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.

Photoelectron spectroscopy, especially at pulsed sources, is ultimately limited by the Coulomb interaction in the electron cloud, changing energy and angular distribution of the photoelectrons. A detailed understanding of this phenomenon is crucial for future pump-probe photoemission studies at (x-ray) free electron lasers and high-harmonic photon sources. Measurements have been performed for Ir(111) at hν=1000 eV with photon flux densities between ∼10 2 and 10 4 photons per pulse and μm 2 (beamline P04/PETRA III, DESY Hamburg), revealing space-charge induced energy shifts of up to 10 eV. In order to correct the essential part of the energy shift and restore the electron distributions close to the Fermi energy, we developed a semi-analytical theory for the space-charge effect in cathode-lens instruments (momentum microscopes, photoemission electron microscopes). The theory predicts a Lorentzian profile of energy isosurfaces and allows us to quantify the charge cloud from measured energy profiles. The correction is essential for the determination of the Fermi surface, as we demonstrate by means of 'k-space movies' for the prototypical high-Z material tungsten. In an energy interval of about 1 eV below the Fermi edge, the bandstructure can be restored up to substantial shifts of ∼7 eV. Scattered photoelectrons strongly enhance the inelastic background in the region several eV below E F , proving that the majority of scattering events involves a slow electron. The correction yields a gain of two orders of magnitude in usable intensity compared with the uncorrected case (assuming a tolerable shift of 250 meV). The results are particularly important for future experiments at SASE-type free electron lasers, since the correction also works for strongly fluctuating (but known) pulse intensities.

A comprehensive mapping of the spin polarization of the electronic bands in ferroelectric α-GeTe(111) films has been performed using a time-of-flight momentum microscope equipped with an imaging spin filter that enables a simultaneous measurement of more than 10.000 data points (voxels). A Rashba type splitting of both surface and bulk bands with opposite spin helicity of the inner and outer Rashba bands is found revealing a complex spin texture at the Fermi energy. The switchable inner electric field of GeTe implies new functionalities for spintronic devices.The strong coupling of electron momentum and spin in low-dimensional structures allows an electrically controlled spin manipulation in spintronic devices [1][2][3][4], e.g. via the Rashba effect [5].The Rashba effect has first been experimentally demonstrated in semiconductor heterostructures, where an electrical field perpendicular to the layered structure, i.e. perpendicular to the electron momentum, determines the electron spin orientation relative to its momentum [6][7][8]. An asymmetric interface structure causes the necessary inversion symmetry breaking and accounts for the special spin-splitting of electron states, the Rashba effect [5], the size of which can be tuned by the strength of the electrical field.For most semiconducting materials the Rashba effect causes only a quite small splitting of the order of 10 −2Å−1 and thus requires experiments at very low temperatures [9][10][11] and also implies large lateral dimensions for potential spintronic applications. A considerably larger splitting has been predicted theoretically [12] and was recently found experimentally for the surface states of GeTe(111) [13,14].GeTe is a ferroelectric semiconductor with a Curie temperature of 700 K. Thus, besides the interface induced Rashba splitting, the ferroelectric properties also imply a broken inversion symmetry within the bulk and thus would allow for the electrical tuning of the bulk Rashba splitting via switching the ferroelectric polarization [12,15,16]. This effect is of great interest for nonvolatile spin orbitronics [10].For GeTe a bulk Rashba splitting of 0.19Å −1 has been predicted theoretically [12]. Experimentally, bulkRashba bands are rare and have only been found in the layered polar semiconductors BiTeCl and BiTeI [17][18][19][20] that, however, are not switchable.A characterization of the ferroelectric properties and a measurement of the spin polarization of the surface states of GeTe(111) at selected k-points has been performed previously by force microscopy [21,22] and spinresolved angular resolved photoemission spectroscopy, respectively [13]. A recent experimental and theoretical study revealed that at the Fermi level the hybridization of surface and bulk states causes surface-bulk resonant states resulting in unconventional spin topologies with chiral symmetry [14].Here, we demonstrate the spin structure of surface and bulk bands of the GeTe(111) surface using the novel photoemission technique of spin-resolved time-of-flight momentum micro...

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Time-resolved soft-x-ray photoemission spectroscopy is used to simultaneously measure the ultrafast dynamics of core-level spectral functions and excited states upon excitation of excitons in WSe 2. We present a many-body approximation for the Green's function, which excellently describes the transient core-hole spectral function. The relative dynamics of excited-state signal and core levels clearly show a delayed core-hole renormalization due to screening by excited quasifree carriers resulting from an excitonic Mott transition. These findings establish time-resolved core-level photoelectron spectroscopy as a sensitive probe of subtle electronic many-body interactions and ultrafast electronic phase transitions.

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