Excited-state band structure mapping

Open Access

Excited-state band structure mapping

M. Puppin, C. W. Nicholson, C. Monney, Y. Deng, R. P. Xian, J. Feldl, S. Dong, A. Dominguez, H. Hübener, A. Rubio, M. Wolf, L. Rettig, and R. Ernstorfer

Phys. Rev. B 105, 075417 – Published 17 February 2022

Abstract

Angle-resolved photoelectron spectroscopy is an extremely powerful probe of materials to access the occupied electronic structure with energy and momentum resolution. However, it remains blind to those dynamic states above the Fermi level that determine technologically relevant transport properties. In this work we extend band structure mapping into the unoccupied states and across the entire Brillouin zone by using a state-of-the-art high repetition rate, extreme ultraviolet femtosecond light source to probe optically excited samples. The wide-ranging applicability and power of this approach are demonstrated by measurements on the two-dimensional semiconductor ${WSe}_{2}$ , where the energy-momentum dispersion of valence and conduction bands are observed in a single experiment. This provides a direct momentum-resolved view, not only on the complete out-of-equilibrium band gap but also on its renormalization induced by electronic screening. Our work establishes a benchmark for measuring the band structure of materials, with direct access to the energy-momentum dispersion of the excited-state spectral function.

Received 17 August 2021
Revised 6 December 2021
Accepted 26 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.075417

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Band gap Electronic structure Valleytronics

Band structure methods GW method Time & angle resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Puppin ^1,2,*, C. W. Nicholson ³, C. Monney³, Y. Deng⁴, R. P. Xian ², J. Feldl ², S. Dong ², A. Dominguez^5,6, H. Hübener ⁷, A. Rubio^7,8,9, M. Wolf², L. Rettig ², and R. Ernstorfer ^2,10,†

¹Laboratoire de Spectroscopie Ultrarapide and Lausanne Centre for Ultrafast Science (LACUS), École Polytechnique Fédérale de Lausanne, ISIC, Station 6, CH-1015 Lausanne, Switzerland
²Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
³Department of Physics and Fribourg Center for Nanomaterials, University of Fribourg, Chemin du Musée 3, CH-1700 Switzerland
⁴Paul Scherrer Institute, SwissFEL, 5232 Villigen PSI, Switzerland
⁵Shenzhen JL Computational Science and Applied Research Institute (CSAR), Shenzhen 518110, China
⁶Beijing Computational Research Center (CSRC), Beijing 100193, China
⁷Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science, Luruper Chaussee 149, Geb. 99 (CFEL), 22761 Hamburg
⁸Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
⁹Nano-Bio Spectroscopy Group, Universidad del Paìs Vasco UPV/EHU, 20018 San Sebastián, Spain
¹⁰Institut für Optik und Atomare Physik, Technische Universität Berlin, Straße des 17, Juni 135, 10632 Berlin, Germany

^*michele.puppin@epfl.ch
^†ernstorfer@fhi-berlin.mpg.de

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Vol. 105, Iss. 7 — 15 February 2022

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Images

Figure 1
(a) Band structure mapping in reciprocal space by angle-resolved photoelectron spectroscopy (ARPES). The reciprocal space region measured by the hemispherical energy analyzer (HEA) for two sample tilt angles is indicated by a green line, the maximum parallel momentum which can be accessed by 20 eV photons is indicated by a violet dashed line. (b) trARPES experiments on $2 H - {WSe}_{2}$ : an optical pump pulse at an energy of 3.1 eV excites the system. At a delay $t$ , an XUV probe pulse at an energy of 21.7 eV generates photoelectrons, which are measured as a function of the emission angle $θ$ with a HEA. The sample angle is scanned across the analyzer slit to collect ARPES maps. (c) Excited-state band structure mapping. (d) trARPES data collected in the conduction band of ${WSe}_{2}$ for pump-probe delays of $- 50$ fs, 100 fs, and 1 ps. Inset: The surface Brillouin zone of ${WSe}_{2}$ . (e) Photoelectron intensity distribution as a function of parallel momentum for three energies at a pump-probe delay of 100 fs; VB and CB energy distribution curves have been independently intensity normalized for better visualization. The experimental data is collected in a region delimited by the dashed line. Outside this region, the results of $G_{0} W_{0}$ calculations are displayed, and the theoretical band dispersion along the $k_{z}$ direction was integrated; the conduction bands were rigidly offset by a scissor operator of $- 0.16$ eV to match the experimental energy.
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Figure 2
Measured ARPES intensity as a function of energy and parallel momentum showing the VB and CB along the $\bar{Γ} − \bar{Σ} − \bar{K}$ , $\bar{K} − \bar{M}$ , $\bar{M} − \bar{Γ}$ directions, indicated in the upper panel. Conduction-band states are displayed by a different color scale. Blue and red curves indicate the quasiparticle energies calculated with the $G_{0} W_{0}$ method for the CB and VB, respectively. The theoretical band structure energy zero was set to the VB position at the $\bar{K}$ point, and the CBs (blue) were rigidly shifted by a $- 0.16$ -eV scissor operator to match the $\bar{Σ}$ valley center energy. The momentum dispersion along the $k_{z}$ direction is indicated by the shaded area.
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Figure 3
(a) Energy distribution curve at the $K$ point, together with the fit used to determine the excited-state band gap $E_{g, exc}$ . The conduction-band signal intensity, displayed on the right-hand axis, was scaled by a factor $10^{3}$ for clarity. (b) Fluence dependence of the excited-state direct band gap at the $\bar{K}$ pointfor a time delay of 100 fs. Schematic description of the (c) fundamental, (d) optical, and (e) excited-state direct band gaps at the $\bar{K}$ valley, where VL indicates the vacuum level. Only the direct gap is considered, i.e., the energy of emitted (absorbed) electrons is measured at the same parallel momentum value. The photoexcitation occurs at time zero at a different reciprocal space location, above the direct band gap. The photoexcited electron and hole distributions renormalize the excited-state bands, indicated by CB* and VB*.
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Figure 4
(a) Conduction-band center energy at the $\bar{K}$ valley, (b) $G_{0} W_{0}$ energy of the K valley, and (c) dispersion along the directions K- $Σ$ (negative $x$ axis) and K-M (positive $x$ axis). The full line indicates the result of parabolic fits to the data.
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Figure 5
(a) ARPES intensity as a function of energy and parallel momentum showing the conduction states along the $\bar{Γ} - \bar{Σ}$ direction at a time delay of $- 50$ fs. The pump-probe temporal cross-correlation is determined by integrating the signal in the rectangular box. (b) Temporal trace showing the integrated intensity in the box of panel (a) as a function of time. Red curve, Gaussian fit to the rising edge, where the FWHM is 95 fs.
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