangle Floquet side bands from laser-assisted photoemission (LAPE), since both lead to similar signatures in ARPES spectra. Here, we investigate the emergence of Floquet state in the transition metal dichalcogenide 2H-WSe2, one of the most promising systems for observing Floquet physics. We discuss how the topological Floquet state manifests in characteristic features in the circular dichroism in photoelectron angular distributions (CDAD) that is determined by the transient band structure modifications and the associated texture of the orbital angular momentum. Combining highly accurate modeling of the photoemission matrix elements with an ab initio description of the light-matter interaction, we investigate regimes which can be realized in current state-of-the-art experimental setups. The predicted features are robust against scattering effects and are expected to be observed in forthcoming experiments.

Steering of circular dichroism in biharmonic ionization of atoms

Circular dichroism in photoelectron angular distributions of general biharmonic (i.e., $n\ensuremath{\omega}+m\ensuremath{\omega}$) atomic ionization is analyzed theoretically and given along with ``experimental guidelines'' on how it can be steered towards its maximum. It is shown that such a maximum circular dichroism can always be achieved for the ionization of an arbitrary atom and for any incident fundamental photon energy by fine control of only two experimental parameters: the relative flux and phase difference of the two components of the radiation field. In this Letter, we provide a simple analytical description of the circular dichroism as well as a set of rules which enables full control over its magnitude. Our findings are demonstrated explicitly for the ionization of helium with a two-color field composing a fundamental beam and its second harmonic.

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.

A plane wave theory of photoionization using the dipole acceleration form: predictions concerning circular dichroism in photoelectron angular distributions at high energies

Photoelectron angular distributions for randomly oriented atoms and molecules are characterized by the linear and circular dichroic parameters β and b 1, respectively. In the region where the photoelectron kinetic energy is several 100 eV, the values of b 1 and β are expected to be constants. In this study, we show that β for all hydrogen atom orbitals other than s orbitals approach values between 0 to 0.5 at the high-energy limit in the nonrelativistic dipole approximation and that the values can be obtained by the plane wave approximation using the dipole acceleration form. These limiting values are smaller than the widely accepted values for molecules. We discuss the implications of this result for the circular dichroism in photoelectron angular distributions of linear molecules.

Theoretical description of circular dichroism in photoelectron angular distributions of randomly oriented chiral molecules after multi-photon photoionization.

Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem., Int. Ed. 51, 4755 (2012) and C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionization of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.

Linear and circular dichroism in photoelectron angular distributions caused by electron correlation

Electron correlation can break the symmetry of photoelectron angular distribution upon two-step ionization to a doubly degenerate ionic state via a doubly degenerate intermediate state. The interference between the two components of the intermediate state prepared using linearly and circularly polarized light is discussed for cyclopropane as an example.

Time–energy mapping of photoelectron angular distribution: application to photoionization stereodynamics of nitric oxide

The time-energy mapping of the photoionization integral cross section and laboratory-frame photoelectron angular distribution is used to study photoionization stereodynamics of a diatomic molecule. The general theoretical formalism [Y. Suzuki and T. Suzuki, Mol. Phys., 2007, 105, 1675] is simplified for application to a diatomic molecule, and a high-resolution photoelectron imaging apparatus is used to determine the transition dipole moments and phase shifts of photoelectron partial waves in near-threshold and non-dissociative photoionization of NO from the A(2)Σ(+) state. The transition dipoles and phase shifts thus determined are in reasonable agreement with those by state-to-state photoionization experiment and Schwinger variational calculations. The difference of the phase shifts from those expected from the quantum defects of Rydberg states suggests occurrence of weak hybridization of different l-waves, in addition to the well-known s-d super complex. The circular dichroism in photoelectron angular distribution is also simulated from our results.

Stereoscopic photographs of atomic arrangements in MoS2 single-crystal

Taking advantage of the circular dichroism in photoelectron angular distribution (PEAD), stereoscopic photographs of atomic arrangements can be obtained directly by using two-dimensional display-type spherical mirror analyzer (DIANA) and circularly polarized lights. By measuring the PEAD patterns from different core levels, the stereoscopic photographs of atomic arrangements surrounding two kinds of atoms Mo and S in MoS2 single-crystal were taken separately. The stereoscopic photographs show us the same hexagonal arrangements resulting from the unique sandwich and the long interlayer structure. The element selective stereo-photography has been confirmed to be efficient not only for single element crystals, but also for compound crystals.

PHOTOELECTRON DIFFRACTION: SPACE, TIME, AND SPIN DEPENDENCE OF SURFACE STRUCTURES

The current status of photoelectron-diffraction studies of surface structures is briefly reviewed, and several recent developments and proposals for future areas of application are then discussed. The application of full-solid-angle diffraction data, together with simultaneous characterization by low-energy electron-diffraction and scanning-tunneling microscopy, to epitaxial growth is considered. Several new avenues that are being opened up by third-generation synchrotron-radiation sources are also considered. These include photoelectron diffraction from surface and interface atoms, the possibility of time-resolved measurements, and circular dichroism in photoelectron angular distributions. The addition of spin to the photoelectron-diffraction measurement is also considered, and can be achieved either through core-level multiplet splittings or by circular-polarized excitation of spin–orbit-split levels. This last development should make it possible to study short-range magnetic order, perhaps even in a holographic fashion.

DIFFRACTION AND HOLOGRAPHY WITH PHOTOELECTRONS AND FLUORESCENT X-RAYS

We consider studies of the atomic and magnetic structure near surfaces by photoelectron diffraction and by the holographic inversion of both photoelectron diffraction data and diffraction data involving the emission of fluorescent x-rays. The current status of photoelectron diffraction studies of surfaces, interfaces, and other nanostructures is first briefly reviewed, and then several recent developments and proposals for future areas of application are discussed. The application of full-solid-angle diffraction data, together with simultaneous characterization by low energy electron diffraction and scanning tunneling microscopy, to the epitaxial growth of oxides and metals is considered. Several new avenues that are being opened up by third-generation synchrotron radiation sources are also discussed. These include site-resolved photoelectron diffraction from surface and interface atoms, the possibility of time-resolved measurements of surface reactions with chemical-state resolution, and circular dichroism in photoelectron angular distributions from both non-magnetic and magnetic systems. The addition of spin to the photoelectron diffraction measurement is also considered as a method for studying short-range magnetic order, including the measurement of surface magnetic phase transitions. This spin sensitivity can be achieved through either core-level multiplet splittings or circular-polarized excitation of spin-orbit-split levels. The direct imaging of short-range atomic structure by both photoelectron holography and two distinct types of x-ray holography involving fluorescent emission is also discussed. Both photoelectron and x-ray holography have demonstrated the ability to directly determine at least approximate atomic structures in three dimensions. Photoelectron holography with spin resolution may make it possible also to study short-range magnetic order in a holographic fashion. Although much more recent in its first experimental demonstrations, x-ray fluorescence holography should permit deriving more accurate atomic images for a variety of materials, including both surface and bulk regions.

Photoelectron diffraction: new dimensions in space, time, and spin

The current status of photoelectron diffraction studies of surface structures is briefly reviewed, and several recent developments and proposals for future areas of application are then discussed. The application of full-solid-angle diffraction data, together with simultaneous characterization by low energy electron diffraction and scanning tunnelling microscopy, to epitaxial growth is first considered. New instrumentation for carrying out such studies with third-generation synchrotron radiation is then presented and several types of results obtained with it are discussed. These results include photoelectron diffraction from surface and interface atoms, the possibility of time-resolved measurements, and circular dichroism in photoelectron angular distributions. The addition of spin to the photoelectron diffraction measurement is also considered, and can be achieved either through core-level multiplet splittings or by circular-polarized excitation of spin-orbit-split levels. This last development makes it possible to study short-range magnetic order, perhaps even in a holographic fashion.

Photoemission from Co/W(110) with unpolarized and circularly polarized radiation

We report on investigations of thin cobalt films evaporated on W(110). The measurements have probed Magnetic Circular Dichroism in photoelectron angular distribution (MCDAD) and spin-resolved photoemission (SPUPS) with unpolarized light. In particular the energetic dependence of the MCDAD-effect and of the spin-resolved intensities were studied. The results of both experiments are compared in order to get a deeper insight into exchange and spin—orbit interactions.

Photoelectron spectroscopic studies of polyatomic molecules: Degree of orientation and ionization of rotationally state selected, oriented molecules

In this paper we report theoretical studies of angle-resolved photoelectron spectroscopy (ARPES) and of circular dichroism in photoelectron angular distribution (CDAD) for ionization in molecules oriented in a single ‖JKJMJ〉 rotational eigenstate. These processes have been investigated also as two of the possible alternatives to photodissociation to determine orientational distribution function of rotationally state selected, oriented molecules. Expressions are derived which can be used to calculate ARPES and CDAD for such molecular species from ab initio methods or to analyze these experimentally observed spectra for extracting information about the degree of orientation of the molecular framework. These formulas are put in their simplest possible forms using the transformation properties of the molecular point group to their full advantage. The ionization amplitude is thus shown to decompose into a sum of transitions each involving the final state wave function belonging to an irreducible representation of the point group of the target molecule. It is found that, similar to the case of photodissociation, one can determine the rotational quantum number J purely from experimental photoionization data. Expressions developed herein are used to study ARPES and CDAD for ionization in a1 orbital of those rotationally state selected and oriented spherical top molecules which transform according to the Td point symmetry group. In this case, the detection-integrated cross section, singly differential in molecular orientation, is found to be independent of the photoionization dynamics and directly gives the molecular orientational function. The other ARPES and CDAD formulas are shown to depend upon the dynamics through the integrated partial cross section σ̄, the angularly asymmetry parameter β̄, the phase shift of the continuum waves representing the photoelectron, and the phase of the dipole transition amplitudes. The formulation presented in this paper sets a methodology for the analysis of measurements and calculation of the photoelectron spectra in rotationally state selected and oriented molecules in general, spherical top Td molecules in particular. It is applied, as an example, to photoionization in 6a21 orbital of oriented CCl4 in a pure ‖JKJMJ〉 rotational state. We find, among other things, that the photoelectron angular distributions change significantly when either or both of the directions of molecular orientation and of polarization of ionizing radiation vary from parallel to perpendicular to the quantization axis.

Circular dichroism in photoelectron angular distributions for the 7P3/2 level of cesium.

Circular dichroism in photoelectron angular distributions (CDAD) is used to examine the alignment of the 7${\mathit{P}}_{3/2}$ and 7${\mathit{P}}_{1/2}$ levels of cesium, prepared by absorption of linearly polarized laser radiation. As expected, the 7${\mathit{P}}_{1/2}$ level exhibits no CDAD, whereas the 7${\mathit{P}}_{3/2}$ level shows a significant CDAD signal, although smaller than that predicted by theory. The difference between experiment and theory is attributed to ${\mathit{m}}_{\mathit{J}}$ mixing due to hyperfine coupling during the finite ionization time of the laser pulse.

Cooper minima and circular dichroism in photoelectron angular distributions

We demonstrate that circular dichroism in photoelectron angular distributions (CDAD), resulting from resonance enhanced multiphoton ionization (REMPI) of an aligned molecular Rydberg state, is a highly sensitive probe of the presence of a Cooper minimum near threshold. To illustrate this application of CDAD, we present the results of ab initio calculations for (1+1′) REMPI via the R21(5.5) branch of the D 2Σ+(3pσ) state of NO, where a Cooper minimum is found in l=2 (d wave) of the kπ continuum at a photoelectron kinetic energy of 3.2 eV. The CDAD signal is found to vary rapidly with photoelectron kinetic energy, go through zero, and change sign in the region of the Cooper minimum. This result is predicted by CDAD theory for photoionization from an aligned atomic p orbital.

Molecular alignment from circular dichroic photoelectron angular distributions in (n+1) resonance enhanced multiphoton ionization

The theory for determination of molecular alignment from circular dichroism in photoelectron angular distributions is generalized to treat the case in which the excitation polarization direction and the laboratory z axis do not coincide. A new method of data analysis is presented here. Alignment created by surface scattering or photofragmentation should be obtainable by these procedures. For studies of orientation with elliptically polarized excitation, differential cross sections at a given collection angle are found to be, to a good approximation, independent of excited-state alignment. Orientation can thus be obtained from differential cross sections by the methods developed by Kummel, Sitz, and Zare [J. Chem. Phys. 88, 6707 (1988)].

Circular dichroism in photoelectron angular distributions from two-color (1+1) REMPI of NO

A detailed experimental and theoretical study of dichroic effects in photoelectron angular distributions is reported for (1+1), two-color REMPI of NO via the A 2Σ+, v=0 state. Optically aligned A state rotational levels are probed through ionization by circularly polarized light. Resultant photoelectron angular distributions exhibit significant left–right asymmetry, the phase and magnitude of which are shown to be related to the curvature of the excited state MJ distribution. Theoretical calculations involving a full ab initio treatment of the ionization dynamics result in circularly dichroic angular distribution (CDAD) parameters in good agreement with those derived experimentally. Additional effects including hyperfine depolarization and coherence are also discussed in relation to the observed CDAD data.

(1+ 1) CDAD: A new technique for studying photofragment alignment

We report a new technique for measuring photofragment alignment in the gas phase by observing circular dichroism in photoelectron angular distributions (CDAD). This technique is well suited for determining the gas phase alignment of linear molecules. The experiment involves excitation of the photofragment with linearly polarized light followed by photoionization with left or right circularly polarized light. The difference between the photoelectron angular distributions for these two cases is the CDAD spectrum. By measuring CDAD through two different excitation branches, one can obtain the ground state photofragment alignment A(2)0 using a simple analytical formula independent of the photoionization dynamics.

Extraction of alignment parameters from circular dichroic photoelectron angular distribution (CDAD) measurements

In a previous paper, we showed that circular dichroism in photoelectron angular distributions (CDAD) can be used to probe alignment in gas phase atoms and linear molecules. Often this alignment is parametrized through the moments of alignment A(2), A(4), etc., which are commonly extracted from fluorescence polarization measurements. In this paper we show how these can be simply extracted from CDAD spectra. This technique can be used in principle to extract the moments to any order.

Circular dichroism in photoelectron angular distributions as a probe of atomic and molecular alignment

In this paper we show that circular dichroism in photoelectron angular distributions (CDAD) can be used to probe atomic and molecular alignment in the gas phase. Careful choice of photon (left or right circularly polarized) propagation and photoelectron collection directions breaks the cylindrical symmetry of the target, giving rise to dichroic effects. CDAD exists in the electric dipole approximation. We illustrate the sensitivity of CDAD to alignment by considering photoionization of the A 2Σ+ state of NO. Most of the cases of alignment we consider are created by multiphoton absorption while the others, more general, might be created in fragmentation, desorption, etc. The alignment created by n-photon absorption quickly reaches a classical limit which is reflected in the CDAD spectrum. Finally, we show that CDAD is also a sensitive probe of gas phase atomic state alignment by considering photoionization of the 7P3/2 state of cesium created by single photon absorption from the ground state.