11. E. B. Watson, T. M. Harrison, Science 308, 841–844 (2005).
12. J. W. Valley et al., Contrib. Mineral. Petrol. 150, 561–580
13. M.-A. Millet et al., Earth Planet. Sci. Lett. 449, 197–205
14. N. D. Greber, N. Dauphas, I. S. Puchtel, B. A. Hofmann,
N. Arndt, Geochim. Cosmochim. Acta 213, 534–552
15. K. J. Orians, E. A. Boyle, K. W. Bruland, Nature 348, 322–325
16. T. Taboada, A. M. Cortizas, C. García, E. García-Rodeja,
Geoderma 131, 218–236 (2006).
17. D. Garcia, M. Fonteilles, J. Moutte, J. Geol. 102, 411–422
18. Materials and methods and supplementary text are available as
19. C. J. Allègre, D. Rousseau, Earth Planet. Sci. Lett. 67, 19–34
20. C. B. Keller, B. Schoene, Nature 485, 490–493 (2012).
22. J.-F. Moyen, H. Martin, Lithos 148, 312–336 (2012).
23. K. C. Condie, C. O’Neill, Am. J. Sci. 310, 775–790 (2011).
24. N. Arndt, J. Geophys. Res. Solid Earth 108 (B6), 2293
25. H. H. Dürr, M. Meybeck, S. H. Dürr, Global Biogeochem. Cycles
19, 1–22 (2005).
26. R. L. Rudnick, S. X. Gao, in Treatise on Geochemistry,
R. L. Rudnick, Ed. (Elsevier, 2003), pp. 1–64.
27. J. F. Moyen, G. Stevens, in Archean Geodynamics
Environments, K. Benn, J.-C. Mareschal, K. C. Condie, Eds.
(American Geophysical Union, 2006),
28. R. H. Smithies, Earth Planet. Sci. Lett. 182, 115–125
29. T. L. Carley et al., Earth Planet. Sci. Lett. 405, 85–97
30. E. Martin, H. Martin, O. Sigmarsson, Terra Nova 20, 463–468
31. S. P. Jakobsson, K. Jónasson, I. A. Sigurdsson, Jokull 58,
32. T. Tyrrell, Nature 400, 525–531 (1999).
33. A. P. Gumsley et al., Proc. Natl. Acad. Sci. U. S.A. 114, 1811–1816
This work was supported by grants from the Swiss National
Science Foundation (grant P2BEP2_158983) to N.D.G.;
NSF (grant CSEDI EAR1502591 and Petrology and Geochemistry
grant EAR1444951) and NASA (grants LARS NNX17AE86G,
EW NNX17AE87G, and SSW NNX15AJ25G) to N.D.; and NSF
(grant EAR-05-45484), NASA (Astrobiology Institute Award
NNA04CC09A), and the Natural Sciences and Engineering
Research Council of Canada Discovery and Accelerator
program to A.B. Comments on an earlier version of the
manuscript by N. Arndt, M.-A. Millet, D. Rowley, R. Rudnick,
and M. Tang are greatly appreciated. We also thank four
reviewers for their constructive comments that improved the
quality of the manuscript. We gratefully acknowledge N. Aubet,
P. Fralick, G. Jackson, B. Krapež, A. Kuznetsov, A. Maslov,
S. Master, P. Medvedev, T. Nägler, C. Noce, L. Ootes,
F. Ossa-Ossa, E. Pecoits, T. Pettke, V. Podkovyrov, R. Rainbird,
B. Rasmussen, R. Ruhanen, M.J. Severson, W. Su, D. Thomson,
P. Thurston, and D. Winston for advice and access to
sample collections. All data used in the paper are either
tabulated in the supplementary material, published in the
cited references, or archived in the PetDB Database
( www.earthchem.org/petdb). N.D.G. and N.D. conceived the
study. A.B., I.N.B., and A.H. selected and provided the
samples. N.D.G. processed the samples and measured their Ti
isotopic compositions. N.D.G., M.P.P., and N.D. compiled
literature data and implemented the three-component
mixing model. All authors contributed to writing and editing
Materials and Methods
Figs. S1 to S9
Data Tables S1 to S10
25 May 2017; accepted 23 August 2017
Angular momentum–induced delays
in solid-state photoemission enhanced
by intra-atomic interactions
Fabian Siek,1 Sergej Neb,1 Peter Bartz,1 Matthias Hensen,1 Christian Strüber,1*
Sebastian Fiechter,2 Miquel Torrent-Sucarrat,3,4,5 Vyacheslav M. Silkin,3,4,5
Eugene E. Krasovskii,3,4,5 Nikolay M. Kabachnik,6,7 Stephan Fritzsche,8
Ricardo Díez Muiño,4,9 Pedro M. Echenique,3,4,9 Andrey K. Kazansky,3,4,5
Norbert Müller,1 Walter Pfeiffer,1† Ulrich Heinzmann1
Attosecond time-resolved photoemission spectroscopy reveals that photoemission from
solids is not yet fully understood. The relative emission delays between four photoemission
channels measured for the van der Waals crystal tungsten diselenide (WSe2) can only be
explained by accounting for both propagation and intra-atomic delays. The intra-atomic
delay depends on the angular momentum of the initial localized state and is determined by
intra-atomic interactions. For the studied case of WSe2, the photoemission events are time
ordered with rising initial-state angular momentum. Including intra-atomic electron-electron interaction and angular momentum of the initial localized state yields excellent
agreement between theory and experiment. This has required a revision of existing models
for solid-state photoemission, and thus, attosecond time-resolved photoemission from
solids provides important benchmarks for improved future photoemission models.
Photoemission spectroscopy is widely used to study electronic properties of solids. The momentum and energy distribution of photoelectrons reflect theelectronic ground state and are well understood based on
theoretically derived electronic ground-state con-
figurations and delocalized photoemission states.
However, as demonstrated here, the dynamics of
the photoemission process is not correctly captured
in common models of solid-state photoemission.
In the very initial stage of the photoemission pro-
cess, the excited-state dynamics is governed by the
local environment, i.e., the inner configuration of
the atom. This gives rise to an angular momentum–
dependent delay that is enhanced by intra-atomic
interactions (top left of Fig. 1 and supplementary
materials section 2.1). These effects are well
established for the photoemission from atoms
(1–4) but are neglected in models of solid-state
photoemission. Realistic modeling of photoelectron
kinematics and photoemission delays thus requires
a revision of these models, i.e., both intra-atomic
delays and propagation effects must be considered
(Fig. 1, top).
The reported results are based on attosecond
time-resolved photoemission spectroscopy using
the streaking approach (5). As depicted in Fig. 1,
the photoelectron excited by an attosecond extreme ultraviolet (EUV) pulse is exposed to an
infrared (IR) streaking field. The delay tIR – tEUV
between the IR and EUV pulses and the photoemission delay, i.e., the time until the photoelectron leaves the solid and feels the streaking
field, determine the streaking signal (5), and the
streaking spectrogram yields delay differences
between the various emission channels. WSe2
is chosen as the substrate because the photoemission spectrum for the EUV photon energy
(Fig. 2A) is dominated by four emission channels
with different initial-state characteristics: a valence
band (VB) emission (Ekin = 87.0 eV) and photoemission from the Se 4s, W 4f, and Se 3d core levels
at Ekin = 73.5 eV, Ekin = 54.2 eV, and Ekin = 32.2 eV
(6), respectively. WSe2 (Fig. 1) allows in situ cleaving
and yields rather inert surfaces. Its layered structure helps identify the depth from which a particular photoelectron is emitted. Together with
the minimization of systematic errors induced by
the chirp of the EUV pulse (<0.01 fs2) and magnetic fields (<1 mT) to less than 2 as, this
procedure allows us to determine the relative
photoemission delays with 10-as resolution.
From fitting the background-corrected spectra
recorded for different delay tIR – tEUV, the delay-dependent energy positions of four spectral components were determined (Fig. 2B). Simultaneous
fitting (continuous lines in the overlay in Fig. 2B)
of these streaking curves yields the photoemission
delays Dt and the corresponding relative photoemission delays DtVB–Se4s, DtSe3d–Se4s, and
1Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25,
33615 Bielefeld, Germany. 2Institut für Solare Brennstoffe,
Helmholtz-Zentrum Berlin für Materialien und Energie GmbH,
Hahn-Meitner-Platz 1, 14109 Berlin, Germany. 3University of
the Basque Country, 20080 San Sebastián, Spain. 4Donostia
International Physics Center, 20018 San Sebastián, Spain.
5IKERBASQUE, Basque Foundation for Science, 48013 Bilbao,
Spain. 6Skobeltsyn Institute of Nuclear Physics, Lomonosov
Moscow State University, Moscow 119991, Russia. 7European
XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany.
8Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena,
Germany. 9Centro de Física de Materiales CFM/MPC
(CSIC-UPV/EHU), 20018 San Sebastián, Spain.
*Present address: Max Born Institute for Nonlinear Optics and
Short Pulse Spectroscopy in the Forschungsverbund Berlin e.V.,
Max-Born-Straße 2 A, 12489 Berlin, Germany. †Corresponding
author. Email: email@example.com