Momentum Microscopy Systems

We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution vF(kF) of tungsten. The 4D spectral function ρ(EB; k) in the entire bulk Brillouin zone and 6 eV binding-energy (EB) 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.

The implementation of graphene in semiconducting technology requires precise knowledge about the graphene–semiconductor interface. In our work the structure and electronic properties of the graphene/n-Ge(110) interface are investigated on the local (nm) and macro (from μm to mm) scales via a combination of different microscopic and spectroscopic surface science techniques accompanied by density functional theory calculations. The electronic structure of freestanding graphene remains almost completely intact in this system, with only a moderate n-doping indicating weak interaction between graphene and the Ge substrate. With regard to the optimisation of graphene growth it is found that the substrate temperature is a crucial factor, which determines the graphene layer alignment on the Ge(110) substrate during its growth from the atomic carbon source. Moreover, our results demonstrate that the preparation route for graphene on the doped semiconducting material (n-Ge) leads to the effective segregation of dopants at the interface between graphene and Ge(110). Furthermore, it is shown that these dopant atoms might form regular structures at the graphene/Ge interface and induce the doping of graphene. Our findings help to understand the interface properties of the graphene–semiconductor interfaces and the effect of dopants on the electronic structure of graphene in such systems.

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.

The electronic band structure and crystal structure are the two complementary identifiers of solid-state materials. Although convenient instruments and reconstruction algorithms have made large, empirical, crystal structure databases possible, extracting the quasiparticle dispersion (closely related to band structure) from photoemission band mapping data is currently limited by the available computational methods. To cope with the growing size and scale of photoemission data, here we develop a pipeline including probabilistic machine learning and the associated data processing, optimization and evaluation methods for band-structure reconstruction, leveraging theoretical calculations. The pipeline reconstructs all 14 valence bands of a semiconductor and shows excellent performance on benchmarks and other materials datasets. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales, while realizing a path towards integration with materials science databases. Our approach illustrates the potential of combining machine learning and domain knowledge for scalable feature extraction in multidimensional data.

Hybrid plasmonic devices involve a nanostructured metal supporting localized surface plasmons to amplify light–matter interaction, and a non-plasmonic material to functionalize charge excitations. Application-relevant epitaxial heterostructures, however, give rise to ballistic ultrafast dynamics that challenge the conventional semiclassical understanding of unidirectional nanometal-to-substrate energy transfer. Epitaxial Au nanoislands are studied on WSe₂ with time- and angle-resolved photoemission spectroscopy and femtosecond electron diffraction: this combination of techniques resolves material, energy, and momentum of charge-carriers and phonons excited in the heterostructure. A strong non-linear plasmon–exciton interaction that transfers the energy of sub-bandgap photons very efficiently to the semiconductor is observed, leaving the metal cold until non-radiative exciton recombination heats the nanoparticles on hundreds of femtoseconds timescales. The results resolve a multi-directional energy exchange on timescales shorter than the electronic thermalization of the nanometal. Electron–phonon coupling and diffusive charge-transfer determine the subsequent energy flow. This complex dynamics opens perspectives for optoelectronic and photocatalytic applications, while providing a constraining experimental testbed for state-of-the-art modelling.

Excitons, Coulomb-bound electron–hole pairs, are the fundamental excitations governing the optoelectronic properties of semiconductors. Although optical signatures of excitons have been studied extensively, experimental access to the excitonic wave function itself has been elusive. Using multidimensional photoemission spectroscopy, we present a momentum-, energy-, and time-resolved perspective on excitons in the layered semiconductor WSe₂. By tuning the excitation wavelength, we determine the energy–momentum signature of bright exciton formation and its difference from conventional single-particle excited states. The multidimensional data allow to retrieve fundamental exciton properties like the binding energy and the exciton–lattice coupling and to reconstruct the real-space excitonic distribution function via Fourier transform. All quantities are in excellent agreement with microscopic calculations. Our approach provides a full characterization of the exciton properties and is applicable to bright and dark excitons in semiconducting materials, heterostructures, and devices.