# Access to the full 3D Brillouin zone with time resolution, using a new tool
for pump-probe ARPES

Paulina Majchrzak  Department of Physics and Astronomy, Interdisciplinary
Nanoscience Center, Aarhus University, 8000 Aarhus C, Denmark  Yu Zhang
Central Laser Facility, STFC Rutherford Appleton Laboratory, Research Complex
at Harwell, Harwell, OX11 0QX, United Kingdom  Andrii Kuibarov  Leibniz IFW
Dresden, Helmholtzstr. 20, 01069 Dresden, Germany  Richard Chapman  Central
Laser Facility, STFC Rutherford Appleton Laboratory, Research Complex at
Harwell, Harwell, OX11 0QX, United Kingdom  Adam Wyatt  Central Laser
Facility, STFC Rutherford Appleton Laboratory, Research Complex at Harwell,
Harwell, OX11 0QX, United Kingdom  Emma Springate  Central Laser Facility,
STFC Rutherford Appleton Laboratory, Research Complex at Harwell, Harwell,
OX11 0QX, United Kingdom  Sergey Borisenko  Leibniz IFW Dresden, Helmholtzstr.
20, 01069 Dresden, Germany  Bernd Büchner  Leibniz IFW Dresden, Helmholtzstr.
20, 01069 Dresden, Germany  Philip Hofmann  Department of Physics and
Astronomy, Interdisciplinary Nanoscience Center, Aarhus University, 8000
Aarhus C, Denmark  Charlotte E. Sanders  Central Laser Facility, STFC
Rutherford Appleton Laboratory, Research Complex at Harwell, Harwell, OX11
0QX, United Kingdom<EMAIL_ADDRESS>
###### Abstract

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., $k_{z}$-) 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.

###### pacs:

73.20.At,73.20.r,07.81.a,07.05.Fb

##  I Introduction

Pump-probe time- and angle-resolved photoemission spectroscopy (TR-ARPES)
presents challenges, both with respect to light sources and to 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” analyser
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 photon
energies that are generated as high harmonics in an Ar gas jet. We suggest
that this measurement configuration offers major benefits as a cost-efficient
laboratory-scale approach to time-resolved TR-ARPES.

###  I.1 State of the Art in Pump-Probe 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 $\Delta$
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 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.

####  I.1.1 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 Petek and Ogawa (1997).

Light sources commonly used to supply the pulsed ultraviolet probe beam
include tabletop laser setups Zhou  _et al._ (2018); Suzuki, Shin, and Ozaki
(2021) and free-electron lasers Zhou  _et al._ (2018); Grychtol  _et al._
(2022); Kutnyakhov  _et al._ (2020). This paper deals with tabletop laser
setups. Wavelengths down to approximately 115 nm (i.e., energies up to
approximately 11 eV) are achievable with commercial off-the-shelf laser
systems Peng  _et al._ (2018). However, even at 11 eV, one can access only a
relatively small section of momentum space up to approximately 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) Brillioun 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 jetSuzuki, Shin, and Ozaki (2021); Frassetto  _et al._
(2011).

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 of
which is used to generate HHG, and the other of which 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 $\Delta$, and then
the two beams are recombined.

In a 3D-dispersing system, the probe photon energy determines which part of
the 3D Brillouin zone is measured. Control of the probe energy also allows for
optimization of photoemission intensity in electronic states of interest, via
control of final state and matrix element effects Damascelli, Hussain, and
Shen (2003); Sobota, He, and Shen (2021); Boschini  _et al._ (2020); Gierz
_et al._ (2011, 2012). While this is the basis for photon-energy-dependent
synchrotron-based studies of out-of-plane-dispersing “$k_{z}$” 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 Peatman (1997), no such continuous spectrum is possible
with laser-based HHG. Rather, HHG produces a “frequency comb” of odd-ordered
harmonics Jaeglé (2000) (Fig. 1(b)). A single frequency from the comb can be
selected with a combination of reflective and transmissive optics Puppin  _et
al._ (2019). 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 Frassetto
_et al._ (2011); Heber  _et al._ (2022). 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 energiesFrassetto  _et
al._ (2011). The power of this type of approach has recently been demonstrated
Heber  _et al._ (2022).

####  I.1.2 Background: Photoelectron Detection and Analysers

The best-established technology for photoelectron spectroscopy is the
hemispherical analyser (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 Iwasawa  _et al._ (2017). The
HA has been the workhorse of the photoemission community, and is likely to
remain so for the foreseeable future. Moreover, 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 be a challenge in the context of pump-probe measurements, where each
data set 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, or when photon-energy-dependent
measurements will cause the 3D Brillouin zone to shrink and expand on the
detector, an alternative approach to detection is desirable. Moreover, in the
case of short-pulse pump-probe applications, the high energy resolution of the
analyser greatly exceeds the Fourier limit of the short light pulses.

Recent years have seen rapid advancements in new types of analyser
technologies Schönhense, Medjanik, and Elmers (2015); Maklar  _et al._ (2020);
Tusche  _et al._ (2020). Some are based on time-of-flight (ToF), among which
are various types of photoemission electron microscopes (PEEMs) and momentum
microscopes (MMs) Suga, Sekiyama, and Tusche (2021). These new techniques are
powerful, permitting sophisticated momentum-space and real-space mapping, but
they 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 Kutnyakhov  _et al._ (2020). This latter issue is discussed below.

Very recently, a new type of simple, economical, and yet highly effective
photoelectron analyser has been developed. The working principle—similar to
that of velocity map imaging Eppink and Parker (1997); Stei  _et al._
(2013)—has been described in a recent paper Borisenko  _et al._ (2022). From
the point of view of pump-probe measurements, we find that this new analyser,
which is available commercially under the name“FeSuMa” (“Fermi Surface
Mapper”), offers advantages over other types of analysers for some of the most
commonly required types of pump-probe ARPES measurements. The technology
offers an efficient approach to 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 $k_{z}$-dispersing states. Additionally, its 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.

##  II Experimental Details

###  II.1 Optical Setup

Figure 1: (a) The spectrum of the Ti:Sapphire laser, centered at about 790 nm
with a bandwidth of approximately 50 nm. (b) High-harmonics spectrum generated
in the argon gas jet. The maximum photon flux is approximately $10^{10}$
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 polarisation, acquired as measured intensity through a polarizer after
the QWP as the HWP is rotated. (d) The spot sizes of the probe (80 $\mu$m,
FWHM) and pump beams (250 $\mu$m, FWHM), captured by FeSuMa. (e) A simplified
schematic of the experimental setup. The locations of delay stages are labeled
“DS,” while “BS” indicates an 80-20 beam splitter.

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 (upgraded from the RedDragon, KMLabs) with a pulse
energy of about 3 mJ at 790 nm. The bandwidth is approximately 50 nm, as shown
in Fig. 1(a). The output laser beam is split into two parts, with 80% focused
onto a 200 $\mu$m 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 usable high-harmonic energies range from
approximately 17 eV 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 monochromatorFrassetto  _et al._ (2008). To avoid space-
charge effects, which are discussed in Section IV.2, the photon flux was
reduced to 108 photons/second/harmonic by an adjustable slit after the
monochromator.

The remaining 20 percent of the output beam is used for pumping, either at its
fundamental wavelength or after frequency-doubling or -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
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 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 pump fluence is about 2 mJ/cm2, with
pump spot size of approximately 250 $\mu$m at FWHM (450 $\mu$m at 1/e2 width).
The XUV spot size of about 80 $\mu$m is measured roughly by the size of the
spot on a scintillating crystal, and confirmed by the FeSuMa in Direct Mode
(see Section II.2). The images of the two beam spots recorded by FeSuMa are
presented in Fig. 1(d). The time resolution is determined from the auto-
correlation spectrum, as shown in the Supplementary Material sup .

###  II.2 Working Principles of FeSuMa

The FeSuMa is a new type of ARPES analyser that combines Fourier electron
optics with retarding field techniques Borisenko  _et al._ (2022). 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, $V_{r}$, 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 $V_{r}$ 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, $V_{r}$ 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 in Fig. 2(a),
where we show a Bi core-level spectrum acquired from the Bi(111) surfacesup .
The spin-orbit splitting in the Bi $5d$ doublet is well resolved when the
spectrum is differentiated, 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 data set 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 Koroteev  _et al._ (2004). The bulk and surface Brillouin
zone (BZ) of Bi(111) is provided in Fig. 2(d) for reference.

Figure 2: (a) Example of static angle-integrated raw data obtained from
Bi(111) by scanning the retarding potential $V_{r}$ ($h\nu$ = 37.4 eV, sample
measurement temperature 300K). (b) Same data as in (b), after differentiation.
The core-level spectrum of Bi(111) is now well resolved. (c) Example of an
($E$, $k_{x}$, $k_{y}$)-resolved data set, acquired without optical pumping
from Bi(111) ($h\nu$ = 22.4 eV, sample measurement temperature 78K). The
directions of the cuts correspond to the directions of the lines (matched in
colour to the frames of the two spectra) in the constant-energy contour at
left. Note the scale bar at the bottom: high-symmetry points
$\bar{\mathrm{K}}$ and $\bar{\mathrm{M}}$ are outside the range shown in the
panel. The asymmetry of intensity in the cut along
$\bar{\mathrm{M}}$-$\bar{\mathrm{\Gamma}}$-$\bar{\mathrm{M}}$ arises from
matrix element effects that can be seen clearly in the constant energy slices
at left. (d) Schematic of the Bi BZ, with high-symmetry points labeled. Panel
(d) is adapted from Ref. Hirahara  _et al._ (2006).

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 $\pm 8^{\circ}$, $\pm 14^{\circ}$ and
$\pm 16^{\circ}$. 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 Gauthier  _et al._ (2021). The FeSuMa’s
ability to instantly detect the angular distribution of intensity allows the
parameters to be quickly adjusted, minimising 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, Direct Mode can also 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 analyser from a flat sample region if the electron
signal is optimised).

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. Zouros and Benis
(2002)), 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 Maklar  _et al._ (2020); Schönhense
_et al._ (2018); Kutnyakhov  _et al._ (2020). 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.

##  III Proof of Principle Data

In the following, we summarise the versatile applications of the FeSuMa
analyser when coupled with a pump-probe setup. To facilitate comparison with
similar approacheas involving HAs and MMs Maklar  _et al._ (2020), we
benchmark the capabilities of the system using a widely studied layered
transition metal dichalcogenide, cleaved bulk trigonal prismatic tungsten
diselenide (2$H$-WSe2). Bulk WSe2 is an indirect bandgap semiconductor Hsu
_et al._ (2017) with a hexagonal BZ that is sketched in Fig. 3(a). Its valence
band maximum (VBM) is located at the $\Gamma$-point, and the conduction band
minimum (CBM) at the $\Sigma$-valley, in between $\Gamma$ and $K$. Upon
optical excitation with a circularly polarized infrared pulse, the material
exhibits spin-, valley-, and layer-polarisation Bertoni  _et al._ (2016).

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 $V_{r}$ set so as to probe just above the Fermi
level. Since every electron with a kinetic energy greater than $eV_{r}$ is
collected by the FeSuMa, all the unoccupied states can be monitored
concurrently, regardless of their energy dispersion. A comprehensive
discussion of the dynamics, both for bulk and single-layer WSe2, can be found
in multiple publications (e.g. Refs. Bertoni  _et al._ (2016); Puppin  _et
al._ (2022); Madéo  _et al._ (2020)). Here, we simply highlight that the
FeSuMa allows detection of localised charge populations in 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 mins,
corresponding to 36 s of acquisition per frame. As can be seen in the 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, maintaining $V_{r}$
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 ($k_{x}$, $k_{y}$,
$E$, $\Delta$), simply by sweeping $V_{r}$ in the manner described above
(leading to longer acquisition times).

Figure 3: (a) Surface (dark blue) and three-dimensional (green) Brillouin
zones of 2$H$-WSe2. (b) ($k_{x}$, $k_{y}$) slices corresponding to different
stages of the ultrafast evolution of the system after pumping with
$s$-polarized light at 800 nm (probe photon energy $h\nu=22.6$ eV, sample
temperature 78K). The sample is rotated such that $\bar{\mathrm{\Gamma}}$ is
at the left edge of the detector. The $\bar{\mathrm{K}}$ and
$\bar{\mathrm{\Sigma}}$ points of the Brillouin zone are labeled. (i) Just
after the optical excitation, only $\bar{\mathrm{K}}$-points are populated.
(ii) Within 50 fs of the optical excitation, electrons can be seen to transfer
from the $\bar{\mathrm{K}}$-valleys to $\bar{\mathrm{\Sigma}}$-valleys.
Retarding potential is set such that $E-E_{F}=0.65$ eV. (iii) At longer times
after the pump arrival, all of the excited electronic population has either
transferred to the $\bar{\mathrm{\Sigma}}$-points or has already relaxed
fully. (c) Ultrafast dynamics of 2$H$-WSe2: orange (green) markers denote
photoemission intensity difference, relative to pre-pumped intensity,
integrated over the $\bar{\mathrm{K}}$($\bar{\mathrm{\Sigma}}$)-points of the
Brillouin zone. These temporal dynamics are in good agreement with previously
published results Bertoni  _et al._ (2016); Maklar  _et al._ (2020).

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 polarisation 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 2$H$-WSe2 pumped
with four polarisations: 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 $\bar{\mathrm{K}}$\- and
$\bar{\mathrm{K}}$’-points and at the corresponding $\bar{\mathrm{\Sigma}}$\-
and $\bar{\mathrm{\Sigma}}$’-points. The excitation with linearly polarised
light leads to negligible linear dichroic (LD) contrast in the population at
$\bar{\mathrm{K}}$\- and $\bar{\mathrm{\Sigma}}$-points. Pumping with LH light
produces a strong signal around the $\bar{\mathrm{\Gamma}}$-point; this is a
known consequence of multi-photon photoemission process enhanced by this
polarisation Miaja-Avila  _et al._ (2006); Keunecke  _et al._ (2020). On the
other hand, we see significant circular dichroic (CD) signal at the adjacent
$\bar{\mathrm{K}}$\- and $\bar{\mathrm{K}}$′-points. This arises due to a
combination of (1) the primarily two-dimensional character of the states at
$\bar{\mathrm{K}}$\- and $\bar{\mathrm{K}}$′, and (2) the surface sensitivity
of the ARPES measurement Bertoni  _et al._ (2016); Riley  _et al._ (2014).
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 Seah and Dench (1979).

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

A powerful aspect of the Artemis setup is its ability to switch efficiently
between different HHG probe energies. (See also Ref. Heber  _et al._ (2022).)
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 $k_{z}$-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-dispersive Voß  _et al._ (1999), and are visible
at all photon energies. However, the scattering from $K$ to $\Sigma$ is well
captured at only one probe energy, 22.4 eV. In this connection, we note both
that the out-of-plane dispersion along the $\Sigma$-$X$ path is more
pronounced than that along $K$-$H$ path Voß  _et al._ (1999), and also that
the photoemission matrix elements are presumably enhanced at particular probe
energies Heber  _et al._ (2022); Boschini  _et al._ (2020); Moser (2017). 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 Co3Sn2S2Liu  _et al._ (2021) and PtTe2 Yan  _et al._ (2017). The
second points to the possibility of using matrix element effects to optimise
signal-to-noise for all types of samples, including those with a primarily 2D
electronic character.

Figure 4: (a) Spin- and valley-polarised excited carriers in the surface
electronic band structure of 2$H$-WSe2 along the
$\bar{\mathrm{\Gamma}}$-$\bar{\mathrm{K}}$ high-symmetry line. At left,
adapted from Ref. Bertoni  _et al._ (2016), red and blue color-coding in the
band structure plot refers to the spin polarisation of the bands. Light and
dark arrows symbolise right- and left-circular polarisation of the pump pulse.
The data shows pump polarization-dependent measurements of excited-state
spectra. The labels at the upper right-hand corners indicate linear vertical
(LV) and horizontal (LH) polarizations, linear dichroism (LD) as a difference
plot of LH-LV, circular right (CR) and left (CL) polarizations, and circular
dichroism (CD) as a difference plot of CL-CR. 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 200 fs after the excitation (bottom row). The probe photon energy is
indicated at the upper right-hand corner at the top of each column. The out-
of-plane electronic dispersion along $\mathrm{\Sigma}$-X leads to a photon-
energy-dependence in the photoemission intensity of the states projected into
$\bar{\mathrm{\Sigma}}$. Meanwhile, the states along K-H are nearly non-
dispersing, and thus the photoemission intensity in those states is nearly
independent of probe photon energy. The schematic of the out-of-plane-
dispersing band structure is adapted from Ref. Bertoni  _et al._ (2016). Data
were acquired with $V_{r}$ set such that $E-E_{F}=0.65$ eV.

##  IV Additional technical considerations

Figure 5:  (a) Electric fields between sample and FeSuMa analyser for normal
operation mode (top) and when ”fisheye voltage” is applied (bottom).
Calculated with SIMION Dahl (2000). (b) Fermi surface of Bi(111) taken with
probe energy of 16.2 eV, with increasing “fisheye voltage” applied. (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-centre on the detector.) (c) Workflow for applying the corrections
required for datasets acquired with “fisheye voltage”. (i) Conversion between
position on the MCP, $(x,y)$, to emission angle, $\theta_{x},\theta_{y}$,
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. Black dot-dashed lines represent the portions of the image that
need correction, while arrows indicate the direction of the corrections.

###  IV.1 “Fisheye” Data Acquisition

Applying a bias voltage to the sample holder is a very convenient approach to
increase the momentum field of view Gauthier  _et al._ (2021). Due to the
additional component of the field towards the analyser (shown schematically in
Fig. 5(a)), electron trajectories are bent, and electrons that initially
deviate strongly from the lens axis are nevertheless able to enter the
analyser. 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. 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 (i.e., non-
cylindrical sample holder, manipulator shape, cables, etc.). Because we can
easily see the momentum distribution “live” before acquiring a spectrum, we
can take some steps to minimize distortions by adjusting of 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.

We introduce two types of corrections to deal with angular and radial
distortions, taking 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 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 centre of the image intact.

###  IV.2 Space-charge

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 towards the analyser Hellmann  _et al._ (2009);
Passlack  _et al._ (2006). The resultant photoemission spectra exhibit reduced
effective energy- and momentum-resolution, as well as other artifacts, such as
shifting of spectra and possible “ghost” peaks Passlack  _et al._ (2006). The
energy shift and broadening are illustrated schematically 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 multiphoton photoemission
and emission from surface defects Oloff  _et al._ (2016). This latter effect
can contribute additional space-charge effects.

In our setup, photoemitted electrons are tightly confined in space and time
only once, at the sample surface, before they interact with the MCP Borisenko
_et al._ (2022). This is an advantageous situation relative to HAs and MMs,
where additional focal planes and spatial confinement can cause further
Coulombic interaction Schönhense, Medjanik, and Elmers (2015); Maklar  _et
al._ (2020); Kutnyakhov  _et al._ (2020). 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 Kutnyakhov  _et al._ (2020).
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 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 XUV beam
diameter and on pulse energy Hellmann  _et al._ (2012). At the relatively low
1-kHz repetition rate of the Artemis set-up 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 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 characterise the spectral modifications due to probe-induced
space-charge. 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
Passlack  _et al._ (2006). Fig 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 Ulstrup  _et al._ (2015). The secondary-electron population scales
non-linearly with the $n^{th}$-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 affects of real ultrafast dynamics
happening in the sample. Up to a fluence of approximately 5 mJ cm-2, the
spectra are virtually unaltered by any pump-induced space-charge. Above this
threshold, the spectral shift shows a power dependence of $F^{x}$ ($x=2.7\pm
0.1$), in agreement with a previous study of the excitation with a 1.55 eV
pump Oloff  _et al._ (2016).

Figure 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. Dark (light) blue peaks represent the electron
distribution just after photoemission (after travel towards the analyser). (c)
Measured probe-induced peak shift of the spectrum at the peak of excitation,
as a function of probe photon flux (measured as photocurrent $I_{PD}$ 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 peak shift of the Fermi edge before the excitation, as a
function of pump fluence. (Horizontal error bars estimated from typical
fluctuation in pump power as measured with power meter sup , vertical error
bars determined by uncertainty in fitting the FL shift).

##  V Conclusions

The FeSuMa offers a simple, affordable approach to high-quality pump-probe
photoemission measurements, particularly for time-resolved ARPES of valence
and conduction states near the Fermi level. Like certain PEEM-based
approaches, it permits 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 benefit for studies of
3D-dispersing states. The FeSuMa is highly complementary to hemispherical
analyzers, and constitutes an attractive option for laboratory-scale
measurements of electron dynamics. Measurements of conduction-band dynamics in
layered 2H-WSe2 yield excellent agreement with previously published results
based on momentum microscopy.

###### Acknowledgements.

We thank Phil Rice, Alistair Cox, and the CLF Engineering Section for
technical support; and Drs. James O. F. Thompson and 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
programme). Supplementary material is available online. It includes a movie of
data acquired with the FeSuMa across a range of delay times before and after
an optically pumped excitation in Bi(111)/Bi2Se3, and information about the
time resolution and laser stability on the beamline used for this experiment.

## References

  * Petek and Ogawa (1997) H. Petek and S. Ogawa, “Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals,” Prog. Surf. Sci. 56, 239–310 (1997).
  * Zhou  _et al._ (2018) 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,” Reports on Progress in Physics 81, 062101 (2018).
  * Suzuki, Shin, and Ozaki (2021) T. Suzuki, S. Shin, and K. Ozaki, “HHG-laser-based time- and angle-resolved photoemission spectroscopy of quantum materials,” J. Electron Spectrosc. Relat. Phenom. 251, 147105 (2021).
  * Grychtol  _et al._ (2022) 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,” Journal of Physics: Conference Series 2380, 012043 (2022).
  * Kutnyakhov  _et al._ (2020) 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,” Review of Scientific Instruments 91, 13109 (2020).
  * Peng  _et al._ (2018) 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. Quantum Electron. 24, 1–12 (2018).
  * Frassetto  _et al._ (2011) 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).
  * Damascelli, Hussain, and Shen (2003) A. Damascelli, Z. Hussain, and Z.-X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Reviews of Modern Physics 75, 473–541 (2003).
  * Sobota, He, and Shen (2021) J. A. Sobota, Y. He, and Z.-X. Shen, “Angle-resolved photoemission studies of quantum materials,” Reviews of Modern Physics 93, 025006 (2021).
  * Boschini  _et al._ (2020) 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 Journal of Physics 22, 23031 (2020).
  * Gierz  _et al._ (2011) 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,” Physical Review B 83, 121408 (2011).
  * Gierz  _et al._ (2012) 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 Letters 12, 3900–3904 (2012).
  * Peatman (1997) W. B. Peatman,  _Gratings, Mirrors, and Slits: Beamline Design for Soft X-Ray Synchrotron Radiation Sources_ (Gordon and Breach Science Publishers, Amsterdam, 1997).
  * Jaeglé (2000) 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.
  * Puppin  _et al._ (2019) M. Puppin, Y. Deng, C. W. Nicholson, J. Feldl, 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).
  * Heber  _et al._ (2022) 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,” Review of Scientific Instruments 93, 083905 (2022).
  * Iwasawa  _et al._ (2017) 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).
  * Schönhense, Medjanik, and Elmers (2015) G. Schönhense, K. Medjanik, and H.-J. Elmers, “Space-, time- and spin-resolved photoemission,” Journal of Electron Spectroscopy and Related Phenomena 200, 94–118 (2015).
  * Maklar  _et al._ (2020) 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,” Review of Scientific Instruments 91, 123112 (2020).
  * Tusche  _et al._ (2020) 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).
  * Suga, Sekiyama, and Tusche (2021) S. Suga, A. Sekiyama, and C. Tusche,  _Photoelectron Spectroscopy: Bulk and Surface Electronic Structures_ , 2nd ed. (Springer Nature, Switzerland, 2021) pp. 351–416.
  * Eppink and Parker (1997) 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).
  * Stei  _et al._ (2013) 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,” Journal of Chemical Physics 138, 214201 (2013).
  * Borisenko  _et al._ (2022) 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,” Nature Communications 13, 4132 (2022).
  * Frassetto  _et al._ (2008) 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,” in  _Proc. SPIE_, Vol. 7077 (2008) p. 707713.
  * (26) See Supplemental Material for a movie of a representative three-dimensional dataset and for details about time resolution and laser stability.
  * Koroteev  _et al._ (2004) 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,” Physical Review Letters 93, 046403 (2004).
  * Hirahara  _et al._ (2006) T. Hirahara, T. Nagao, I. Matsuda, G. Bihlmayer, E. V. Chulkov, Y. M. Koroteev, P. M. Echenique, M. Saito, and S. Hasegawa, “Role of spin-orbit coupling and hybridization effects in the electronic structure of ultrathin bi films,” Physical Review Letters 97, 146803 (2006).
  * Gauthier  _et al._ (2021) 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,” Review of Scientific Instruments 92, 123907 (2021).
  * Zouros and Benis (2002) T. J. M. Zouros and E. P. Benis, “The hemispherical deflector analyser revisted. I. Motion in the ideal 1/r potential, generalized entry conditions, Kepler orbits and spectrometer basic equation,” Journal of Electron Spectroscopy and Related Phenomena 125, 221–248 (2002).
  * Schönhense  _et al._ (2018) 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 Journal of Physics 20, 033004 (2018).
  * Hsu  _et al._ (2017) 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,” Nature Communications 8, 929 (2017).
  * Bertoni  _et al._ (2016) 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,” Physical Review Letters 117, 277201 (2016).
  * Puppin  _et al._ (2022) 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,” Physical Review B 105, 075417 (2022).
  * Madéo  _et al._ (2020) 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).
  * Miaja-Avila  _et al._ (2006) 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,” Physical Review Letters 97, 113604 (2006).
  * Keunecke  _et al._ (2020) 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,” Physical Review B 102, 161403 (2020).
  * Riley  _et al._ (2014) 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,” Nature Physics 10, 835–839 (2014).
  * Seah and Dench (1979) 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. (1979), 10.1002/sia.740010103.
  * Voß  _et al._ (1999) 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,” Physical Review B 60, 14 311–14317 (1999).
  * Moser (2017) S. Moser, “An experimentalist’s guide to the matrix element in angle resolved photoemission,” Journal of Electron Spectroscopy and Related Phenomena 214, 29–52 (2017).
  * Liu  _et al._ (2021) 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,” Physical Review B 104, 205140 (2021).
  * Yan  _et al._ (2017) 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,” Nature Communications 8, 257 (2017).
  * Dahl (2000) D. A. Dahl, “SIMION for the personal computer in reflection,” International Journal of Mass Spectrometry 200, 3–25 (2000).
  * Hellmann  _et al._ (2009) S. Hellmann, K. Rossnagel, M. Marczynski-Bühlow, and L. Kipp, “Vacuum space-charge effects in solid-state photoemission,” Physical Review B 79, 035402 (2009).
  * Passlack  _et al._ (2006) 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,” Journal of Applied Physics 100, 024912 (2006).
  * Oloff  _et al._ (2016) 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,” Journal of Applied Physics 119, 225106 (2016).
  * Hellmann  _et al._ (2012) S. Hellmann, T. Ott, L. Kipp, and K. Rossnagel, “Vacuum space-charge effects in nano-ARPES,” Physical Review B 85, 075109 (2012).
  * Ulstrup  _et al._ (2015) 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,” Journal of Electron Spectroscopy and Related Phenomena 200, 340–346 (2015).