RAPID COMMUNICATIONS
PHYSICAL REVIEW B 88, 081401(R) (2013)
Anisotropic Eliashberg function and electron-phonon coupling in doped graphene
D. Haberer,
1,2
L. Petaccia,
3
A. V. Fedorov,
1,4
C. S. Praveen,
5
S. Fabris,
5
S. Piccinin,
5
O. Vilkov,
4,6
D. V. Vyalikh,
4,6
A. Preobrajenski,
7
N. I. Verbitskiy,
8,9
H. Shiozawa,
8
J. Fink,
1
M. Knupfer,
1
B. B¨ uchner,
1
and A. Gr ¨ uneis
1,8
1
IFW Dresden, P. O. Box 270116, D-01171 Dresden, Germany
2
Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
3
Elettra Sincrotrone Trieste, Strada Statale 14 km 163.5, I-34149 Trieste, Italy
4
St. Petersburg State University, 198504 St. Petersburg, Russia
5
CNR-IOM DEMOCRITOS Theory@Elettra Group and SISSA, via Bonomea 265, I-34136 Trieste, Italy
6
Institut f ¨ ur Festk¨ orperphysik, TU Dresden, Mommsenstrasse 13, D-01069 Dresden, Germany
7
MAX-IV Laboratory, Lund University, Box 118, S-22100 Lund, Sweden
8
Faculty of Physics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria
9
Department of Materials Science, Moscow State University, Leninskiye Gory 1/3, 119992 Moscow, Russia
(Received 26 April 2013; published 6 August 2013)
We investigate, with high-resolution angle-resolved photoemission spectroscopy, the spectral function of
potassium-doped quasi-free-standing graphene on Au. Angle-dependent x-ray photoemission and density
functional theory calculations demonstrate that potassium intercalates into the graphene/Au interface, leading
to an upshift of the K-derived electronic band above the Fermi level. This empty band is what makes this
system perfectly suited to disentangle the contributions to electron-phonon coupling coming from the π band
and K-derived bands. From a self-energy analysis we find an anisotropic electron-phonon coupling strength
λ of 0.1 (0.2) for the KŴ (KM) high-symmetry directions in momentum space, respectively. Interestingly, the
high-energy part of the Eliashberg function which relates to graphene’s optical phonons is equal in both directions
but only in KM does an additional low-energy part appear.
DOI: 10.1103/PhysRevB.88.081401 PACS number(s): 73.22.Pr, 63.22.Rc, 71.20.Gj, 79.60.−i
Superconductivity with remarkable transition temperatures
in graphene-related systems has been reported so far for
graphite intercalation compounds (GICs),
1–3
boron-doped
diamond,
4,5
carbon nanotubes,
6–8
and doped C
60
fullerene
crystals.
9–11
However, despite all the outstanding properties
inherent to graphene
12,13
and theoretical suggestions for
superconductivity therein,
14–16
an experimental observation
of superconductivity in monolayer graphene remains suspi-
ciously absent. In the closely related GICs, it is generally
accepted that electron-phonon coupling (EPC) is the most
likely origin for superconductivity.
17–22
It can be mediated by
a coupling of interlayer states or π
∗
states to soft intercalant
or graphene phonon modes.
17–19,23
A strong isotope effect
which was reported for CaC
6
highlights the importance of the
intercalant modes for superconductivity.
24
The other impor-
tant contribution to EPC originates from the carbon-derived
high-energy in-plane phonon modes.
21,22,25
From an angle-
resolved photoemission spectroscopy (ARPES) experiment an
approximation to determine the EPC constant λ is to extract
the complex self-energy =
′
+ i
′′
from the measured
spectral function. The slope d
′
/dE at the Fermi level is then
equal to λ. However, this approach critically depends on data
quality as well as the analysis procedure and has led to various
results in the case of graphene.
26–30
From previous ARPES
measurements it was reported for GICs
21,22,26
and for doped
graphene on SiC (Ref. 26) that the EPC is anisotropic around
the Dirac cone, in contradiction with calculations carried
out for unsupported graphene,
31,32
which have suggested an
isotropic coupling to Ŵ and K point phonons around the
Dirac cone. Other ARPES experiments conducted on doped
graphene on metal substrates led to an isotropic EPC.
28
The
underlying and fundamental quantity which governs EPC is
the Eliashberg function α
2
F (ω,ǫ,k), which is equal to the
transition probability from and to a photohole state (ǫ,k) via
coupling to a phonon mode ω.
33
The integral over ω gives the
total EPC constant λ according to
λ = 2
∞
0
α
2
F (ω)
ω
dω. (1)
In all the previous experiments, only the total λ has been
determined while the constituting phonon modes, i.e., α
2
F (ω),
remained hidden in the data. However, knowledge of the
complete momentum-dependent Eliashberg function is key
to understanding the reasons for a possible asymmetry and
to disentangle graphene and dopant induced contributions to
EPC. It has been shown by Plummer et al. that the Eliashberg
function of a material can be extracted from ARPES data.
34,35
This procedure, however, is complicated by the effects of
electron-electron interactions
36
and the presence of multiple
non-carbon-related electronic states which modify the value of
λ.
15,19
It has been shown previously that on a metal substrate,
electron-electron interactions in graphene are well screened by
the substrate,
29
but for the second problem no solutions exist
to date.
Here we provide a workaround to this problem by perform-
ing ARPES on a graphene/K/Au sandwich structure. In this
system we find that the close interaction of K with Au fully
ionizes K and upshifts the K 4s -derived band above E
F
, which
prevents phonon scattering to this band. Thus it is possible
to analyze the contributions of graphene-related electronic π
bands alone and to investigate the isotropy of λ around the
Dirac cone.
Graphene intercalated with one monolayer of Au was
prepared in situ under ultrahigh vacuum conditions with
chemical vapor deposition on Ni(111).
37–39
We evaporated
081401-1 1098-0121/2013/88(8)/081401(5) ©2013 American Physical Society