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Momentum Microscopy Systems

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  1. (2017) Direct 3D mapping of the Fermi surface and Fermi velocity

    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.



    K. Medjanik, O. Fedchenko, S. Chernov, D. Kutnyakhov, M. Ellguth, A. Oelsner, B. Schönhense, T. R. F. Peixoto, P. Lutz, C.-H. Min, F. Reinert, S. Däster, Y. Acremann, J. Viefhaus, W. Wurth, H. J. Elmers, G. Schönhense
    Nature Materials 16, pp. 615–621
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  2. (2018) The graphene/n-Ge(110) interface: structure, doping, and electronic properties

    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.



    J. Tesch, F. Paschke, M. Fonin, M. Wietstruk, S. Böttcher, R. J. Koch, A. Bostwick, C. Jozwiak, E. Rotenberg, A. Makarova, B. Paulus, E. Voloshina, Y. Dedkov
    Nanoscale, 10, pp. 6088-6098
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  3. (2019) Imaging properties of hemispherical electrostatic energy analyzers for high resolution momentum microscopy

    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.



    C. Tusche, Y. J. Chen, C. M. Schneider and J. Kirschner
    Ultramicroscopy 206 (2019)
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  4. (2022) A machine learning route between band mapping and band structure

    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.



    R. Patrick Xian, Vincent Stimper, Marios Zacharias, Maciej Dendzik, Shuo Dong, Samuel Beaulieu, Bernhard Schölkopf, Martin Wolf, Laurenz Rettig, Christian Carbogno, Stefan Bauer, Ralph Ernstorfer
    Nat Comput Sci (2022) https://doi.org/10.1038/s43588-022-00382-2
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  5. (2022) Observation of Multi-Directional Energy Transfer in a Hybrid Plasmonic–Excitonic Nanostructure

    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.



    Tommaso Pincelli, Thomas Vasileiadis, Shuo Dong, Samuel Beaulieu, Maciej Dendzik,
    Daniela Zahn, Sang-Eun Lee, Hélène Seiler, Yingpeng Qi, R. Patrick Xian, Julian Maklar,
    Emerson Coy, Niclas S. Mueller, Yu Okamura, Stephanie Reich, Martin Wolf,
    Laurenz
    Advanced Materials 2023, 2209100
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  6. (2021) Direct measurement of key exciton properties: Energy, dynamics, and spatial distribution of the wave function

    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.



    Shuo Dong, Michele Puppin, Tommaso Pincelli, Samuel Beaulieu, Dominik Christiansen, Hannes Hübener, Christopher W. Nicholson, Rui Patrick Xian, Maciej Dendzik, YunpeiDeng, Yoav William Windsor, Malte Selig, Ermin Malic, Angel Rubio, Andreas Knorr, Martin
    NatSci. 2021;1:e10010
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  7. (2022) Polarization-Modulated Angle-Resolved Photoemission Spectroscopy: Toward Circular Dichroism without Circular Photons and Bloch Wave-function Reconstruction

    Angle-resolved photoemission spectroscopy (ARPES) is the most powerful technique to investigate the electronic band structure of crystalline solids. To completely characterize the electronic structure of topological materials, one needs to go beyond band structure mapping and access information about the momentum-resolved Bloch wave function, namely, orbitals, Berry curvature, and topological invariants. However, because phase information is lost in the process of measuring photoemission intensities, retrieving the complex-valued Bloch wave function from photoemission data has yet remained elusive. We introduce a novel measurement methodology and associated observable in extreme ultraviolet angle-resolved photoemission spectroscopy, based on continuous modulation of the ionizing radiation polarization axis. Tracking the energy- and momentum-resolved amplitude and phase of the photoemission intensity modulation upon polarization axis rotation allows us to retrieve the circular dichroism in photoelectron angular distributions (CDAD) without using circular photons, providing direct insights into the phase of photoemission matrix elements. In the case of two relevant bands, it is possible to reconstruct the orbital pseudospin (and thus the Bloch wave function) with moderate theory input, as demonstrated for the prototypical, layered, semiconducting, transition metal dichalcogenide 2HWSe2. This novel measurement methodology in ARPES, which is articulated around the manipulation of the photoionization transition dipole matrix element, in combination with a simple tight-binding theory, is general and adds a new dimension to obtaining insights into the orbital pseudospin, Berry curvature, and Bloch wave functions of many relevant crystalline solids.



    Michael Schüler, Tommaso Pincelli, Shuo Dong, Thomas P. Devereaux, Martin Wolf, Laurenz Rettig, Ralph Ernstorfer, and Samuel Beaulieu
    Phys. Rev. X 12, 011019
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  8. (2021) Ultrafast dynamical Lifshitz transition

    Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal Td-MoTe2. We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.



    Samuel Beaulieu, Shuo Dong, Nicolas Tancogne-Dejean, Maciej Dendzik, Tommaso Pincelli, Julian Maklar, R. Patrick Xian, Michael A. Sentef, Martin Wolf, Angel Rubio, Laurenz Rettig, Ralph Ernstorfer
    Sci. Adv. 2021; 7 : eabd9275
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  9. (2022) Structure of the moiré exciton captured by imaging its electron and hole

    Interlayer excitons (ILXs) — electron–hole pairs bound across two atomically thin layered semiconductors — have emerged as attractive platforms to study exciton condensation, single-photon emission and other quantum information applications. Yet, despite extensive optical spectroscopic investigations, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, in a WSe2/MoS2 heterostructure, we captured images of the time-resolved and momentum-resolved distribution of both of the particles that bind to form the ILX: the electron and the hole. We thereby obtain a direct measurement of both the ILX diameter of around 5.2 nm, comparable with the moiré-unit-cell length of 6.1 nm, and the localization of its centre of mass. Surprisingly, this large ILX is found pinned to a region of only 1.8 nm diameter within the moiré cell, smaller than the size of the exciton itself. This high degree of localization of the ILX is backed by Bethe–Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, allowing the formation of extended arrays of localized excitations for quantum technology.



    Ouri Karni, Elyse Barré, Vivek Pareek, Johnathan D. Georgaras, Michael K. L. Man, Chakradhar Sahoo, David R. Bacon, Xing Zhu, Henrique B. Ribeiro, Aidan L. O’Beirne, Jenny Hu, Abdullah Al-Mahboob, Mohamed M. M. Abdelrasoul, Nicholas S. Chan, Arka Karmakar
    Nature 603, pages 247–252 (2022)
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  10. (2020) Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors

    Resolving momentum degrees of freedom of excitons, which are electron-hole pairs bound by the Coulomb attraction in a photoexcited semiconductor, has remained an elusive goal for decades. In atomically thin semiconductors, such a capability could probe the momentum-forbidden dark excitons, which critically affect proposed opto-electronic technologies but are not directly accessible using optical techniques. Here, we probed the momentum state of excitons in a tungsten diselenide monolayer by photoemitting their constituent electrons and resolving them in time, momentum, and energy. We obtained a direct visual of the momentum-forbidden dark excitons and studied their properties, including their near degeneracy with bright excitons and their formation pathways in the energy-momentum landscape. These dark excitons dominated the excited-state distribution, a surprising finding that highlights their importance in atomically thin semiconductors.



    Julien Madéo, Michael K. L. Man, Chakradhar Sahoo, Marshall Campbell, Vivek Pareek, E. Laine Wong, Abdullah Al-Mahboob, Nicholas S. Chan, Arka Karmakar, Bala Murali Krishna Mariserla, Xiaoqin Li, Tony F. Heinz, Ting Cao, Keshav M. Dani
    Science 370, 1199–1204 (2020)
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