Ultrafast Electron-Phonon Decoupling in Graphite

Abstract

We report the ultrafast dynamics of the 47.4 THz coherent phonons of graphite interacting with a photoinduced non-equilibrium electron-hole plasma. Unlike conventional materials, upon photoexcitation the phonon frequency of graphite upshifts, and within a few picoseconds relaxes to the stationary value. Our first-principles density functional calculations demonstrate that the phonon stiffening stems from the light-induced decoupling of the non-adiabatic electron-phonon interaction by creating the non-equilibrium electron-hole plasma. Time-resolved vibrational spectroscopy provides a window on the ultrafast non-equilibrium electron dynamics.

Full text

arXiv:0712.1879v1 [cond-mat.other] 12 Dec 2007
arXiv/cond-mat
Ultrafast Electron-Phonon Decoupling in Graphite
Kunie Ishioka,
∗
Muneaki Hase,
†
and Masahiro Kitajima
Advanced Nano-Characterization Center,
National Institute for Materials Sci ence, Tsukuba, 305-0047 Japan
Ludger Wirtz
Institute for Electronics , Microelectronics,
and Nanotechno l ogy, 59652 Villeneuve d’Ascq Cedex , France
Angel Rubio
European Theoretical Spectrosco py Facility, Universidad del Pa´ıs Vasco,
Centro Mixto CSIC-UPV/EHU and DIPC,
Edificio Korta, Avd. Tolosa 72, 20018 Donostia, Spain
Hrvoje Petek
Department of Physics and Astronomy,
University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
(Dated: February 2, 2008)
Abstract
We report the ultrafast dynamics of the 47.4 THz coherent phonons of graphite interacting with
a photoinduced non-equilibrium electron-hole plasma. Unlike conventional materials, upon pho-
toexcitation the phonon frequency of graphite upshifts, and within a few picoseconds relaxes to the
stationary value. Our first-principles density functional calculations demonstrate that th e phonon
stiffening stems from the light-ind uced decoupling of the non-adiabatic electron-phonon interac-
tion by creating the non-equilibrium electron-hole plasma. Time-resolved vibrational spectroscopy
provides a window on the ultrafast non-equilibrium electron dyn amics.
PACS numbers: 78.47.+p, 63.20.-Kr, 71.15.Mb, 81.05.Uw
∗
Electronic address: ishioka.kunie@nims.go.jp
†
Present address: Institute of Applied Physics, University of Tsukuba
1

Graphite possesses highly a nisotropic crystal structure, with strong covalent bonding of
atoms within and weak van der Waals bonding between the hexagonal symmetry graphene
sheets. The layered lattice structure translates to a quasi-2D electronic structure, in which
the electronic bands disperse linearly near the Fermi level (E
F
) and form point-like Fermi
surfaces. The discovery of massless relativistic behavior of quasiparticles at E
F
of graphene
and graphite has aroused great interest in the nature of carrier transport in these materials
[1, 2, 3]. Because of t he linear dispersion of the electronic bands, the quasiparticle mass
associated with t he charge carrier interaction with the periodic crystalline lattice nearly
vanishes, leading to extremely high electron mobilities and unusual half-integer quantum
Hall effect in graphene [1, 2]. Since graphite has a quasi-2D band structure very similar to
that of graphene, t hese electronic properties may be expressed also in graphite.
The electron-phonon (e-p) interaction contributes to the carrier mass near E
F
and limits
the high-field transport through the carrier scattering. The strong e-p interaction in graphite
is a distinctive characteristic of ineffective screening of the Coulomb interaction in semimetals
[4, 5]. It is expressed in the phonon frequency shift by carrier doping [6], electron scattering-
mediated vibrational spectrum [7] and strong electronic renormalization of the phonon bands
(Kohn anomalies) [8 ]. Time-resolved measurements on the optically generated non-t hermal
electron-hole (e-h) plasma in gra phite provide evidence for the carrier thermalization within
0.5 ps bo t h through electron-electron (e-e) scattering and optical phonon emission [9]. The
non-thermal carriers decay non-uniformly in phase space because of the anisotropic band
structure of graphite [5, 10]. Quasiparticle correlations in non-thermal plasmas can also
be probed from the p erspective of the coherent optical phonons. In t he present study we
probe the transient changes in the e-p coupling induced by the optical perturbation of the
non-adiabatic Ko hn anomaly through the time-dependent complex self-energy (frequency
and lifetime) of the 47 THz E
2g2
phonon of graphite.
To probe the ultraf ast response of the coherent phonons we perform transient a nisotropic
reflectivity measurements [11, 12] o n a natural single crystal and highly oriented pyrolytic
graphite (HOPG) samples. HOPG has long range order along the c-axis, but each layer
consists of µm-size domains with random azimuthal orientatio n. Because the phonon prop-
erties were identical, we repor t the results for HOPG only, whose better surface optical
quality gave superior signal-to-noise ratio. The light source for the pump-probe reflectivity
measurements is a Ti:sapphire femtosecond laser oscillator with <10 fs pulse duration. The
2

543210
time delay (ps)
∆
R
eo
/R
0.80.60.40.20.0
a
FT amplitude
605040302010
Hz
E
2g2
E
2g1
b
-10x10
-6
-5
0
5
10
Phonon amplitude
18013590450
pump polarization (degree)
E2g1
E2g2
T
FIG. 1: (Color online) (a) Anisotropic reflectivity change ∆R
eo
/R = (∆R
y
− ∆R
x
)/R at pump
power of 50 mW. The inset shows an enlargement of the trace to show the high-frequency mod -
ulation. (b) FT spectrum of the time-domain trace in (a). Inset shows the pump polarization
dependence of the amplitud es of the two coherent phonons (A
1
and A
2
) obtained from isotropic
reflectivity (∆R/R) measurement. The polarization angle is measured from the plane of incidence.
The probe beam is polarized at 90
◦
. Solid and broken curves are fits to cos 2θ function.
fundamental output is frequency-doubled in a β-barium borate crystal to obtain 395 nm
excitation light. The 3.14 eV photons excite vertical transitions from the valence (π) to
the conduction (π
∗
) bands near the K point [13]. A spherical mirror brings parallel linearly
polarized pump and probe beams to a common 10 m focus on the sample with angles of 20
◦
and 5◦ from the surface normal, respectively. Pump power is varied between 5 and 50 mW
(pulse fluence of 0.1 - 1mJ/cm
2
), while probe power is kept at 2 mW. Isotropic reflectivity
change (∆R) gives a straightforward polarization dependence, while anisotropic reflectivity
change (∆R
eo
= ∆R
s
− ∆R
p
) eliminates the mostly isotropic electronic r esponse to isloate
the much weaker anisotropic contribution, which is dominated by the coherent phonon re-
sponse [11]. Time delay t between the pump and probe pulses is modulated at 20 Hz to
enable accumulation and averaging of up to 25,000 scans with a digital oscilloscope. The
delay scale is calibrated with recording the interference fringes of a He-Ne laser [12].
Figure 1a shows the anisotropic reflectivity change of graphite, ∆R
eo
/R, normalized
to the reflectivity without pump pulse. After a fast and intense electronic response at
t=0, the reflectivity is modulated at two disparate periods of 21 and 770 fs. The slower
coherent oscillation was previously assigned to the Raman active interlayer shear phonon
(E
2g1
mode) [14]. The faster oscillation of 47.4 THz or 1580 cm
−1
is the in- plane E
2g2
3

L
A
K
M
H
H'
K'
Γ
1.0
0.9
0.8
0.7
Dephasing rate (ps
-1
)
1.00.80.60.40.20.0
Laser fluence (mJ/cm
2
)
47.55
47.50
47.45
47.40
Frequency (THz)
FIG. 2: (Color online) Laser fluence dependence of the dephasing rate Γ
2
and the frequency ω
2
of the coherent E
2g2
phonon obtained from a fit to an exponentially damped oscillator function .
The lines are to guide the eye. Inset shows the Brillouin zone of graph ite.
carbon stretching mode [6] corresp onding to the G-peak in the Raman spectra of graphitic
materials. After decay of the electronic response, the reflectivity signal for t >100 fs can
be fitted approximately to a sum of damped oscillations: f(t) = A
1
exp(−Γ
1
t) sin(2πω
1
t +
δ
1
) + A
2
exp(−Γ
2
t) sin(2πω
2
t + δ
2
). The amplitudes of both phonons, A
1
and A
2
, exhibit
a cos 2θ dependence on the pump polarization angle θ with respect to the optical plane, as
shown in t he inset of Fig. 1b, confirming their generation through the Raman mechanism
[14]. Hereafter we focus on the previously unobserved dynamics of the fast E
2g2
phonon.
We measure the laser fluence dependence of the coherent phonon amplitude A
2
, dephasing
rate Γ
2
, and frequency ω
2
of the E
2g2
phonon that ar e extracted from the fit of ∆R
eo
/R to
the damped oscillator model. The amplitude increases linearly with the fluence as expected
for a π−π
∗
transition with a single photon. As shown in Fig. 2, the dephasing rate decreases
as the laser fluence is increased, which is contrary to the coherent phonon response observed
for ot her materials [15 , 16, 17]. The f r equency upshift at higher fluence in Fig. 2 is equally
exceptional. Laser heating can be excluded as the origin, because the E
2g2
frequency down-
shifts with temperature [18]. In fact, the frequency upshift under intense optical excitation
has not been o bserved experimentally or predicted theoretically for graphite or any other
solid.
To f urther cha racterize the unexpected frequency upshift, in Fig. 3 we analyze the tran-
sient reflectivity response with a time-windowed Fourier transform (FT). This analysis re-
4

47.7
47.6
47.5
47.4
47.3
Frequency (THz)
43210
Delay time (ps)
1 mJ/cm
2
0.6 mJ/cm
2
0.2 mJ/cm
2
Raman frequency 47.36 THz
FIG. 3: (Color online) Time evolution of the E
2g2
phonon frequency, obtained from time-windowed
FT, for different laser fluences. The widths of the Gaussian time windows are 80 fs for t < 0.4 ps,
300 fs for 0.4 < t < 2 ps, and 800 fs for t ≥2 ps.
veals that the phonon frequency blue-shift occurs promptly (its dynamics are obscured by
the strong electronic response for delays of <100 fs), and recovers to its near-equilibrium
value after several picoseconds. With increasing laser fluence the initial blue-shift increases,
while the asymptotic value converges on the 47.4 THz Raman frequency. The experimen-
tal phonon frequency for t >100 fs follows a biexponential recovery, ω(t) − ω(t = ∞) =
∆ω
1
exp(−t/τ
1
) + ∆ω
2
exp(−t/τ
2
), with time constants of τ
1
=210 fs and τ
2
=2.1 ps, inde-
pendent of excitation density. The time scales for the recovery are in reasonable agreement
with the analysis of transient terahertz spectroscopy, which gave 0.4 and 4 ps, respectively
for the carrier thermalization and carrier-lattice equilibration [9]. The time evolution of
the E
2g2
frequency implicates the interaction of coherent phonons with the photoexcited
non-equilibrium carriers, as will be discussed below.
It is only recently that the observed anomalous dispersion of the high-energy phonon
branches of graphite [19] could be explained theoretically by a momentum dependent e-p
interaction (a Kohn anomaly), which leads to the renormalization (softening) of the phonon
frequency [8]. Sta ndard use of the adiabatic approximation in the previous study, however,
predicted that perturbing the electronic system by electron doping would result in a down-
shift of phonons at the Γ point. Recent experiments and theoretical calculations have shown
this approach to be inappropriate as the “non-adiabatic” electronic effects, where electrons
near E
F
cannot respond instantaneously to the lattice distortion, become important for low
5

dimensional materials such as graphene and nanotubes [20, 21, 22].
We perform density functional theory (DF T) calculations for a single sheet o f photoex-
cited graphite with a new computational method that accounts fo r the non-adiabatic effects.
We use DFT in the local-density approximation (LDA) as implemented in the code ABINIT
[23]. Core electrons are described by Trouiller-Martins pseudopotentials and the wave-
functions are expanded in plane waves with energy cutoff at 35 Hartree. Fo r the present
work the specific form of the exchange-correlation f unctional (LDA or GGA) does not change
the emerging physical picture. For reasons of computational feasibility, we have performed
calculations on single-layer gra phene, as it is often done for the description of the optical
phonons of graphite [19, 24]. In order to ensure convergence of the E
2g2
phonon mode to
within 0.01 THz, we use a large 61×61 two-dimensional k-point sampling. The phonons
are computed using density-functional perturbation theory [25]. “Non-adiabatic effects” are
accounted for by keeping the electronic population fixed when computing the dynamical
matrix. This means that the occupation of each electronic level is specified in the input of
the calculation and is kept constant upon the displacement of the atoms. We neglect t he
effects of lattice relaxation on the phonon frequency since we checked that the effect of neu-
tral excitation on the bond- length is very weak (< 0.001
˚
A) for the a ppropriate excitation
densities. Our approach is similar to the time-dependent perturbation scheme [20, 21, 22]
for the inclusion of non-adiabaticity in the combined treatment of phonons and electrons in
graphite. Furthermore, it enables us t o calculate the effect of an arbitrary electron occupa-
tion far from equilibrium such as created by the vertical excitation of e-h pairs with 3.1 eV
photons.
Because t he photoexcited electron distribution is time-dependent and, in principle, not
known exactly, we employ three different limiting distributions. “As excited” distribution
(AED), correspondiing to the vertical excitation of e-h pairs with 3.1 eV photons within
an energy window of ±0.2 eV, simulates the distribution right after excitation with a laser
pulse having a finite spectral width. The laser fluence determines the amount of charge
transferred from π to π
∗
bands. Non-thermal distribution (NTD), in which electrons are
completely depopulated in an small energy window f r om top of the valence band to the
bottom of conduction band, mimics the e-h distribution after the ultrafast (≪100 fs [10, 26])
decay of the primary excitation into the secondary e-h pairs a r ound E
F
. The width of
the energy window is determined by the excited charge density. Hot thermal distribution
6

3.1eV
AED
E
F
TD
E
NTD
B
C
A
D
Electronic temperature for TD (K)
315
2210
3150 4630
1.0
0.8
0.6
0.4
0.2
0.0
E
2g2
frequency shift (THz)
0.0150.0100.0050.000
Excited charge (electrons/atom)
FIG. 4: (Color online) Calculated E
2g2
frequency change as a function of the excitation charge
density for the as-excited distribution (AED; square), hot non-thermal distribution (NTD; trian-
gle), thermal distribution (TD; filled circle), and ionized distribution (ID; open circle). The top
axis shows the corresponding electronic temperature T
e
for TD. Arrows show schematically the
excitation and relaxation pathways for the e − h distribution: quasi-instantaneous excitation by a
laser pu lse (A), de-excitation within <100 fs through the creation of secondary e-h pairs around the
Fermi level E
F
(B), thermalization of the e-h plasma in ∼0.2 ps (C), and cooling down of the e-h
plasma in ∼2 ps through optical phonon emission (D). Ultrafast phonon stiffening is ascribed to
steps A and B. The highest density excitation (fluence of 1 mJ/cm
2
) in our exp eriment corresponds
to 5.8×10
20
electron-hole pairs/cm
3
or 0.005 electrons/atom.
(TD), in which the occupation follows the Fermi-Dirac distribution with a high electronic
temperature, simulates the distribution after thermalization of the electronic system (&0.5
ps [9]). To compare with the effect of static doping reported previously [20, 21, 22], we also
present calculations with an ionized distribution (ID), in which electrons are removed from
the to p of the π band.
Figure 4 shows tha t all the three excited state distributions, as well as the statically doped
one, lead to a stiffening of the E
2g2
phonon. For a fixed density of the excited charge, the
closer the e-h pairs are to the E
F
, the more pronounced is their non-a diabatic interaction
with the lattice, and therefore, the stronger is their effect on the phonon stiffening. We
note that the stiffening is not accompanied by lattice deformation for the three excited
distributions, contrary to the case of ID, for which the lattice both stiffens and contracts.
7

The lattice stiffening fo r ID can be attributed to the depopulation of orbitals around the K
and H points, which (i) suppresses the non-adiabaticity in the e- p coupling a nd (ii) removes
electrons with strong anti-bo nding admixture [20, 21]. Because the effect (ii) should also
lead to a lattice contraction, the C-C bond stiffening under the three excited distributions
is attributed to the effect (i). This implies that the stiffening is causedd by transfer cold
electrons and holes from near the E
F
to a hot population, which increases the ability of
the electronic system to follow the ions adiabatically. In contrast to the static doping
studies [20, 21], our observations on a neutral but non-equilibrium system address a phonon
frequency shift solely of the electronic origin.
The strong dependence of the phonon stiffening on the e-h distribution in Fig. 4 justifies
interpretation of the experimental ultrafast phonon frequency changes in terms of the tem-
poral evolution of the photoexcited e-h plasma. The photoexcitation of carriers weakens the
non-adiabatic e-p coupling. The reduced real part (frequency) and the increased imaginary
part (decay rate) of the self-energy of e-p interaction increases the frequency and reduces
the dephasing rate of the E
2g2
mode. The f r equency r ecovers biexponentially on the time
scales of electron thermalization and energy transfer to the lattice. Thus, we conclude that
the experimentally observed time evolution of the phonon frequency is governed by the r e-
laxation processes of the highly non-thermal electronic population created at t=0 near the
K-point (arrow A in Fig. 4). The very efficient e - e scattering first brings the no n-thermal
e-h carriers close to the Fermi level (near K point) within a few tens of fs (arrow B), and
then to electronic-thermalization in about 0.2 ps ( arrow C). This hot- thermal distribution
equilibrates with the lattice through optical phonon emission on 2 ps time scale (arrow D).
In summary, we have explored the influence of the non-equilibrium e-h plasma on the fem-
tosecond dynamics of the in-plane E
2g2
coherent phonon of g r aphite. The time-dependent
phonon frequency probes sensitively the time evolution of the transient electronic occupa-
tion distributions. The unusual electronic stiffening of the phonon can be attributed to the
excitation-induced reduction of the e-p coupling due to quasi-2D electronic structure. Our
results offer a new par adigm of e- p coupling, where non-equilibrium electrons impart excep-
tional properties to the lattice. Similar interactions are likely to govern the e-p coupling
in related graphitic materials, such as carbon nanotubes and graphene, that are o f topical
interest for high-performance, nanometer scale carbon-based electronic devices.
The authors thank O.V. Misochko for supplying single crystal graphite. Calculations are
8

performed at IDRIS (project 061 827), Ba r celona Supercomputing Center and UPV/EHU
(SGIker Arina). This work is supported by Kakenhi-18340093, the EU Network of Excel-
lence Nanoquanta (NMP4-CT-2004-500198), Spanish MEC (FIS2007- 65702-C02-01), French
ANR, EU projects SANES (NMP4-CT-2006-017310), DNANANODEVICES (IST-2006-
029192), and the NSF CHE-0650756. H.P. thanks Donostia International Physics Center
and Ikerbasque for support during the writing of this manuscript.
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