We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution v(k) of tungsten. The 4D spectral function ρ(E; k) in the entire bulk Brillouin zone and 6 eV binding-energy (E) interval was acquired in ∼3 h thanks to a new multidimensional photoemission data-recording technique (combining full-field k-microscopy with time-of-flight parallel energy recording) and the high brilliance of the soft X-rays used. A direct comparison of bulk and surface spectral functions (taken at low photon energies) reveals a time-reversal-invariant surface state in a local bandgap in the (110)-projected bulk band structure. The surface state connects hole and electron pockets that would otherwise be separated by an indirect local bandgap. We confirmed its Dirac-like spin texture by spin-filtered momentum imaging. The measured 4D data array enables extraction of the 3D dispersion of all bands, all energy isosurfaces, electron velocities, hole or electron conductivity, effective mass and inner potential by simple algorithms without approximations. The high-Z bcc metals with large spin-orbit-induced bandgaps are discussed as candidates for topologically non-trivial surface states.

Time-resolved photoemission with ultrafast pump and probe pulses is an emerging technique with wide application potential. Real-time recording of nonequilibrium electronic processes, transient states in chemical reactions, or the interplay of electronic and structural dynamics offers fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction for electronic, chemical, and structural analyses requires few 10 fs soft X-ray pulses with some 10 meV spectral resolution, which are currently available at high repetition rate free-electron lasers. We have constructed and optimized a versatile setup commissioned at FLASH/PG2 that combines free-electron laser capabilities together with a multidimensional recording scheme for photoemission studies. We use a full-field imaging momentum microscope with time-of-flight energy recording as the detector for mapping of 3D band structures in (kx, ky, E) parameter space with unprecedented efficiency. Our instrument can image full surface Brillouin zones with up to 7 Å−1 diameter in a binding-energy range of several eV, resolving about 2.5 × 105 data voxels simultaneously. Using the ultrafast excited state dynamics in the van der Waals semiconductor WSe2 measured at photon energies of 36.5 eV and 109.5 eV, we demonstrate an experimental energy resolution of 130 meV, a momentum resolution of 0.06 Å−1, and a system response function of 150 fs.

This article reviews photoemission experiments that simultaneously resolve at least two of the following degrees of freedom: space (real and momentum space), time (intrinsic time scale of a fast experiment or time-of-flight) and spin. In the spatiotemporal domain, imaging of fast processes by PEEM gives direct insight into plasmon dynamics or magnetization processes. In the category real space & spin the novel concept of imaging spin filters is discussed. In the time & spin chapter we address time-of-flight spin detectors and ultrafast spin processes that are accessible by pump-and-probe techniques. A main part of the paper is devoted to the resolution of momentum-space & time. This is implemented in form of the time-of-flight momentum microscope, a very recent development of which the first instrument has been in operation since 2014. In an extended outlook chapter, the potential of new developments and of a novel, highly parallelized delay-line type electron detector will be discussed. The combination of all three degrees of freedom k-space, time & spin is emerging through the combination of the ToF momentum microscope with imaging spin filter. Outline

A new undulator beamline (P22) for hard X-ray photoelectron spectroscopy (HAXPES) was built at PETRA III (DESY, Hamburg) to meet the increasing demand for HAXPES-based techniques. It provides four special instruments for high-resolution studies of the electronic and chemical structure of functional nano-materials and catalytic interfaces, with a focus on measurements under operando and/or ambient conditions: (i) a versatile solid-state spectroscopy setup with optional wide-angle lens and in-situ electrical characterization, (ii) a HAXPEEM instrument for sub-µm spectro-microscopy applications, (iii) an ambient pressure system (> 1 bar) for operando studies of catalytic reactions and (iv) a time-of-flight spectrometer as a full-field k-microscope for measurements of the 4D spectral function ρ(E B ,k). The X-ray optics were designed to deliver high brightness photon flux within the HAXPES energy range 2.4-15 keV. An LN 2-cooled double-crystal monochromator with interchangeable pairs of Si(111) and (311) crystals is optionally combined with a double channel-cut post-monochromator to generate X-rays with variable energy bandpass adapted to the needs of the experiment. Additionally, the beam polarization can be varied using a diamond phase plate integrated into the beamline. Adaptive beam focusing is realized by Be compound refractive lenses and/or horizontally deflecting mirrors down to a spot size of ~20x17 µm 2 with a flux of up to 1.1x10 13 ph/s (for Si(111) at 6 keV).