Photoemission Delays Research Articles

Berry curvature in the photoelectron emission delay

Density fluctuation potential induced by a screening of the photohole scatters the photoelectron and generally causes its emission delay from the scattering matrix in the photoemission spectroscopy, where the photoemission delay usually quantifies the extrinsic loss of the photoelectron depending on the atomic orbital. Without the potential scattering, however, the photoemission from the coherent two-state mixture created by the laser driving is found to undergo the unexpected photoemission delay, which originates from the mixed photoemission matrix. Using the Haldane model, we analytically calculate such coherent mixing induced photoemission delay in an angle-resolved mode, which is found to reveal the local Berry curvature structure as long as the coherent mixing is sustained. This finding is confirmed through the streaking computation for the photoemission delay by solving the time-dependent Schrödinger equation and suggests that the photoemission delay be a new spectroscopic diagnosis of the material topology of two-dimensional semiconductors.

Attosecond delays in X-ray molecular ionization.

The photoelectric effect is not truly instantaneous but exhibits attosecond delays that can reveal complex molecular dynamics1-7. Sub-femtosecond-duration light pulses provide the requisite tools to resolve the dynamics of photoionization8-12. Accordingly, the past decade has produced a large volume of work on photoionization delays following single-photon absorption of an extreme ultraviolet photon. However, the measurement of time-resolved core-level photoionization remained out of reach. The required X-ray photon energies needed for core-level photoionization were not available with attosecond tabletop sources. Here we report measurements of the X-ray photoemission delay of core-level electrons, with unexpectedly large delays, ranging up to 700 as in NO near the oxygen K-shell threshold. These measurements exploit attosecond soft X-ray pulses from a free-electron laser to scan across the entire region near the K-shell threshold. Furthermore, we find that the delay spectrum is richly modulated, suggesting several contributions, including transient trapping of the photoelectron owing to shape resonances, collisions with the Auger-Meitner electron that is emitted in the rapid non-radiative relaxation of the molecule and multi-electron scattering effects. The results demonstrate how X-ray attosecond experiments, supported by comprehensive theoretical modelling, can unravel the complex correlated dynamics of core-level photoionization.

A multiple scattering theoretical approach to time delay in high energy core-level photoemission of heteronuclear diatomic molecules

We present analytical expressions of momentum-resolved core-level photoemission time delay in a molecular frame of a heteronuclear diatomic molecule upon photoionization by a linearly polarized soft x-ray attosecond pulse. For this purpose, we start to derive a general expression of photoemission time delay based on the first order time dependent perturbation theory within the one electron and single channel model in the fixed-in-space system (atoms, molecules and crystals) and apply it to the core-level photoemission within the electric dipole approximation. By using multiple scattering theory and applying series expansion, plane wave and muffin-tin approximations, the core-level photoemission time delay is divided into three components, , and , which are atomic photoemission time delay, delays caused by the propagation of photoelectron among the surrounding atoms and the scattering of photoelectron by them, respectively. We applied a single scattering approximation to and obtained for a linearly polarized soft x-ray field with polarization vector parallel to the molecular axis for a heteronuclear diatomic molecule, where is the angle of measured photoelectron from the molecular axis. The core-level photoemission time delay is approximated well with this simplified expression in the high energy regime ( a.u.−1, where is the amplitude of photoelectron momentum ), and the validity of this estimated result is confirmed by comparing it with multiple scattering calculations for C 1s core-level photoemission time delay of CO molecules. shows a characteristic dependence on θ, it becomes zero at θ = 0°, exhibits extended x-ray absorption fine structure type oscillation with period at θ = 180°, where R is the bondlength, and gives just the travelling time of photoelectron from the absorbing atom to the neighbouring atom at θ = 90°. We confirmed these features also in the numerical results performed by multiple scattering calculations.

Scattering effects from neighboring atoms in core-level WSe2 photoemission

Methods of attosecond science originally developed to investigate systems in the gas phase are currently being adapted to obtain temporal information on the electron dynamics that takes place in condensed-matter systems. In particular, streaking measurements have recently been performed to determine photoemission time delays from the ${\mathrm{WSe}}_{2}$ dichalcogenide. In this work we present a fully atomistic description of the photoemission process in ${\mathrm{WSe}}_{2}$ and provide angularly resolved photoemission cross sections and time delays from the W $4f$, Se $3d$ and Se $4s$ core states of the system. Since these states are spatially localized, we propose a cluster approach in which we build up from smaller to larger clusters, so that we can assess the importance of scattering effects by each new layer of neighboring atoms. We use a static-exchange density functional theory method with $B$-spline functions, where a one-center angular-momentum expansion is supplemented by off-center expansions with fewer partial waves. This enhances convergence in comparison with a one-center expansion, which would require very high angular momenta to characterize the localized fast oscillations near each off-center atomic core. We find that the photoemission delays and fully differential cross sections are strongly affected by scattering events that take place off the neighboring atoms, implying the need to consider their effects for quantitative descriptions of the photoemission process.

Attosecond photoemission delay in the inhomogeneous field.

We investigate the photoemission process of the hydrogen atom in a spatial-dependent infrared (IR) field. The results show that the inhomogeneous field induces an additional contribution to the photoemission time delay, which results in the increase (decrease) of the photoemission time delay due to the enhancement (decay) of the IR field intensity in space when compared to the case in the homogeneous field. Based on the photoemission time delay in the inhomogeneous field, we demonstrate a method to extract the inhomogeneous parameter that is vital for characterizing the spatial distribution of IR field. The proposed method might pave an accessible route toward describing the plasmon-enhanced fields in the vicinity of a nanostructure.

Measurement of Temporal Coherence of Free Electrons by Time-Domain Electron Interferometry.

The temporal properties of an electron beam are decisive for modern ultrafast electron microscopy and for the quantum optics of the free electron in laser fields. Here, we report a time-domain interferometer that measures and distinguishes the pure and ensemble coherences of a free-electron beam in a transmission electron microscope via symmetry-breaking shifts of photon-order sideband peaks. This result is a free-electron analog to the reconstruction of attosecond busts and photoemission delays in optical attosecond spectroscopy. We find a substantial pure electron coherence that is connected to the thermodynamics of the emitter material and a lower ensemble coherence that is governed by space-charge effects. Pure temporal coherences above 5fs are measured at >10^{9} electrons per second in a high-brightness beam.

Two-center interference and stereo Wigner time delay in photoionization of asymmetric molecules

We present numerical simulations of the time delay in photoemission of asymmetric diatomic molecules using the technique of reconstruction of attosecond beating by interference of two-photon transitions (RABITT) by solving the time-dependent Schr\"odinger equation. Our results show an obvious time delay between photoelectrons emitted to the left and right and this relative time delay oscillates as the photoelectron energy changes. More interestingly, the amplitude of this oscillation increases when the asymmetry degree of diatomic molecules decreases. With the method of the selected continuum wave functions, we calculate the Wigner time delay in photoionization. The obtained stereo Wigner time delay also oscillates with photoelectron energy. This oscillation is traced back to two-center interferences and it could explain the relative time delay in the RABITT measurement. Furthermore, our results indicate that the continuum-continuum time delay in photoemission of heteronuclear molecules is asymmetric.

Universal time delays in the inelastic core level photoemission of metals

Proposing a theoretical model of the core level photoemission of metals, we investigate the plasmon-driven inelastic photoemission delays based on a nonperturbative treatment of many-electron responses due to the long-range Coulomb potential. Being irrelevant to the plasmon coupling strength as well as the plasmon frequency, the emission delays $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{n}$ of the $n\mathrm{th}$-order plasmon satellites ($n=1,2,3,...$) are found to be universal order by order among the metals in the core level photoemission where the recoil-less approximation would be valid. In particular, for a main line with its weight ${e}^{\ensuremath{-}\ensuremath{\gamma}}$, where $\ensuremath{\gamma}$ quantifies the plasmon coupling strength, the average inelastic photoemission delay $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}\ensuremath{\tau}\ensuremath{\rangle}$ is found to be $\ensuremath{\gamma}{(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\gamma}})}^{\ensuremath{-}1}\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$ and thus is simply scaled by a universal time delay $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$. This finding is sharply contrasted with the emission delays under the localized potential, which indicates a fundamental difference in the emission process between extended and localized screenings.

Reconstruction of atomic resonances with attosecond streaking.

Recent development of spectroscopic techniques based on attosecond radiation has given the community the right tools to study the timing of the photoelectron process. In this work we investigate the effect of Fano resonances in attosecond streaking spectrograms and the application of standard phase-reconstruction algorithms. We show that while the existence of the infrared coupling (ac-Stark shift) hinders the applicability of FROG-like methods, under certain conditions it is still possible to use standard reconstruction algorithms to retrieve the photoemission delay of the bare resonance. Finally, we propose two strategies to study the strength of IR coupling using the attosecond streaking technique.

Comment on “Distinction of Electron Dispersion in Time-Resolved Photoemission Spectroscopy”

In a recent paper [Phys. Rev. Lett. 125, 043201 (2020)] (Ref.1) Liao et al. propose a theory of the interferometric photoemission delay based on the concepts of the photoelectron phase and photoelectron effective mass. The present comment discusses the applicability and limitations of the proposed approach based on an ab initio analysis supported by vast literature. Two central assumptions of the paper are questioned, namely that the photoelectron can be characterized by a phase (have a well-defined phase velocity), and that it can always be ascribed an effective mass Theories based on these concepts are concluded to be inapplicable to real solids, which is illustrated by the example of the system addressed in Ref. 1. That the basic assumptions of the theory are never fulfilled in nature discredits the underlying idea of the "time-domain interferometric solid-state energy-momentum-dispersion imaging method" suggested in Ref. 1. Apart from providing a necessary caution to experimentalists, the present comment also gives an insight into the photoelectron wave function and points out problems and pitfalls inherent in modeling real crystals.

Determination of the photoemission position in single-photon ionization with attosecond streaking spectroscopy

Attosecond metrology can directly measure attosecond emission time of photoexcited electrons from matter, providing unprecedented understanding of transition processes of electrons from bound to continuum states. However, some fundamental details of the electron dynamics in the entire emission process upon photoexcitation still remain debatable or unknown. The photoemission time delays deduced from attosecond streaking spectroscopy originate from photoelectron propagation in the coupled Coulomb-laser fields, encoding the spatial and spectral information of electrons upon photoexcitation. Here we demonstrate that attosecond photoemission delays can be used to image picometer-resolved photoemission position via a classical model. The electronic dynamics in the laser-assisted single-photon ionization process is fully captured by a quantum path-integral model. We trace the imaged photoemission position to the average position of spatially coherent superposition of electron waves upon photoexcitation and, in particular, predict emission position coinciding with the orbital radius of the ground state of hydrogen-like atoms, in contrast with previous predictions.

Attosecond spectroscopy of liquid water.

Electronic dynamics in liquids are of fundamental importance, but time-resolved experiments have so far remained limited to the femtosecond time scale. We report the extension of attosecond spectroscopy to the liquid phase. We measured time delays of 50 to 70 attoseconds between the photoemission from liquid water and that from gaseous water at photon energies of 21.7 to 31.0 electron volts. These photoemission delays can be decomposed into a photoionization delay sensitive to the local environment and a delay originating from electron transport. In our experiments, the latter contribution is shown to be negligible. By referencing liquid water to gaseous water, we isolated the effect of solvation on the attosecond photoionization dynamics of water molecules. Our methods define an approach to separating bound and unbound electron dynamics from the structural response of the solvent.

Distinction of Electron Dispersion in Time-Resolved Photoemission Spectroscopy.

While recent experiments provided compelling evidence for an intricate dependence of attosecond photoemission-time delays on the solid's electronic band structure, the extent to which electronic transport and dispersion in solids can be imaged in time-resolved photoelectron (PE) spectra remains poorly understood. Emphasizing the distinction between photoemission time delays measured with two-photon, two-color interferometric spectroscopy, and transport times, we demonstrate how the effect of energy dispersion in the solid on photoemission delays can, in principle, be observed in interferometric photoemission. We reveal analytically a scaling relation between the PE transport time in the solid and the observable photoemission delay and confirm this relation in numerical simulations for a model system. We trace photoemission delays to the phase difference the PE accumulates inside the solid and, in particular, predict negative photoemission delays. Based on these findings, we suggest a novel time-domain interferometric solid-state energy-momentum-dispersion imaging method.

Probing molecular environment through photoemission delays

Attosecond chronoscopy has revealed small but measurable delays in photoionization, characterized by the ejection of an electron on absorption of a single photon. Ionization-delay measurements in atomic targets provide a wealth of information about the timing of the photoelectric effect, resonances, electron correlations and transport. However, extending this approach to molecules presents challenges, such as identifying the correct ionization channels and the effect of the anisotropic molecular landscape on the measured delays. Here, we measure ionization delays from ethyl iodide around a giant dipole resonance. By using the theoretical value for the iodine atom as a reference, we disentangle the contribution from the functional ethyl group, which is responsible for the characteristic chemical reactivity of a molecule. We find a substantial additional delay caused by the presence of a functional group, which encodes the effect of the molecular potential on the departing electron. Such information is inaccessible to the conventional approach of measuring photoionization cross-sections. The results establish ionization-delay measurements as a valuable tool in investigating the electronic properties of molecules. Ionization delays from ethyl iodide around a giant dipole resonance are measured by attosecond streaking spectroscopy. Using theoretical knowledge of the iodine atom as a reference, the contribution of the functional ethyl group can be obtained.

Photoemission delays in 2D model molecules

SynopsisPhotoelectron spectroscopy is one of the main techniques used to probe matter since the understand-ing of the photoelectric effect. Within the last decade, a new aspect has been given to spectroscopy, revisiting it in the time domain. It allows one to resolve the electron dynamics at the attosecond (10−18 s) time scale. Achieving such resolution experimentally brought one to establish innovative set up, and theoretical background is needed to validate, predict and interpret measurements. Much progress has been made in the attoscience field, this work is a step forward in understanding the electron dynamics for molecular continuum states at the attosecond timescale.

Attosecond delays in photoionization studied with coherent-controlled FEL

SynopsisWhen an electron is ejected from an atom after absorption of a photon, the photoelectron wave packet has an extremely short group delay between the photon absorption and the electron emission. This interval, called the Eisenbud-Wigner-Smith delay, is on the order of a few attoseconds. Here, we present a new method to measure the photoemission delay, using coherent-controlled free-electron laser pulses.

Photoemission time versus streaking delay in attosecond time-resolved solid state photo-emission

Time-dependent Schrodinger equation simulations for a one-dimensional model potential reveal that the delay extracted from a streaking spectrogram does not reflect the photoemission time if the streaking field inside the solid cannot be neglected.

Atomic scale electronic structure and response in attosecond photoemission delays: A case study using non-centrosymmetric BiTeCl

Attosecond time-resolved photoemission from the differently terminated BiTeCl surfaces yield a photoelectron streaking that cannot be explained by bulk propagation effects alone. Instead, the atomic scale electronic structure and dynamical screening for both surface terminations have to be taken into account.

Photoionization delays in xenon using single-shot referencing in the collinear back-focusing geometry

Attosecond photoemission delays for all the valence (5p3/2, 5p1/2, 5s, 4d5/2, 4d3/2) subshells of xenon have been accessed using the interferometric RABBITT technique. The 4d subshell delays in Xe have been accessed for the first time, to the best of our knowledge, due to the high photon energy used. A novel technique of single-shot referencing in the collinear back-focusing geometry has been introduced. This enables us to distinguish the signal from principal photoelectron peaks due to ionization by extreme ultraviolet radiation only and infrared-induced sideband contributions, especially in the regions of spectral overlap.

Energy-resolved attosecond interferometric photoemission from Ag(111) and Au(111) surfaces

Photoelectron emission from solid surfaces induced by attosecond pulse trains into the electric field of delayed phase-coherent infrared (IR) pulses allows the surface-specific observation of energy-resolved electronic phase accumulations and photoemission delays. We quantum-mechanically modeled interferometric photoemission spectra from the (111) surfaces of Au and Ag, including background contributions from secondary electrons and direct emission by the IR pulse, and adjusted parameters of our model to energy-resolved photoelectron spectra recently measured at a synchrotron light source by Roth et al. [J. Electron Spectrosc. 224, 84 (2018)]. Our calculated spectra and photoelectron phase shifts are in fair agreement with the experimental data of Locher et al. [Optica 2, 405 (2015)]. Our model's not reproducing the measured energy-dependent oscillations of the Ag(111) photoemission phases may be interpreted as evidence for subtle band-structure effects on the final-state photoelectron-surface interaction not accounted for in our simulation.