Materials with unique quantum characteristics–quantum materials—have become of great importance for information technology. Among others, their unique transport phenomena are in many cases closely connected to details of the electronic structure. Exploring the electronic states and the interplay of the interactions in this material class down to the electron spin is, therefore, mandatory to understand and further design their physical behavior. We discuss several quantum materials studied by an advanced photoelectron spectroscopy approach—spin-resolved momentum microscopy with tunable synchrotron radiation—and illustrate the role of a progressive symmetry reduction leading to particular features of their electronic structures observed in the experiment.

Spin-polarized electrons confined in low-dimensional structures are of high interest for spintronics applications. Here, we investigate the electronic structure of an ordered array of Bi monomer and dimer chains on the Ag(110) surface. By means of spin-resolved photoemission spectroscopy, we find Rashba-Bychkov split bands crossing the Fermi level with one-dimensional constant energy contours. These bands are up-spin polarized for positive wave vectors and down-spin polarized for negative wave vectors, at variance with the Rashba-Bychkov model that predicts a pair of states with opposite spin in each half of the surface Brillouin zone. Density functional theory shows that spin-selective hybridization with the Ag bulk bands originates this unconventional spin texture.

Topological semimetals have recently attracted great attention due to prospective applications governed by their peculiar Fermi surfaces. Weyl semimetals host chiral fermions that manifest as pairs of non-degenerate massless Weyl points in their electronic structure, giving rise to novel macroscopic quantum phenomena such as the chiral anomaly, an unusual magnetoresistance, and various kinds of Hall effects These properties enable the engineering of non-local electric transport devices, magnetic sensors and memories, and spintronics devices. Nevertheless, little is known about the underlying spin- and orbital-degrees of freedom of the electron wave functions in Weyl semimetals, that govern the electric transport. Here, we give evidence that the chirality of the Weyl points in the Type-II Weyl semimetal MoTe$_2$ is directly linked to the spin texture and orbital angular momentum of the electron wave functions. By means of state-of-the-art spin- and momentum-resolved photoemission spectroscopy the spin- and orbital texture in the Fermi surface is directly resolved. Supported by first-principles calculations, we examined the relationship between the topological chiral charge and spin texture, which significantly contributes to the understanding of the electronic structure in topological quantum materials.

Hemispherical deflection analyzers are the most widely used energy filters for state-of-the-art electron spectroscopy. Due to the high spherical symmetry, they are also well suited as imaging energy filters for electron microscopy. Here, we review the imaging properties of hemispherical deflection analyzers with emphasis on the application for cathode lens microscopy. In particular, it turns out that aberrations, in general limiting the image resolution, cancel out at the entrance and exit of the analyzer. This finding allows more compact imaging energy filters for momentum microscopy or photoelectron emission microscopy. For instance, high resolution imaging is possible, using only a single hemisphere. Conversely, a double pass hemispherical analyzer can double the energy dispersion, which means it can double the energy resolution at certain transmission, or can multiply the transmission at certain energy resolution.

Time-resolved potoemission with femtosecond pump and probe pulses is an emerging technique with a large potential. Real-time recording of ultrafast electronic processes, transient states in chemical reactions or the interplay of electronic and structural dynamics bears fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction as powerful tools for electronic, chemical and structural analysis requires fs soft X-ray pulses with some 10~meV resolution, available at high repetition rate free-electron lasers. An optimized setup has been commissioned at FLASH (DESY, Hamburg), combining the superior source parameters of beamline PG2 with a revolutionary multidimensional recording scheme. FLASH/PG2 provides a high pulse rate of 5000~pulses/s, 60~fs time resolution and 40~meV spectral resolution in an energy range of 25 -- 830~eV with a photon spot of 150~microns in diameter. As detector we use a full-field imaging momentum microscope with time-of-flight energy recording for mapping of the entire band structure in 3D ($k_x$, $k_y$, E) parameter space with unprecedented efficiency. This instrument can image the full surface Brillouin zone with up to 7~\angstrom$^{-1}$ diameter in a binding-energy range of several eV, resolving about $2.5\times10^5$ data voxels. As example we show results for the ultrafast excited state dynamics in the prototypical van der Waals semiconductor WSe$_2$.