G–E2gphonons would not be visible above the
hot-electron background in our experiment.
In this work, we have shown a proof-of-
principle extraction of the mode-projected
e-ph matrix elementhg^2 A′ 1 iin graphite. We
remark thathg^2 iis a fundamental quantity,
defined as the momentum average of the
change in the electronic Hamiltonian in
response to the ionic displacements of a
phonon (eq. S13). In particular,hg^2 iis in-
dependentofdopingandspecifiedfora
well-defined set of initial and final electronic
states and a well-defined bosonic mode (in
this case, theA′ 1 optical phonon with mo-
mentum K in graphite). Nonetheless, it is
instructive to estimate the EPC constant
l¼ 2 hg^2 iDðEFÞ=ðℏWÞfor comparison with
other approaches ( 7 ). Commonly seen in re-
lation to the critical temperature in supercon-
ductivity, the quantitylis doping-dependent
and integrated over all bosonic and electronic
degrees of freedom. Therefore, caution must
be applied in comparing the two quantities.
In pristine and low-doping graphene or
graphite systems, the vanishing DOS at the
Dirac point of graphene (crossing point of
graphite) makes extraction oflvery diffi-
cult, with reported values ranging from 4 ×
10 −^4 to 1.1 ( 20 , 47 , 59 – 63 ), while DFT predicts
l< 0.05 ( 17 ). Even forgoing doping depen-
dence, the large range of reportedlvalues
clearly illustrates the difficulty ARPES has in
extracting the EPC of this particular system.
In this work, we extracthg^2 A′ 1 ifor the DTP state
at 0.6 eV, corresponding to a value of the
mode-projected EPClA′ 1 ¼ 0 : 0182 T 0 :004.
This value characterizes a system where the
Fermi level is doped up to 0.6 eV above the
crossing point (the value at zero doping would
belA′ 1 ¼ 0 : 006 T 0 :001). We would ideally com-
pare this value with that extracted by kink
analysis in graphite, but the strong curvature
of the bare-band dispersion ( 61 )andthelack
of studies at comparable doping make this
particularly challenging. Thus, we instead com-
pare this value to what is reported in ( 20 ), a
doping-dependent study oflin graphene that
is additionally supported by DFT calculations
( 17 ). When the system is doped such that the
Dirac point is 0.6 eV belowEF(corresponding
to a carrier density ofn≈4×10^13 cm−^2 ), then
l≈0.035 is extracted. From this, we see that
lA′ 1 ≈l=2, which is consistent with the fact that
lA′ 1 captures only one of two strongly coupled
modes in the system (the other beingE2g),
whereaslas extracted from kink analysis is
integrated over all modes. Together, these re-
sults suggest that time-domain measurements
have the ability to access the EPC in a precise,
sensitive, and mode-projected way.
In principle, this technique is applicable to
materials in which electrons are sufficiently
strongly coupled to one or a few bosonic modes,
such that distinct boson-induced replicas can
be observed. Beyond graphite and graphene,
quasi-2D materials such as transition-metal
dichalcogenides feature gapped bands at the
KandK′points, with further restrictions of
the phase space for scattering stemming from
valley degrees of freedom, and would be ideal
candidates for similar TR-ARPES studies. In
addition, conventional and unconventional
superconductors, such as MgB 2 or cuprate- or
Fe-based superconductors, respectively, fa-
mously feature strong coupling to bosonic
modes, which may drive electronic renorm-
alizations (kinks). By monitoring quantized
decay processes across the full BZ, this non-
equilibrium technique will offer a distinct
approach for studying the microscopic origin
and momentum dependence of electron-boson
coupling and its role in the emergence of
superconductivity.
These results also prove that a fresh an-
alytical perspective can be achieved in TR-
ARPES by taking advantage of femtosecond
sources that combine high photon energy (to
access large electronic momenta) with high-
energy resolution (to resolve the low-energy
quasiparticle dynamics). With the develop-
ment of tunable pumps, polarization control
for pump and probe, and bandwidth control
to balance the trade-off between energy and
time resolution, a growing versatility will be
available for TR-ARPES experiments. By mon-
itoring the population of electrons injected into
momentum- and energy-selected states by di-
rect optical excitation, it would be possible to
formulate a series of studies on empty state
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ACKNOWLEDGMENTS
We gratefully acknowledge M. Berciu, G. A. Sawatzky, A. Nocera,
Z. Ye, and D. Manske for critical reading of the manuscript and
useful discussions, as well as C. Gutierréz for guidance on figure
presentation.Funding:This research was undertaken thanks in
part to funding from the Max Planck-UBC-UTokyo Centre for
Quantum Materials and the Canada First Research Excellence
Fund, Quantum Materials and Future Technologies Program.
This project is funded in part by the Gordon and Betty Moore
Foundation’s EPiQS Initiative, Grant GBMF4779 to A.D. and D.J.J.;
the Killam, Alfred P. Sloan, and Natural Sciences and Engineering
Research Council of Canada’s (NSERC’s) Steacie Memorial
Fellowships (A.D.); the Alexander von Humboldt Fellowship (A.D.);
the Canada Research Chairs Program (A.D.); NSERC, Canada
Foundation for Innovation (CFI); British Columbia Knowledge
Development Fund (BCKDF); and the CIFAR Quantum Materials
Program. E.R. acknowledges support from the Swiss National
Science Foundation (SNSF) grant P300P2_164649. A.F.K.
acknowledges support by the National Science Foundation under
grant DMR-1752713. B.N. and T.P.D. acknowledge funding from
the Department of Energy, Basic Energy Sciences, Division of
Materials Science.Author contributions:This study was
conceived of by M.X.N., A.K.M., F.B., M.M., D.J.J., and A.D.; and
Naet al.,Science 366 , 1231–1236 (2019) 6 December 2019 5of6
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