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.

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

The energy dispersion of the unoccupied Dirac bands of the topological insulator Bi₂Se₃ has been studied up to large parallel momenta and intermediate state energies using a setup for laser-based time-resolved momentum microscopy with 6 eV probe-photons. A strongly momentum-dependent evolution of the topologically protected Dirac states into a conduction band resonance is observed, highlighting the anisotropy dictated by the symmetry of the surface. The results are in remarkable agreement with the theoretical surface spectrum obtained from a GW-corrected tight-binding model, suggesting the validity of the approach in the prediction of the quasiparticle excitation spectrum of large systems with non-trivial topology. After photoexcitation with 0.97 eV photons, assigned to a bulk valence band-conduction band transition, the out-of-equilibrium population of the surface state evolves on a multi-picosecond time scale, in agreement with a simple thermodynamical model with a fixed number of particles, suggesting a significant decoupling between bulk and surface states.

Stefano Ponzoni, Felix Paßlack, Matija Stupar, David Maximilian Janas, Giovanni Zamborlini, Mirko Cinchetti
Adv. Physics Res.2023, 2200016

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)

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)

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 T_d-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

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 2H−WSe2. 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