Here, we report the first time- and angle-resolved photoemission spectroscopy (TR-ARPES) with the new Fermiologics “FeSuMa” analyzer. The new experimental setup has been commissioned at the Artemis laboratory of the UK Central Laser Facility. We explain here some of the advantages of the FeSuMa for TR-ARPES and discuss how its capabilities relate to those of hemispherical analyzers and momentum microscopes. We have integrated the FeSuMa into an optimized pump–probe beamline that permits photon-energy (i.e., kz)-dependent scanning, using probe energies generated from high harmonics in a gas jet. The advantages of using the FeSuMa in this situation include the possibility of taking advantage of its “fisheye” mode of operation.

Pump–probe time- and angle-resolved photoemission spectroscopy (TR-ARPES) presents challenges, with respect to both light sources and detection, that do not arise in “static” ARPES measurements of systems at equilibrium. In this paper, we describe the commissioning of the newly developed “FeSuMa” analyzer on a beamline for high-harmonic generation (HHG) at the UK Central Laser Facility’s Artemis Laboratory. We demonstrate efficient acquisition of high-quality ARPES spectra of optically pumped excitations close to the Fermi level, and we use the FeSuMa’s “fisheye” measurement mode in combination with the beamline’s capability to switch rapidly between ultraviolet (UV) photon energies that are generated as high harmonics in an Ar gas jet. We suggest that this measurement configuration offers major benefits as a laboratory-scale approach to TR-ARPES.

Compared to its static equivalent, an ultrafast TR-ARPES measurement adds a “pump” laser pulse, which—arriving at a well-defined delay time Δt before the system is probed—promotes the system into an optically excited state. The transient, out-of-equilibrium state and its evolution in time are the subject of study. Both the probe and the pump pulses must be short (i.e., must have a narrow width in the time domain) relative to the time scales of the physical phenomena to be measured, and the pulse train of the pump must be well synchronized to that of the probe. The pulse widths and the pulse synchronization determine the limits of time resolution in the experiment.

1. Background: Light sources

Pump–probe methods require the simultaneous generation of synchronized pulse trains of very different energies. In TR-ARPES, an infrared (IR) or visible pulsed beam is needed for excitation, while an ultraviolet (UV) or extreme ultraviolet (XUV) beam probes the system via photoexcitation. The Fourier limit places a strict boundary on the energy resolution achievable in an experiment, depending on what time resolution is needed (or, vice versa, if energy resolution is critical, then the Fourier limit determines the maximum achievable time resolution). The demands on the resolution are set by the time and energy scales of the physical phenomena of interest: for example, studies of electron–electron interactions typically demand time resolution of no worse than tens of fs.1 

Light sources commonly used to supply the pulsed ultraviolet probe beam include tabletop laser setups2,3 and free-electron lasers.2,4,5 This paper deals with tabletop laser setups. Wavelengths down to ∼115 nm (i.e., energies up to ∼11 eV) are achievable with commercial off-the-shelf laser systems.6 However, even at 11 eV, one can access only a relatively small section of momentum space up to ∼1.3 Å−1. Off-the-shelf laser systems cannot generate photons in the tens-of-eV range that allows ARPES to access the full three-dimensional (3D) Brillouin zone of most crystalline materials, or that gives access to shallow-lying core-level states. To reach this range in a tabletop setup, one typically relies on HHG—usually in a gas jet.3,7

It is possible to use a single powerful laser to generate both the IR pump and the HHG XUV beam. An advantage of this approach is that the pulse trains of the two beams are automatically synchronized. The method works by taking the IR beam from a commercial laser system and splitting it into two parts: one is used to generate HHG, and the other is sent along a separate beam path for use as a pump. A movable delay stage in one of the beamlines (typically the pump beamline) controls the pulse separation Δt, and then, the two beams are recombined.

In a 3D-dispersing system, the probe photon energy determines which part of the 3D Brillouin zone (BZ) is measured. Control of the probe energy also allows for optimization of photoemission intensity in electronic states of interest via the control of final state and matrix element effects.8–12 While this is the basis for photon-energy-dependent synchrotron-based studies of out-of-plane-dispersing “kz” states, the situation is more challenging for laser-based experiments: while a synchrotron or FEL undulator can generate probe photons with continuously tunable energy across a wide range,13 no such continuous spectrum is possible with laser-based HHG. Rather, HHG produces a “frequency comb” of odd-ordered harmonics14 [Fig. 1(b)]. A single frequency from the comb can be selected with a combination of reflective and transmissive optics.15 At Artemis, we take an alternative approach, using a grating monochromator, which spatially separates the frequencies of the HHG comb into a “fan,” and a slit that picks out a single frequency from the fan.7,16 When the monochromator is properly aligned, any frequency in the comb can be quickly selected on-the-fly, which provides great flexibility to choose different photon energies.7 The power of this type of approach has recently been demonstrated.16 

FIG. 1.

(a) The spectrum of the Ti:sapphire laser, centered at about 790 nm with a bandwidth of ∼50 nm. (b) High-harmonics spectrum generated in the argon gas jet. The maximum photon flux is ∼1010 photons/second/harmonic at 27 eV. A time-preserving monochromator is used to choose between the probe energies. (c) Calibration curves for the incident pump polarization, acquired as measured intensity through a polarizer after the QWP as the HWP is rotated. When the polarizer selects linear vertical, the red points are measured. When the polarizer selects linear horizontal, the blue points are measured. Having fit these two curves to sinusoidal functions, we can readily set the pump polarization by rotating the HWP. Linear vertical and linear horizontal polarizations correspond to 205° and 249° angles, respectively. The two circular polarizations correspond to 227° and 272°. (d) The spot sizes of the probe beam (vertical × horizontal = 130 × 210 μm2, FWHM) and pump beam (194 × 420 μm2, FWHM), as captured by FeSuMa. Note that the horizontal dimension is elongated, because the sample here is rotated 45° away from the beam. The vertical dimension differs slightly from the rough estimate made with the camera image of the scintillator crystal. (e) A simplified schematic of the experimental setup. The locations of delay stages are labeled “DS,” while “BS” indicates an 80–20 beam splitter.

FIG. 1.

(a) The spectrum of the Ti:sapphire laser, centered at about 790 nm with a bandwidth of ∼50 nm. (b) High-harmonics spectrum generated in the argon gas jet. The maximum photon flux is ∼1010 photons/second/harmonic at 27 eV. A time-preserving monochromator is used to choose between the probe energies. (c) Calibration curves for the incident pump polarization, acquired as measured intensity through a polarizer after the QWP as the HWP is rotated. When the polarizer selects linear vertical, the red points are measured. When the polarizer selects linear horizontal, the blue points are measured. Having fit these two curves to sinusoidal functions, we can readily set the pump polarization by rotating the HWP. Linear vertical and linear horizontal polarizations correspond to 205° and 249° angles, respectively. The two circular polarizations correspond to 227° and 272°. (d) The spot sizes of the probe beam (vertical × horizontal = 130 × 210 μm2, FWHM) and pump beam (194 × 420 μm2, FWHM), as captured by FeSuMa. Note that the horizontal dimension is elongated, because the sample here is rotated 45° away from the beam. The vertical dimension differs slightly from the rough estimate made with the camera image of the scintillator crystal. (e) A simplified schematic of the experimental setup. The locations of delay stages are labeled “DS,” while “BS” indicates an 80–20 beam splitter.

Close modal

2. Background: Photoelectron detection and analyzers

The best-established technology for photoelectron spectroscopy is the hemispherical analyzer (HA). This tool measures photoemission intensity as a function of momentum and energy across a wide range of binding energies and with energy resolution that is better than 1 meV.17 The HA has been the workhorse of the photoemission community and is likely to remain so for the foreseeable future. Moreover, the state-of-the art HA technology increasingly incorporates advanced features; for example, spin detection. However, if electronic states of interest do not correspond to a single set of emission angles along the slit direction of the analyzer, then multiple HA measurements must be taken—either by rotating the sample in front of the analyzer or by applying “deflector” voltages to the electron lens column, in order to sample emission angles away from the slit direction. This works well but can pose a challenge in the context of pump–probe measurements, where each dataset is intrinsically time consuming (on account of the need to acquire spectra at multiple time delays). When important physics arise simultaneously in multiple parts of the Brillouin zone, an alternative approach to detection can be useful. We note that, in the case of short-pulse pump–probe applications, the high energy resolution of the HA greatly exceeds the Fourier limit of the short light pulses.

Recent years have seen rapid advancements in new types of analyzer technologies.18–20 Some achieve energy discrimination by a time-of-flight (ToF) approach. Among these analyzers are various types of photoemission electron microscopes (PEEMs) and momentum microscopes (MMs).21 They are powerful, permitting sophisticated momentum-space and real-space mapping, but also present new challenges. In the case of PEEM and ToF-MM, a large potential difference must be applied between the sample and the objective lens of the electron optics. Because these are close together (on the order of several mm), there is a possibility of dielectric breakdown across the small vacuum gap and, as a result, sample damage. Another challenge, in the case of pulsed-probe measurements, arises with space-charge effects in the electron optics.5 The latter issue is discussed below.

Very recently, a new type of simple, economical, and yet highly effective photoelectron analyzer has been developed. The working principle—similar to that of velocity map imaging22,23—has been described in a recent paper.24 From the point of view of pump–probe measurements, we find that this new analyzer, which is available commercially under the name “FeSuMa” (“Fermi Surface Mapper”), offers certain advantages over other types of analyzers for some of the most commonly required types of pump–probe ARPES measurements. The technology offers an efficient approach to the measurement of the full Brillouin zone. It has a very straightforward application to states near the Fermi surface, which are the primary states of interest for many pump–probe ARPES studies; however, it can also probe deeper-lying states, including shallow-lying core levels. When used on a beamline with photon-energy control, it offers an efficient method for 3D measurements of kz-dispersing states. The “fisheye” mode of operation, which we discuss below, allows for such measurements to be made without the shrinking and expanding of k-space on the detector. In addition, the analyzer’s user-friendly operation and compact profile make it easy to incorporate into crowded lab spaces and into vacuum chambers that might contain several other tools for various other types of measurements. In the sections that follow, we describe how these advantages have been integrated into our tabletop HHG beamline at Artemis to take advantage of the special capabilities of the FeSuMa in the context of pump–probe ARPES measurements.

In Fig. 1, we present the layout of the Artemis optical setup for the tests described here. The pump and probe pulses are generated from the output of a 1-kHz Ti:sapphire laser (KMLabs RedDragon, upgraded by Crunch Tech) with a pulse energy of about 3 mJ at 790 nm. The bandwidth is ∼50 nm, as shown in Fig. 1(a). The output laser beam is split into two parts, with 80% focused onto a 200 μm Ar gas jet, via a lens of 500-mm focal length, for HHG. An example of the resulting XUV spectrum, i.e., the frequency comb, is shown in panel (b). For these conditions, the useable high-harmonic energies range from ∼17 to 45 eV, with a maximum photon flux of about 1010 photons/second/harmonic at 27 eV. A single harmonic is selected by a time-preserving grating monochromator.25 To avoid space-charge effects, which are discussed in Sec. IV B, the photon flux was reduced to 108 photons/second/harmonic by an adjustable slit after the monochromator.

The remaining 20% of the output beam is used for pumping, either at its fundamental wavelength or after frequency-doubling or frequency-quadrupling by beta barium borate crystals. A delay stage in the pump beamline enables time-resolved measurements. A half-wave plate (HWP) and a quarter-wave plate (QWP) are added into the pump beamline for polarization control: Fig. 1(c) shows the calibration data for the HWP rotation angle (QWP angle was held fixed). The pump beam is, finally, focused on the sample, using a lens with a focal length of 1.5 m. The pump and probe beams reach the sample almost collinearly, with an angle of 45° relative to the sample normal when the sample is at normal emission relative to the detector. The XUV spot size of about 80 μm is measured roughly by the size of the spot on a scintillator crystal nearly normal to the beam. The beam spot can also be directly imaged on the sample by the FeSuMa in direct mode (see Sec. II B). The images of the two beam spots, as recorded by FeSuMa, are presented in Fig. 1(d). Time resolution is determined from the auto-correlation spectrum, which is shown in the supplementary material.

The FeSuMa is a new type of ARPES analyzer that combines Fourier electron optics with retarding field techniques.24 The lens of the device consists of several cylindrical elements that represent the simplest element of electron optics—the Einzel lens. It focuses parallel electron beams, originating from the sample surface, into corresponding points in the focal plane. This is similar to the action of a convex optical lens, which makes a Fourier transformation of light. The novelty of the approach is in placing the detector, a multichannel plate (MCP), directly in the focal plane, and applying a retarding potential Vr to the front of the MCP. In practice, the focal points lie not on a plane but on a curved surface, and the detector is placed so as to achieve a reasonable balance between angular acceptance and angular resolution. The signal is amplified by a pair of MCPs in “chevron” geometry and is converted into photons by a phosphorus screen. A camera outside the vacuum captures the image and sends it to the computer for further processing.

By setting Vr such that only Fermi-level electrons can reach the detector from an unpumped sample, one can observe the Fermi surface map directly on the screen. In order to obtain information about electrons with higher binding energies, Vr is reduced step-by-step while the detector collects the integrated signal. Subsequent differentiation results in a conventional photoemission spectrum. An example of such a measurement is shown in Fig. 2(a), where we show a Bi core-level spectrum acquired from the Bi(111) surface (see also the supplementary material). The spin–orbit splitting in the Bi 5d doublet is well resolved when the spectrum is differentiated, as shown in Fig. 2(b). In like manner, to obtain the intensity distribution of a photoemission signal from valence states as a function of momentum and energy, a three-dimensional dataset is recorded and then differentiated along the energy axis across a smaller range of energies close to the Fermi level. We show the example for the case of Bi(111) in Fig. 2(c), where the Fermi surface, momentum distribution, and underlying dispersion of the electronic states are visible. Due to the semimetallic nature of bulk Bi, the photoemission intensity at the Fermi level is dominated by surface states.26 The bulk and surface Brillouin zone (BZ) of Bi(111) is provided in Fig. 2(d), for reference.

FIG. 2.

(a) Example of static angle-integrated raw data obtained from Bi(111) by scanning the retarding potential Vr ( = 37.4 eV, sample at room temperature). (b) Same data as in (b), after differentiation. The core-level spectrum of Bi(111) is now well resolved. The dataset in (a) and (b) was acquired as three sweeps of 149 steps, 5 s/step. (c) Example of an (E, kx, ky)-resolved dataset, acquired without optical pumping from Bi(111) ( = 22.4 eV, sample measurement temperature 78 K). The directions of the cuts correspond to the directions of the lines (matched in color to the frames of the two spectra) in the constant-energy contour at left. Note the scale bar at the bottom: high-symmetry points K̄ and M̄ are outside the range shown in the panel. The asymmetry of intensity in the cut along M̄Γ̄M̄ arises from matrix element effects that can be seen clearly in the constant energy slices at left. These data were acquired as 111 sweeps of 12 steps, 20 s/step. (d) Schematic of the Bi BZ, with high-symmetry points labeled. (d) is adapted with permission from Hirahara et al., Phys. Rev. Lett. 97, 146803 (2006). Copyright 2006 American Physical Society.27 

FIG. 2.

(a) Example of static angle-integrated raw data obtained from Bi(111) by scanning the retarding potential Vr ( = 37.4 eV, sample at room temperature). (b) Same data as in (b), after differentiation. The core-level spectrum of Bi(111) is now well resolved. The dataset in (a) and (b) was acquired as three sweeps of 149 steps, 5 s/step. (c) Example of an (E, kx, ky)-resolved dataset, acquired without optical pumping from Bi(111) ( = 22.4 eV, sample measurement temperature 78 K). The directions of the cuts correspond to the directions of the lines (matched in color to the frames of the two spectra) in the constant-energy contour at left. Note the scale bar at the bottom: high-symmetry points K̄ and M̄ are outside the range shown in the panel. The asymmetry of intensity in the cut along M̄Γ̄M̄ arises from matrix element effects that can be seen clearly in the constant energy slices at left. These data were acquired as 111 sweeps of 12 steps, 20 s/step. (d) Schematic of the Bi BZ, with high-symmetry points labeled. (d) is adapted with permission from Hirahara et al., Phys. Rev. Lett. 97, 146803 (2006). Copyright 2006 American Physical Society.27 

Close modal

The FeSuMa operates in three regimes: Fourier mode, direct mode, and optical mode. Within the first of these regimes, there are actually three settings, characterized by angular acceptances of ±8°, ±14°, and ±16°. Angular acceptance in the Fourier modes can be extended by applying a bias potential (see discussion below and Fig. 5)—a technique that is also used in conventional ARPES.28 The FeSuMa’s ability to instantly detect the angular distribution of intensity allows the parameters to be quickly adjusted, minimizing the distortion of the electric field caused by any non-cylindrical symmetry in the sample environment.

In the direct mode, the lens projects an image of the electron source in real coordinates; thus, it can be used to characterize and track the beam spot in two dimensions [see Fig. 1(d)]. This is a significant advantage in comparison with conventional HAs, where only one spatial coordinate, corresponding to the direction along the entrance slit, is accessible.

Since the MCP is sensitive to UV photons, an optical mode can be used to detect reflected or scattered light from surface features and sample edges and thus either to track the position of the photon beam or to find flat portions of the surface (since no photons should enter the analyzer from a flat sample region if the electron signal is optimized).

For the measurements shown here, direct and optical modes were used as “live” modes for quick setup, alignment, and beam spot characterization.

A key difference between the FeSuMa and other electron analyzers is that it detects all photoelectrons of a given binding energy under the same conditions: the electrons are counted by the MCP after being decelerated to the kinetic energy that is selected by the choice of retarding voltage. Typically, this implies a detected kinetic energy of 2–20 meV. In point of fact, the efficiency of MCP detectors at such low electron energies is not yet fully understood and remains an area of ongoing investigation. Although the most recent study29 indicates that the efficiency stays constant down to 30 eV, significant variations below this energy are expected.30 Such variations are crucial for understanding the true line shape of the photoemission spectrum. Our own observations imply that the MCP exhibits an enhanced probability for detecting electrons in the energy range relevant for the FeSuMa; our interpretation is that very slow electrons, whose initial trajectories would otherwise end between the channels, are guided into the channel by the field in that region. By this reasoning, one might predict that the FeSuMa would detect photoelectrons of a given kinetic energy quite effectively, because of this enhancement, and that this could reduce typical measurement times. This remains, however, to be further studied. In the supplementary material, we show a representative time-dependent dataset acquired from the pumped conduction band of cleaved bulk 2H–WSe2 over a period of 20 min.

We finally mention here an advantage of the FeSuMa for pump–probe experiments: unlike in HAs and MMs, electron trajectories in the FeSuMa (being an order of magnitude shorter) do not pass through auxiliary focal planes or crossing points. In HAs, there are two imaging planes and one crossing point where electron trajectories are brought together (e.g., Ref. 31), and Coulombic electron–electron interactions are presumably enhanced at such points. It is generally desirable to avoid such space-charge effects, as they degrade angular and energy resolution. In the case of MMs, electron–electron interactions both inside the focusing column and in front of the objective lens are complex and problematic.5,19,32 The FeSuMa’s design, which reduces the effects of space-charge inside the electron optics, is beneficial to pump–probe measurements. This will be discussed further below.

The energy resolution of the FeSuMa analyzer is ∼12 meV, and the angular resolution is better than 0.2° in all angularly resolving modes.24 This resolution is not a limiting factor for short-pulse measurements, where the energy broadening of the laser pulses is intrinsically large.

In the following, we summarize the versatile applications of the FeSuMa analyzer when coupled with a pump–probe setup. To facilitate comparison with similar approaches involving HAs and MMs,19 we benchmark the capabilities of the system using a widely studied layered transition metal dichalcogenide, cleaved bulk trigonal prismatic tungsten diselenide (2H–WSe2). Bulk WSe2 is an indirect bandgap semiconductor33 with a hexagonal BZ that is sketched in Fig. 3(a). Its valence band maximum (VBM) is located at the Γ-point, and the conduction band minimum (CBM) is located at the Σ-valley, in between Γ and K. Upon optical excitation with a circularly polarized infrared pulse, the material exhibits spin-, valley-, and layer-polarization.34 

FIG. 3.

(a) Surface (dark blue) and three-dimensional (green) Brillouin zones of 2H–WSe2. (b) (kx, ky) slices corresponding to different stages of the ultrafast evolution of the system after pumping with s-polarized light at 800 nm (probe photon energy = 22.6 eV, sample temperature 78 K, and pump fluence 3.5 mJ/cm2). The sample is rotated such that Γ̄ is at the left edge of the detector. The K̄ and Σ̄ points of the Brillouin zone are labeled. (i) Just after the optical excitation, only K̄-points are populated. (ii) Within 50 fs of the optical excitation, electrons can be seen to transfer from the K̄-valleys to Σ̄-valleys. The retarding potential Vr is set such that EEF = 0.65 eV. (iii) At longer times after the pump arrival, all the excited electronic population has either transferred to the Σ̄-points or has relaxed fully. (c) Ultrafast dynamics of 2H–WSe2: orange (green) markers denote the photoemission intensity difference, relative to pre-pumped intensity, integrated over the K̄(Σ̄)-points of the Brillouin zone. Time zero (Δt = 0) was determined by fitting the K̄-point intensity with an exponential decay convoluted with a Gaussian instrument-response function. The time resolution was taken to be 57 fs. (See the supplementary material for details on the experimental determination of time resolution.) The temporal dynamics in (c) are in good agreement with previously published results.5,19,34

FIG. 3.

(a) Surface (dark blue) and three-dimensional (green) Brillouin zones of 2H–WSe2. (b) (kx, ky) slices corresponding to different stages of the ultrafast evolution of the system after pumping with s-polarized light at 800 nm (probe photon energy = 22.6 eV, sample temperature 78 K, and pump fluence 3.5 mJ/cm2). The sample is rotated such that Γ̄ is at the left edge of the detector. The K̄ and Σ̄ points of the Brillouin zone are labeled. (i) Just after the optical excitation, only K̄-points are populated. (ii) Within 50 fs of the optical excitation, electrons can be seen to transfer from the K̄-valleys to Σ̄-valleys. The retarding potential Vr is set such that EEF = 0.65 eV. (iii) At longer times after the pump arrival, all the excited electronic population has either transferred to the Σ̄-points or has relaxed fully. (c) Ultrafast dynamics of 2H–WSe2: orange (green) markers denote the photoemission intensity difference, relative to pre-pumped intensity, integrated over the K̄(Σ̄)-points of the Brillouin zone. Time zero (Δt = 0) was determined by fitting the K̄-point intensity with an exponential decay convoluted with a Gaussian instrument-response function. The time resolution was taken to be 57 fs. (See the supplementary material for details on the experimental determination of time resolution.) The temporal dynamics in (c) are in good agreement with previously published results.5,19,34

Close modal

We start by demonstrating a simple approach to a common (but historically challenging) application of TR-ARPES: namely, characterization of excited carrier relaxation between local conduction band minima in different parts of the BZ. In Fig. 3(b), we present the evolution of excited state signals that have been collected with Vr set so as to probe just above the Fermi level. Since every electron with a kinetic energy greater than eVr is collected by the FeSuMa, all the unoccupied states can be monitored concurrently, regardless of their energy dispersion. A comprehensive discussion of the dynamics, for both bulk and single-layer WSe2, can be found in multiple publications (e.g., Refs. 34–36). Here, we simply highlight that the FeSuMa allows for the detection of localized charge populations across a large portion of the BZ simultaneously, allowing for identification of scattering pathways in the material. The time traces in Fig. 3(c) were collected over 20 min, corresponding to 36 s of acquisition per frame. As can be seen in this figure, the statistics are excellent, despite having been acquired with a low probe flux of only 108 photons/second.

We note certain limitations of the efficient approach just described: here, time-resolved measurements are performed by integration, while maintaining Vr at a set value. The analysis of data acquired in this way can be challenging if there are multiple excitations at different binding energies but similar k; furthermore, access to information about band curvatures is restricted. Of course, the dataset can be extended to four dimensions (kx, ky, E, and Δt), simply by sweeping Vr in the manner described above. Sweeping Vr increases acquisition times in a way similar to the sweeping of deflector voltages in a HA.

An advantage that the FeSuMa shares with PEEM and momentum microscopy is the capability for maintaining a fixed sample geometry while mapping the momentum space. Incident light polarization can remain fixed and photoemission matrix elements unchanged throughout an experiment, and one can straightforwardly extract information such as dichroism from excited-state populations. In Fig. 4(a), we show the excited carrier distributions that arise in 2H–WSe2 pumped with four polarizations: linear vertical (LV), linear horizontal (LH), circular right (CR), and circular left (CL). Here, the choices of photon energy and acceptance angle do not image the whole BZ but allow us to simultaneously see dynamics at the inequivalent K̄- and K̄’-points and at the corresponding Σ̄- and Σ̄’-points. The excitation with linearly polarized light leads to negligible linear dichroic (LD) contrast in the population at K̄- and Σ̄-points. Pumping with LH light produces a strong signal around the Γ̄-point; this is a known consequence of multi-photon photoemission processes that are enhanced by this polarization.37,38 Meanwhile, we see a significant circular dichroic (CD) signal at the adjacent K̄- and K̄-points. This arises due to a combination of (1) the primarily two-dimensional character of the states at K̄ and K̄ and (2) the surface sensitivity of the ARPES measurement.34,39 Indeed, the low photoelectron kinetic energies in the measurements described here mean that these spectra are highly sensitive to the physics of the topmost atomic layer of the crystalline structure.40 

FIG. 4.

(a) Spin- and valley-polarized excited carriers in the surface electronic band structure of 2H–WSe2 along the Γ̄K̄ high-symmetry line. At left, adapted from Ref. 34, the red and blue arrows overlaid on the band structure plot refer to the spin polarization of the bands. The light green and dark blue arrows indicate the polarizations of the pump pulse. The data show pump polarization-dependent measurements of excited-state spectra. The labels at the upper right-hand corners indicate linear vertical (LV) and linear horizontal (LH) polarizations, linear dichroism (LD) as a difference plot of LH–LV, circular right (CR) and circular left (CL) polarizations, and circular dichroism (CD) as a difference plot of CL–CR. The probe energy was 22.6 eV, and the spectra were collected at the time delay of 200 fs. (b) Probe-photon-energy-dependent excited-state spectra at the peak of excitation (top row) and at 400 fs after the excitation (bottom row). The probe photon energy is indicated at the upper-right-hand corner at the top of each column. Assuming an inner potential value of V0 = 13 eV39 and free-electron-like final states, the photon energy range covers an out-of-plane momentum range from ∼2.5 to 3.4 Å−1 (one Brillouin zone). The out-of-plane electronic dispersion along Σ–X leads to a photon-energy-dependence in the photoemission intensity of the states projected into Σ̄. Meanwhile, the states along K–H are nearly non-dispersing, and thus, the photoemission intensity in those states is more nearly independent of probe photon energy. Data in (a) and (b) were acquired with a pump fluence of 3.5 mJ/cm2 at 800 nm, and Vr set such that EEF = 0.65 eV. (b) is adapted with permission from Bertoni et al., Phys. Rev. Lett. 117, 277201 (2016). Copyright 2016 American Physical Society.

FIG. 4.

(a) Spin- and valley-polarized excited carriers in the surface electronic band structure of 2H–WSe2 along the Γ̄K̄ high-symmetry line. At left, adapted from Ref. 34, the red and blue arrows overlaid on the band structure plot refer to the spin polarization of the bands. The light green and dark blue arrows indicate the polarizations of the pump pulse. The data show pump polarization-dependent measurements of excited-state spectra. The labels at the upper right-hand corners indicate linear vertical (LV) and linear horizontal (LH) polarizations, linear dichroism (LD) as a difference plot of LH–LV, circular right (CR) and circular left (CL) polarizations, and circular dichroism (CD) as a difference plot of CL–CR. The probe energy was 22.6 eV, and the spectra were collected at the time delay of 200 fs. (b) Probe-photon-energy-dependent excited-state spectra at the peak of excitation (top row) and at 400 fs after the excitation (bottom row). The probe photon energy is indicated at the upper-right-hand corner at the top of each column. Assuming an inner potential value of V0 = 13 eV39 and free-electron-like final states, the photon energy range covers an out-of-plane momentum range from ∼2.5 to 3.4 Å−1 (one Brillouin zone). The out-of-plane electronic dispersion along Σ–X leads to a photon-energy-dependence in the photoemission intensity of the states projected into Σ̄. Meanwhile, the states along K–H are nearly non-dispersing, and thus, the photoemission intensity in those states is more nearly independent of probe photon energy. Data in (a) and (b) were acquired with a pump fluence of 3.5 mJ/cm2 at 800 nm, and Vr set such that EEF = 0.65 eV. (b) is adapted with permission from Bertoni et al., Phys. Rev. Lett. 117, 277201 (2016). Copyright 2016 American Physical Society.

Close modal

A full movie of dynamics in a different material system—Bi(111)—is available in the supplementary material.

A powerful aspect of the Artemis setup is its ability to switch efficiently between different HHG probe energies. (See also Ref. 16 for a description of a similar capability previously established at a different facility.) This is possible because of carefully optimized optical alignment in the beamline and fine angular control of the final toroidal focusing mirror. Thus, we can coarsely map the out-of-plane dispersion of unoccupied states, in a manner analogous to that by which the occupied-state kz-dispersion is obtained at synchrotron light sources. We demonstrate this principle in Fig. 4(b). Varying the probe energy leads to strikingly different excited state signals across the BZ. The lowest-lying conduction-band states along the K–H path are nearly non-dispersive41 and are visible at all photon energies. However, the scattering from K to Σ is well captured at only one probe energy, 22.5 eV. In this connection, we note both that the out-of-plane dispersion along the Σ–X path is more pronounced than that along the K–H path41 and that the photoemission matrix elements are presumably enhanced at particular probe energies.10,16,42 The first of these points highlights the importance of thoughtful HHG photon-energy selection in studies of materials in which 3D-dispersing band structures play an important role; this is the case, for example, in Weyl candidates Co3Sn2S243 and PtTe2.44 The second points to the possibility of using matrix element effects to optimize signal-to-noise for all types of samples, including those with a primarily two-dimensional electronic character.

Applying a bias voltage to the sample holder is a convenient approach to increase the momentum field of view.28 Due to the additional component of the field toward the analyzer [schematically shown in Fig. 5(a)], electron trajectories are bent, and electrons that initially deviate strongly from the lens axis are, nevertheless, able to enter the analyzer. Thus, using photon energies of only 16.2, 22.2, 28.6, and 34.2 eV, we cover portions of the momentum space at the Fermi level that are much larger than we would otherwise be able to access without the fisheye voltage, achieving radii of 0.81, 0.88, 0.9, and 0.97 Å−1, respectively. (Note that we would expect angular resolution to change in proportion to the changing angular acceptance.) The drawback of this approach is that it can lead to distortions resulting from the presence of the electrical field, especially when cylindrical symmetry around the lens axis is broken by the sample’s immediate environment (non-cylindrical sample holder, manipulator shape, cables, etc.). However, because we can easily see the momentum distribution “live” before acquiring a spectrum, we can take some steps to minimize distortions by adjusting the geometry of the experiment. Further processing after the measurement, based on purely symmetry-driven considerations, allows us to eliminate all visible distortions of the angular distribution. This will now be explained.

FIG. 5.

(a) Electric fields between the sample and the FeSuMa analyzer for normal operation mode (top) and when “fisheye voltage” is applied (bottom). Calculated with SIMION.45 (b) Fermi surface of Bi(111), acquired with a probe energy of 16.2 eV and three values of applied fisheye voltage. [The focusing conditions were optimized at condition (ii), with the result that the focusing conditions are slightly non-optimal in (i) and (iii) and the image appears off-center on the detector.] (c) Workflow for applying the corrections needed for datasets acquired with fisheye voltage. (i) Conversion between position on the MCP (x, y) to emission angle, θx, θy, based on the calibration radial function (red curve) obtained from ray tracing. (ii) Angle-to-momentum transformation. (iii) Angular and radial corrections to the image based on the expected symmetry of the intensity distribution. The black dotted-dashed lines represent the portions of the image that need correction, while the arrows indicate the direction of the corrections.

FIG. 5.

(a) Electric fields between the sample and the FeSuMa analyzer for normal operation mode (top) and when “fisheye voltage” is applied (bottom). Calculated with SIMION.45 (b) Fermi surface of Bi(111), acquired with a probe energy of 16.2 eV and three values of applied fisheye voltage. [The focusing conditions were optimized at condition (ii), with the result that the focusing conditions are slightly non-optimal in (i) and (iii) and the image appears off-center on the detector.] (c) Workflow for applying the corrections needed for datasets acquired with fisheye voltage. (i) Conversion between position on the MCP (x, y) to emission angle, θx, θy, based on the calibration radial function (red curve) obtained from ray tracing. (ii) Angle-to-momentum transformation. (iii) Angular and radial corrections to the image based on the expected symmetry of the intensity distribution. The black dotted-dashed lines represent the portions of the image that need correction, while the arrows indicate the direction of the corrections.

Close modal

A detailed and thorough approach to correcting distortions has recently been developed.46 Here, we use a simple approach, with only two basic corrections to deal with angular and radial distortions that we see in the present case. We can take as our starting point the known symmetries of our material systems. In the angular case, we are concerned with a segment of the dataset where there are distortions like those illustrated schematically by black dashed lines in the left panel of Fig. 5(c-iii). We take the two axes A and B, as indicated by the dashed lines leading to the red and green triangles, respectively, in the left panel of Fig. 5(c-iii). In the affected segment of the data, we then shift all points that lie along the A-axis onto the B-axis. For all other points in this segment, a linear interpolation then squeezes the part of the image that lies to the left of B and stretches the part of the image that lies to the right of B.

For the radial correction, we show an illustrative example in Fig. 5(iii). In this simple cartoon, we only need to correct one portion of the image that is obviously compressed relative to the others. Identifying the two points C and D that lie along the same axis [orange and purple triangles in the central panel of Fig. 5(c-iii)], we perform a linear interpolation such that C is moved onto D, and all other points in a segment are stretched (or squeezed) linearly while keeping the center of the image intact.

As sketched schematically in Fig. 6(a), space-charge arises due to Coulombic repulsive interactions within the dense cloud of photoelectrons emitted from the sample surface, leading to energy shifts and distortions of electron trajectories as they move toward the analyzer.47,48 The resultant photoemission spectra exhibit reduced energy resolution and momentum resolution, as well as other artifacts, such as shifting of spectra and possible “ghost” peaks.48 The energy shift and broadening are schematically illustrated in Fig. 6(b). In addition to the fact that a dense cloud of Coulombically interacting photoelectrons can be generated by the probe pulse, the pump beam can produce an unwanted cloud of “slow” secondary electrons via multi-photon photoemission and emission from surface defects.49 The latter effect can contribute additional space-charge effects.

FIG. 6.

(a) Cartoon of space-charge generated in a pump–probe photoemission experiment. Coulombic interactions occur between charged particles in a dense cloud of photoemitted electrons. (b) Qualitative impact of space-charge on photoemission spectra. The dark (light) blue peaks represent the electron distribution just after photoemission (after travel toward the analyzer). (c) Measured probe-induced shift of the spectrum at the peak of excitation, as a function of probe photon flux (measured as photocurrent IPD induced in a photodiode that can be extended into the beampath. Error bars are estimated from the standard deviation in detected photoelectron counts.) (d) Measured pump-induced shift of the Fermi edge before the excitation, as a function of pump fluence at 800 nm. (Horizontal error bars are estimated from typical fluctuations; vertical error bars are obtained from the least-squares fits. See the supplementary materialSupplement.)

FIG. 6.

(a) Cartoon of space-charge generated in a pump–probe photoemission experiment. Coulombic interactions occur between charged particles in a dense cloud of photoemitted electrons. (b) Qualitative impact of space-charge on photoemission spectra. The dark (light) blue peaks represent the electron distribution just after photoemission (after travel toward the analyzer). (c) Measured probe-induced shift of the spectrum at the peak of excitation, as a function of probe photon flux (measured as photocurrent IPD induced in a photodiode that can be extended into the beampath. Error bars are estimated from the standard deviation in detected photoelectron counts.) (d) Measured pump-induced shift of the Fermi edge before the excitation, as a function of pump fluence at 800 nm. (Horizontal error bars are estimated from typical fluctuations; vertical error bars are obtained from the least-squares fits. See the supplementary materialSupplement.)

Close modal

In our setup, photoemitted electrons are tightly confined in space and time only once, at the sample surface, before they interact with the MCP.24 This is an advantageous situation relative to HAs and MMs, where additional focal planes and spatial confinement can cause further Coulombic interaction.5,18,19 Moreover, in a ToF, a long-range electric field develops as slow electrons produced by the pump propagate through the lens tube, and fast valence electrons experience an accelerating or decelerating force, depending on the time delay, culminating in a “fake time zero” at a large (tens-of-ps) time delay.5 These effects are largely avoided in the FeSuMa. The retarding voltage readily repels the slowest secondaries—possibly even at the very entrance of the lens column, depending on their kinetic energies—so as to reduce their interaction with the other photoelectrons in the lens tube.

Of course, the severity of distortions always depends also on the XUV beam diameter and on pulse energy.50 At the relatively low 1-kHz repetition rate of the Artemis setup that was used for this particular experiment, the choice of photon flux was a compromise between the space-charge and the acquisition time required to achieve a sufficient signal-to-noise ratio. In future experiments on the Artemis 100-kHz beamline, we expect to see this issue partially remedied.

In Fig. 6(c), we characterize the spectral modifications due to probe-induced space-charge. More detailed analysis is included in the supplementary material. We use Bi(111) spectra to estimate the shift of the Fermi edge, which occurs across the entire investigated XUV range as a function of flux.48, Figure 6(d) shows the pump-induced Fermi-edge shift. The pump-induced spectral distortions exhibit a complex dependence on the time delay and are present over a range of several picoseconds after temporal overlap.51 The secondary-electron population scales non-linearly with the nth power of the laser fluence and, in general, affects primarily the low kinetic energy portion of a spectrum. These pump-fluence-dependent measurements were made at a time delay of 150 fs before the optical excitation, in order to exclude the effects of real ultrafast dynamics happening in the sample. Up to a fluence of ∼5 mJ/cm2, the spectra are virtually unaltered by any pump-induced space-charge. Above this threshold, the spectral shift shows a power dependence of Fx (x = 2.7 ± 0.1), in agreement with a previous study of the excitation with a 1.55 eV pump.49 

The FeSuMa offers a simple approach to high-quality pump–probe photoemission measurements, particularly for time-resolved ARPES of valence and conduction states near the Fermi level. Like PEEM- and MM-based approaches, it permits the measurement of dynamics spanning the entire Brillouin zone. In the context of an HHG beamline that permits scanning of the probe energy, the fisheye mode of operation offers particular benefits for studies of 3D-dispersing states. The FeSuMa is highly complementary to HAs and constitutes an attractive option for tabletop measurements. The measurements of conduction-band dynamics in layered 2H–WSe2 yield excellent agreement with previously published results based on momentum microscopy.

The supplementary material can be found at the publisher’s website. It includes the following: information about beamline specifications (time resolution of the pump–probe measurements, stability of the pump laser); details about sample preparation; further discussion of spectral broadening and Fermi-level shift as a function of pump fluence and probe flux; a movie showing a representative 20-min data acquisition, with time dependence, of conduction-band excitations in WSe2 [sample at room temperature, pump fluence 6.7 mJ/cm2, pump wavelength 800 nm, LV pump polarization, XUV photon energy 22.6 eV, XUV polarization LH, fisheye voltage 76.4 V, retarding voltage Vr = 94.7 eV (selected to integrate over all conduction band states)]; and a movie showing a scan through constant energy contours in a small range around the Fermi surface of Bi(111), while the system is excited with an 800-nm pump (Δt = 0, sample temperature T = 84 K, pump fluence 5.6 mJ/cm2, LV pump polarization, XUV photon energy 16.2 eV, XUV polarization LH).

We thank Phil Rice, Alistair Cox, and the CLF Engineering Section for technical support and Dr. James O. F. Thompson and Dr. Marco Bianchi for helpful discussion. We acknowledge funding from Villum Fonden through the Centre of Excellence for Dirac Materials (Grant No. 11744) and from the Independent Research Fund Denmark (Grant No. 1026-00089B). Work at the Artemis Facility is funded by the UK Science and Technology Facilities Council. The research leading to these results has received funding from Laserlab Europe (Grant Agreement No. 871124, European Union’s Horizon 2020 research and innovation program).

Dr. Sergey Borisenko is the founder and head of the Fermiologics company, which makes the FeSuMa analyzer. All other authors declare no conflict of interest.

Paulina Majchrzak: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Yu Zhang: Formal analysis (equal); Investigation (lead); Methodology (supporting); Software (lead); Writing – original draft (supporting); Writing – review & editing (supporting). Andrii Kuibarov: Formal analysis (equal); Investigation (supporting); Methodology (supporting); Software (lead); Writing – original draft (supporting); Writing – review & editing (supporting). Richard Chapman: Formal analysis (equal); Investigation (supporting); Methodology (supporting); Project administration (supporting); Software (lead); Writing – original draft (supporting); Writing – review & editing (supporting). Adam Wyatt: Methodology (supporting); Project administration (supporting); Writing – review & editing (supporting). Emma Springate: Funding acquisition (lead); Methodology (supporting); Project administration (supporting); Resources (equal); Supervision (supporting); Writing – review & editing (supporting). Sergey Borisenko: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (supporting); Resources (equal); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Bernd Büchner: Conceptualization (supporting); Formal analysis (supporting); Investigation (equal); Methodology (equal); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Philip Hofmann: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Project administration (equal); Resources (supporting); Supervision (lead); Writing – review & editing (equal). Charlotte E. Sanders: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are openly available in eData, the STFC Research Data repository, at https://doi.org/10.5286/edata/912.

1.
H.
Petek
and
S.
Ogawa
, “
Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals
,”
Prog. Surf. Sci.
56
,
239
310
(
1997
).
2.
X.
Zhou
,
S.
He
,
G.
Liu
,
L.
Zhao
,
L.
Yu
, and
W.
Zhang
, “
New developments in laser-based photoemission spectroscopy and its scientific applications: A key issues review
,”
Rep. Prog. Phys.
81
,
062101
(
2018
).
3.
T.
Suzuki
,
S.
Shin
, and
K.
Okazaki
, “
HHG-laser-based time- and angle-resolved photoemission spectroscopy of quantum materials
,”
J. Electron Spectrosc. Relat. Phenom.
251
,
147105
(
2021
).
4.
P.
Grychtol
,
N.
Kohlstrunk
,
J.
Buck
,
S.
Thiess
,
V.
Vardanyan
,
D.
Doblas-Jimenez
,
J.
Ohnesorge
,
S.
Babenkov
,
M.
Dommach
,
D.
La Civita
,
M.
Vannoni
,
K.
Rossnagel
,
G.
Schönhense
,
S.
Molodtsov
, and
M.
Izquierdo
, “
The SXP instrument at the European XFEL
,”
J. Phys.: Conf. Ser.
2380
,
012043
(
2022
).
5.
D.
Kutnyakhov
,
R. P.
Xian
,
M.
Dendzik
,
M.
Heber
,
F.
Pressacco
,
S. Y.
Agustsson
,
L.
Wenthaus
,
H.
Meyer
,
S.
Gieschen
,
G.
Mercurio
,
A.
Benz
,
K.
Bühlman
,
S.
Däster
,
R.
Gort
,
D.
Curcio
,
K.
Volckaert
,
M.
Bianchi
,
C.
Sanders
,
J. A.
Miwa
,
S.
Ulstrup
,
A.
Oelsner
,
C.
Tusche
,
Y.-J.
Chen
,
D.
Vasilyev
,
K.
Medjanik
,
G.
Brenner
,
S.
Dziarzhytski
,
H.
Redlin
,
B.
Manschwetus
,
S.
Dong
,
J.
Hauer
,
L.
Rettig
,
F.
Diekmann
,
K.
Rossnagel
,
J.
Demsar
,
H.-J.
Elmers
,
P.
Hofmann
,
R.
Ernstorfer
,
G.
Schönhense
,
Y.
Acremann
, and
W.
Wurth
, “
Time- and momentum-resolved photoemission studies using time-of-flight momentum microscopy at a free-electron laser
,”
Rev. Sci. Instrum.
91
,
013109
(
2020
).
6.
Q.-J.
Peng
,
N.
Zong
,
S.-J.
Zhang
,
Z.-M.
Wang
,
F.
Yang
,
F.-F.
Zhang
,
Z.-Y.
Xu
, and
X.-J.
Zhou
, “
DUV/VUV all-solid-state lasers: Twenty years of progress and the future
,”
IEEE J. Sel. Top. Quantum Electron.
24
,
1602312
(
2018
).
7.
F.
Frassetto
,
C.
Cacho
,
C. A.
Froud
,
E.
Turcu
,
P.
Villoresi
,
W. A.
Bryan
,
E.
Springate
, and
L.
Poletto
, “
Single-grating monochromator for extreme-ultraviolet ultrashort pulses
,”
Opt. Express
19
,
19169
19181
(
2011
).
8.
A.
Damascelli
,
Z.
Hussain
, and
Z.-X.
Shen
, “
Angle-resolved photoemission studies of the cuprate superconductors
,”
Rev. Mod. Phys.
75
,
473
541
(
2003
).
9.
J. A.
Sobota
,
Y.
He
, and
Z.-X.
Shen
, “
Angle-resolved photoemission studies of quantum materials
,”
Rev. Mod. Phys.
93
,
025006
(
2021
).
10.
F.
Boschini
,
D.
Bugini
,
M.
Zonno
,
M.
Michiardi
,
R. P.
Day
,
E.
Razzoli
,
B.
Zwartsenberg
,
M.
Schneider
,
E. H.
da Silva Neto
,
S.
dal Conte
,
S. K.
Kushwaha
,
R. J.
Cava
,
S.
Zhdanovich
,
A. K.
Mills
,
G.
Levy
,
E.
Carpene
,
C.
Dallera
,
C.
Giannetti
,
D. J.
Jones
,
G.
Cerullo
, and
A.
Damascelli
, “
Role of matrix elements in the time-resolved photoemission signal
,”
New J. Phys.
22
,
023031
(
2020
).
11.
I.
Gierz
,
J.
Henk
,
H.
Höchst
,
C. R.
Ast
, and
K.
Kern
, “
Illuminating the dark corridor in graphene: Polarization dependence of angle-resolved photoemission spectroscopy on graphene
,”
Phys. Rev. B
83
,
121408
(
2011
).
12.
I.
Gierz
,
M.
Lindroos
,
H.
Höchst
,
C. R.
Ast
, and
K.
Kern
, “
Graphene sublattice symmetry and isospin determined by circular dichroism in angle-resolved photoemission spectroscopy
,”
Nano Lett.
12
,
3900
3904
(
2012
).
13.
W. B.
Peatman
,
Gratings, Mirrors and Slits: Beamline Design for Soft X-Ray Synchrotron Radiation Sources
(
Gordon and Breach Science Publishers
,
Amsterdam
,
1997
).
14.
P.
Jaeglé
, “
Vacuum ultraviolet lasers
,” in
Vacuum Ultraviolet Spectroscopy
, edited by
J. A. R.
Samson
and
D. L.
Ederer
(
Academic Press
,
London
,
2000
), pp.
101
118
.
15.
M.
Puppin
,
Y.
Deng
,
C. W.
Nicholson
,
J.
Feldl
,
N. B. M.
Schröter
,
H.
Vita
,
P. S.
Kirchmann
,
C.
Monney
,
L.
Rettig
,
M.
Wolf
, and
R.
Ernstorfer
, “
Time- and angle-resolved photoemission spectroscopy of solids in the extreme ultraviolet at 500 kHz repetition rate
,”
Rev. Sci. Instrum.
90
,
023104
(
2019
).
16.
M.
Heber
,
N.
Wind
,
D.
Kutnyakhov
,
F.
Pressacco
,
T.
Arion
,
F.
Roth
,
W.
Eberhardt
, and
K.
Rossnagel
, “
Multispectral time-resolved energy–momentum microscopy using high-harmonic extreme ultraviolet radiation
,”
Rev. Sci. Instrum.
93
,
083905
(
2022
).
17.
H.
Iwasawa
,
E. F.
Schwier
,
M.
Arita
,
A.
Ino
,
H.
Namatame
,
M.
Taniguchi
,
Y.
Aiura
, and
K.
Shimada
, “
Development of laser-based scanning μ-ARPES system with ultimate energy and momentum resolutions
,”
Ultramicroscopy
182
,
85
91
(
2017
).
18.
G.
Schönhense
,
K.
Medjanik
, and
H.-J.
Elmers
, “
Space-, time- and spin-resolved photoemission
,”
J. Electron Spectrosc. Relat. Phenom.
200
,
94
118
(
2015
).
19.
J.
Maklar
,
S.
Dong
,
S.
Beaulieu
,
T.
Pincelli
,
M.
Dendzik
,
Y. W.
Windsor
,
R. P.
Xian
,
M.
Wolf
,
R.
Ernstorfer
, and
L.
Rettig
, “
A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments
,”
Rev. Sci. Instrum.
91
,
123112
(
2020
).
20.
C.
Tusche
,
Y.-J.
Chen
,
L.
Plucinski
, and
C. M.
Schneider
, “
From photoemission microscopy to an ‘all-in-one’ photoemission experiment
,”
e-J. Surf. Sci. Nanotechnol.
18
,
48
56
(
2020
).
21.
S.
Suga
,
A.
Sekiyama
, and
C.
Tusche
,
Photoelectron Spectroscopy: Bulk and Surface Electronic Structures
, 2nd ed. (
Springer Nature
,
Switzerland
,
2021
), pp.
351
416
.
22.
A. T. J. B.
Eppink
and
D. H.
Parker
, “
Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen
,”
Rev. Sci. Instrum.
68
,
3477
3484
(
1997
).
23.
M.
Stei
,
J.
von Vangerow
,
R.
Otto
,
A. H.
Kelkar
,
E.
Carrascosa
,
T.
Best
, and
R.
Wester
, “
High resolution spatial map imaging of a gaseous target
,”
J. Chem. Phys.
138
,
214201
(
2013
).
24.
S.
Borisenko
,
A.
Fedorov
,
A.
Kuibarov
,
M.
Bianchi
,
V.
Bezguba
,
P.
Majchrzak
,
P.
Hofmann
,
P.
Baumgärtel
,
V.
Voroshnin
,
Y.
Kushnirenko
,
J.
Sánchez-Barriga
,
A.
Varykhalov
,
R.
Ovsyannikov
,
I.
Morozov
,
S.
Aswartham
,
O.
Feia
,
L.
Harnagea
,
S.
Wurmehl
,
A.
Kordyuk
,
A.
Yaresko
,
H.
Berger
, and
B.
Büchner
, “
Fermi surface tomography
,”
Nat. Commun.
13
,
4132
(
2022
).
25.
F.
Frassetto
,
S.
Bonora
,
P.
Villoresi
,
L.
Poletto
,
E.
Springate
,
C. A.
Froud
,
I. C. E.
Turcu
,
A. J.
Langley
,
D. S.
Wolff
,
J. L.
Collier
,
S. S.
Dhesi
, and
A.
Cavalleri
, “
Design and characterization of the XUV monochromator for ultrashort pulses at the ARTEMIS facility
,”
Proc. SPIE
7077
,
707713
(
2008
).
26.
Y. M.
Koroteev
,
G.
Bihlmayer
,
J. E.
Gayone
,
E. V.
Chulkov
,
S.
Blügel
,
P. M.
Echenique
, and
P.
Hofmann
, “
Strong spin-orbit splitting on Bi surfaces
,”
Phys. Rev. Lett.
93
,
046403
(
2004
).
27.
T.
Hirahara
et al, “
Role of spin-orbit coupling and hybridization effects in the electronic structure of ultrathin Bi films
,”
Phys. Rev. Lett.
97
,
146803
(
2006
).
28.
N.
Gauthier
,
J. A.
Sobota
,
H.
Pfau
,
A.
Gauthier
,
H.
Soifer
,
M. D.
Bachmann
,
I. R.
Fisher
,
Z.-X.
Shen
, and
P. S.
Kirchmann
, “
Expanding the momentum field of view in angle-resolved photoemission systems with hemispherical analyzers
,”
Rev. Sci. Instrum.
92
,
123907
(
2021
).
29.
A.
Apponi
,
F.
Pandolfi
,
I.
Rago
,
G.
Cavoto
,
C.
Mariani
, and
A.
Ruocco
, “
Absolute efficiency of a two-stage microchannel plate for electrons in the 30–900 eV energy range
,”
Meas. Sci. Technol.
33
,
025102
(
2022
).
30.
Peng
et al, “
Nuclear instruments and methods in physics
,”
Res. Sect. A
1062
,
169163
(
2024
).
31.
T. J. M.
Zouros
and
E. P.
Benis
, “
The hemispherical deflector analyser revisited. I. Motion in the ideal 1/r potential, generalized entry conditions, Kepler orbits and spectrometer basic equation
,”
J. Electron Spectrosc. Relat. Phenom.
125
,
221
248
(
2002
).
32.
B.
Schönhense
,
K.
Medjanik
,
O.
Fedchenko
,
S.
Chernov
,
M.
Ellguth
,
D.
Vasilyev
,
A.
Oelsner
,
J.
Viefhaus
,
D.
Kutnyakhov
,
W.
Wurth
,
H. J.
Elmers
, and
G.
Schönhense
, “
Multidimensional photoemission spectroscopy—The space-charge limit
,”
New J. Phys.
20
,
033004
(
2018
).
33.
W.-T.
Hsu
,
L.-S.
Lu
,
D.
Wang
,
J.-K.
Huang
,
M.-Y.
Li
,
T.-R.
Chang
,
Y.-C.
Chou
,
Z.-Y.
Juang
,
H.-T.
Jeng
,
L.-J.
Li
, and
W.-H.
Chang
, “
Evidence of indirect gap in monolayer WSe2
,”
Nat. Commun.
8
,
929
(
2017
).
34.
R.
Bertoni
,
C. W.
Nicholson
,
L.
Waldecker
,
H.
Hübener
,
C.
Monney
,
U.
De Giovannini
,
M.
Puppin
,
M.
Hoesch
,
E.
Springate
,
R. T.
Chapman
,
C.
Cacho
,
M.
Wolf
,
A.
Rubio
, and
R.
Ernstorfer
, “
Generation and evolution of spin-, valley-, and layer-polarized excited carriers in inversion-symmetric WSe2
,”
Phys. Rev. Lett.
117
,
277201
(
2016
).
35.
M.
Puppin
,
C. W.
Nicholson
,
C.
Monney
,
Y.
Deng
,
R. P.
Xian
,
J.
Feldl
,
S.
Dong
,
A.
Dominguez
,
H.
Hübener
,
A.
Rubio
,
M.
Wolf
,
L.
Rettig
, and
R.
Ernstorfer
, “
Excited-state band structure mapping
,”
Phys. Rev. B
105
,
075417
(
2022
).
36.
J.
Madéo
,
M. K. L.
Man
,
C.
Sahoo
,
M.
Campbell
,
V.
Pareek
,
E. L.
Wong
,
A.
Al-Mahboob
,
N. S.
Chan
,
A.
Karmakar
,
B. M. K.
Mariserla
,
X.
Li
,
T. F.
Heinz
,
T.
Cao
, and
K. M.
Dani
, “
Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors
,”
Science
370
,
1199
1204
(
2020
).
37.
L.
Miaja-Avila
,
C.
Lei
,
M.
Aeschlimann
,
J. L.
Gland
,
M. M.
Murnane
,
H. C.
Kapteyn
, and
G.
Saathoff
, “
Laser-assisted photoelectric effect from surfaces
,”
Phys. Rev. Lett.
97
,
113604
(
2006
).
38.
M.
Keunecke
,
M.
Reutzel
,
D.
Schmitt
,
A.
Osterkorn
,
T. A.
Mishra
,
C.
Möller
,
W.
Bennecke
,
G. S. M.
Jansen
,
D.
Steil
,
S. R.
Manmana
,
S.
Steil
,
S.
Kehrein
, and
S.
Mathias
, “
Electromagnetic dressing of the electron energy spectrum of Au(111) at high momenta
,”
Phys. Rev. B
102
,
161403
(
2020
).
39.
J. M.
Riley
,
F.
Mazzola
,
M.
Dendzik
,
M.
Michiardi
,
T.
Takayama
,
L.
Bawden
,
C.
Granerød
,
M.
Leandersson
,
T.
Balasubramanian
,
M.
Hoesch
,
T. K.
Kim
,
H.
Takagi
,
W.
Meevasana
,
P.
Hofmann
,
M. S.
Bahramy
,
J. W.
Wells
, and
P. D. C.
King
, “
Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor
,”
Nat. Phys.
10
,
835
839
(
2014
).
40.
M. P.
Seah
and
W. A.
Dench
, “
Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids
,”
Surf. Interface Anal.
1
,
2
(
1979
).
41.
D.
Voß
,
P.
Krüger
,
A.
Mazur
, and
J.
Pollmann
, “
Atomic and electronic structure of WSe2 from ab initio theory: Bulk crystal and thin film systems
,”
Phys. Rev. B
60
,
14311
14317
(
1999
).
42.
S.
Moser
, “
An experimentalist’s guide to the matrix element in angle resolved photoemission
,”
J. Electron Spectrosc. Relat. Phenom.
214
,
29
52
(
2017
).
43.
D. F.
Liu
,
Q. N.
Xu
,
E. K.
Liu
,
J. L.
Shen
,
C. C.
Le
,
Y. W.
Li
,
D.
Pei
,
A. J.
Liang
,
P.
Dudin
,
T. K.
Kim
,
C.
Cacho
,
Y. F.
Xu
,
Y.
Sun
,
L. X.
Yang
,
Z. K.
Liu
,
C.
Felser
,
S. S. P.
Parkin
, and
Y. L.
Chen
, “
Topological phase transition in a magnetic Weyl semimetal
,”
Phys. Rev. B
104
,
205140
(
2021
).
44.
M.
Yan
,
H.
Huang
,
K.
Zhang
,
E.
Wang
,
W.
Yao
,
K.
Deng
,
G.
Wan
,
H.
Zhang
,
M.
Arita
,
H.
Yang
,
Z.
Sun
,
H.
Yao
,
Y.
Wu
,
S.
Fan
,
W.
Duan
, and
S.
Zhou
, “
Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2
,”
Nat. Commun.
8
,
257
(
2017
).
45.
D. A.
Dahl
, “
SIMION for the personal computer in reflection
,”
Int. J. Mass Spectrom.
200
,
3
25
(
2000
).
46.
R. P.
Xian
,
L.
Rettig
, and
R.
Ernstorfer
, “
Symmetry-guided nonrigid registration: The case for distortion correction in multidimensional photoemission spectroscopy
,”
Ultramicroscopy
202
,
133
139
(
2019
).
47.
S.
Hellmann
,
K.
Rossnagel
,
M.
Marczynski-Bühlow
, and
L.
Kipp
, “
Vacuum space-charge effects in solid-state photoemission
,”
Phys. Rev. B
79
,
035402
(
2009
).
48.
S.
Passlack
,
S.
Mathias
,
O.
Andreyev
,
D.
Mittnacht
,
M.
Aeschlimann
, and
M.
Bauer
, “
Space charge effects in photoemission with a low repetition, high intensity femtosecond laser source
,”
J. Appl. Phys.
100
,
024912
(
2006
).
49.
L.-P.
Oloff
,
K.
Hanff
,
A.
Stange
,
G.
Rohde
,
F.
Diekmann
,
M.
Bauer
, and
K.
Rossnagel
, “
Pump laser-induced space-charge effects in HHG-driven time- and angle-resolved photoelectron spectroscopy
,”
J. Appl. Phys.
119
,
225106
(
2016
).
50.
S.
Hellmann
,
T.
Ott
,
L.
Kipp
, and
K.
Rossnagel
, “
Vacuum space-charge effects in nano-ARPES
,”
Phys. Rev. B
85
,
075109
(
2012
).
51.
S.
Ulstrup
,
J. C.
Johannsen
,
F.
Cilento
,
A.
Crepaldi
,
J. A.
Miwa
,
M.
Zacchigna
,
C.
Cacho
,
R. T.
Chapman
,
E.
Springate
,
F.
Fromm
,
C.
Raidel
,
T.
Seyller
,
P. D. C.
King
,
F.
Parmigiani
,
M.
Grioni
, and
P.
Hofmann
, “
Ramifications of optical pumping on the interpretation of time-resolved photoemission experiments on graphene
,”
J. Electron Spectrosc. Relat. Phenom.
200
,
340
346
(
2015
).

Supplementary Material