Temperature Dependence of Electric Transport in Few-layer Graphene under Large Charge Doping Induced by Electrochemical Gating

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Abstract The temperature dependence of electric transport properties of single-layer and few-layer graphene at large charge doping is of great interest both for the study of the scattering processes dominating the conductivity at different temperatures and in view of the theoretically predicted possibility to reach the superconducting state in such extreme conditions. Here we present the results obtained in 3-, 4- and 5-layer graphene devices down to 3.5 K, where a large surface charge density up to about 6.8·10 14 cm −2 has been reached by employing a novel polymer electrolyte solution for the electrochemical gating. In contrast with recent results obtained in single-layer graphene, the temperature dependence of the sheet resistance between 20 K and 280 K shows a low-temperature dominance of a T 2 component – that can be associated with electron-electron scattering – and, at about 100 K, a crossover to the classic electron-phonon regime. Unexpectedly, this crossover does not show any dependence on the induced charge density, i.e. on the large tuning of the Fermi energy.

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SUBJECT AREAS:

GRAPHENE

NANOSCIENCE AND

TECHNOLOGY

ELECTRONIC PROPERTIES AND

MATERIALS

Received
30 November 2014

Accepted
26 February 2015

Published

23  April 2015

Correspondence and

requests for materials

should be addressed to

[R.S.G. (renato.](mailto:renato.gonnelli@polito.it)

[gonnelli@polito.it)](mailto:renato.gonnelli@polito.it)

- Current address:

Max Planck Institute for

Solid State Research,

Stuttgart, Germany.

{ Current address:

Istituto Nazionale di

Ricerca Metrologica

(INRIM), Torino,

10135 Torino.

{ Current address:

Nokia Technologies,

Cambridge, CB3 0FA,

United Kingdom.

## Temperature Dependence of Electric Transport in Few-layer Graphene under Large Charge Doping Induced by Electrochemical Gating

R. S. Gonnelli 1, F. Paolucci 1 *, E. Piatti 1, Kanudha Sharda 1, A. Sola 1 {, M. Tortello 1, Jijeesh R. Nair 1,
C. Gerbaldi 1, M. Bruna 2 { & S. Borini 2 {

1Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, 10129 Torino, Italy, 2Istituto Nazionale di Ricerca
Metrologica (INRIM), Torino, 10135 Torino.

The temperature dependence of electric transport properties of single-layer and few-layer graphene at large
charge doping is of great interest both for the study of the scattering processes dominating the conductivity
at different temperatures and in view of the theoretically predicted possibility to reach the superconducting
state in such extreme conditions. Here we present the results obtained in 3-, 4- and 5-layer graphene devices
down to 3.5 K, where a large surface charge density up to about 6.8?10 14 cm 22 has been reached by
employing a novel polymer electrolyte solution for the electrochemical gating. In contrast with recent results
obtained in single-layer graphene, the temperature dependence of the sheet resistance between 20 K and
280 K shows a low-temperature dominance of a T 2 component – that can be associated with
electron-electron scattering – and, at about 100 K, a crossover to the classic electron-phonon regime.
Unexpectedly, this crossover does not show any dependence on the induced charge density, i.e. on the large
tuning of the Fermi energy.

he electric transport properties of single-layer graphene (SLG) have been the subject of a very extensive
experimental and theoretical research activity in the past ten years after the breakthrough discovery of the
possibility to isolate and characterize this 2D material 1,2 . A comprehensive review paper covering the first six
# T
years of this activity can be found in literature 3, while some additional information is also present in Ref. 4.
Although the transport properties of multi-layer graphene have been experimentally studied 5,6, the electric
transport of few-layer graphene (FLG, with number of layers N between 2 and 5) has been much less intensively
investigated 7 . This is particularly true when one considers the low-temperature behavior of these transport
properties. On the other hand, this information can provide important clues on the scattering processes dominating the conductivity of FLG and on the quantum corrections to the Drude conductivity which may occur at
low temperature 3,4 . Moreover, the possibility to strongly change the number of charge carriers by doping the FLG
above the limits of the standard solid-dielectric backgate technique 1,2,8,9 adds an additional degree of freedom to
the study of the electron scattering in these materials. But, in our opinion, there is another important reason for
performing low-temperature high-doping transport experiments in FLG, related to the theoretically predicted
possibility of the appearance of a superconducting state in highly-doped or metal (K, Li) decorated SLG 10–16 or in
hole-doped graphane 17, which is a reversibly idrogenated graphene 18 . In particular, a conventional BCS phononmediated superconductivity at about 8 K has been predicted in Li-covered SLG 13 with a Tc that can increase up to
17–18 K in case of lithium coverage on both sides of graphene 13 or up to 13.5 K in case of a C6-Li-C6-Li layered
structure 14 . Another proposed route for the possible obtainment of an unconventional chiral superconductivity in
graphene 15 or a more conventional two-gap BCS superconductivity with Tc up to about 13 K 16 relies on a very
strong (n-)doping of SLG. Due to the very large interest in the possible applications of graphene in electronics, the
observation of superconductivity (even at low T) in this material would obviously lead to new nanoscale device
concepts or to the performance improvement of the existing ones.

Independently of the different approaches and the different results, in all the mentioned papers the key
ingredients for the obtainment of superconductivity appear to be: i) a large increase of the carrier density, able
to shift the Fermi level far from the Dirac point and close to a Van-Hove singularity (VHS); ii) the presence of a

parabolic interlayer-like band that is produced by the deposited
metal adatoms 10,13,14 or by the large doping itself 12,15,16 . We believe
that both these ingredients could be also present in the few-layer
graphene stacks at a very high level of induced charge density.

Interestingly, double multi-layer graphene structures separated by
an insulator have been proposed to realize strong-coupling electronhole superfluidity (leading to counter flow superconductivity) 19 . In
addition, VHSs in double 3- and 4-layer graphene devices have been
exploited to enhance critical temperature and onset density of the
electron-hole superfluid transition 20 .

For this reason, even in absence of precise model predictions for
superconductivity in FLG, we thought it was worthwhile to perform
electric transport measurements in FLG at low temperature and high
doping.

In the past few years the possibility to dope various materials at an
unprecedented level of surface charge density – even inducing superconductivity in materials initially insulating – has been proven 21,22 . It
relies on the use of a polymer electrolyte or a liquid gating technique.
In practice an electrochemical cell is incorporated into a top-gate
field-effect transistor (FET) architecture replacing the solid gate
insulator by a polymer electrolyte solution (PES) or a liquid electrolyte that acts as gate dielectric. A voltage application between a gate
electrode and another electrode in contact with the material under
study causes solvated ions in the PES to densely accumulate on the
surface of a channel over the sample, thus forming an electric double
layer (EDL) that acts as a nanoscale capacitor at the interface. As a
consequence of the very large specific geometric capacitance of the
EDL (of the order of some mF?cm 22 ) an intense electric field as high
as 50 MV/cm can be applied at the sample surface inducing a huge
surface charge density n2D, up to 10 14 –10 15 charges/cm 2 depending
on the electronic properties of the material [Ref. 22 and references
therein]. This technique has been recently used in Raman and IR
conductivity experiments in SLG and bilayer graphene up to induced
charges of the order of 5?10 13 cm 22 (refs 23–26). However, not so
many papers are present in literature concerning the application of
this technique to transport measurements in SLG or FLG. In a first
experiment in SLG a charge induction up to,6?10 13 cm 22 has been
demonstrated by using polyethylene oxide (PEO) as polymer and
lithium perchlorate as electrolyte 27 . This large surface density has
been further increased up to n2D . 10 14 cm 22 by using the same
PES at gate voltages up to 15 V, but employing a rapid cooling
method in order to reduce the expected electrochemical reactions
between PES and graphene 28 . The authors found a quartic temperature dependence of the resistivity at low T (as expected for scattering
with 2D phonon modes) and a crossover to the classic high-T linear
behavior at a temperature strongly tunable by the induced charge 28 .
More recently the technique has been also applied to FLG. The Dirac
curves of single, bi, and trilayer graphene have been compared at room
T and deeply analyzed up to charge densities of the order of
2?10 14 cm 22 (ref 29) and the low-temperature magnetoconductance
of epitaxial trilayer graphene grown on a 6H-SiC surface has been
studied up to n, 7?10 14 cm 22 claiming the evidence for a gate modulation of the weak spin-orbit interaction in this material 30 . No sign of
superconductivity has been observed in the low-temperature sheet
resistance curves shown in these articles 27,28,30 .

In this paper we present the results of electric transport measurements in 3-, 4- and 5-layer exfoliated graphene samples (3LG, 4LG
and 5LG in the following) down to 3.5 K and up to an induced
surface charge density that ranges from about 5?10 14 cm 22 in 3LG
to about 7?10 14 cm 22 in 5LG obtained by using a novel PES of
improved efficiency. No trace of superconducting transition has been
found in these experiments, but the sheet resistances in the temperature range 20–280 K reproducibly show a peculiar behavior with a
dominant low-temperature T 2 component and a crossover to the classic electron phonon linear regime at about 90 100 K independently of

the strong Fermi energy tuning produced by the electrochemical
gating.

Results and Discussion
The FLG flakes used in this work have been obtained by using the
standard adhesive tape exfoliation technique followed by a transfer
onto a SiO2 on Si substrate. The number of graphene layers has been
determined by optical contrast 31 and by Raman spectroscopy measurements. The latter technique was also used for selecting only the
3LG, 4LG and 5LG flakes that showed a Bernal stacking 32,33 . The
electric contacts for the four-wire measurements were realized by
using the standard photolithographic, thermal evaporation and
lift-off techniques. Afterwards, the FLG channel was shaped into a
Hall-bar by reactive ion etching and an additional windowing by
photoresist was realized on the device in order to leave uncovered
only a part of the contact pads (for wire bonding) and the gated
channel over the flake. Figure 1a shows a picture of one of the devices
used in our experiments, taken under an optical microscope. In the
inset a zoom in the region of the contacts and of the FLG Hall-barshaped flake is presented, where the detail of the photoresist window
defining the channel geometry can be seen.

The EDL gating was realized by using a novel PES that proved to be
able to induce record surface charges up to 4.5?10 15 cm 22 in previous
experiments we performed on thin films of Au, Cu and Ag 34,35 . In
Figure 1b a schematic view of the device with the FLG channel
covered by the PES, the Pt wire used as gate electrode and the various
connections used for longitudinal (Rxx) and Hall (Rxy) resistance
measurements are shown. Before cooling down the device the ambipolar nature of the field effect in FLG was always checked by performing sheet conductance measurements during slow gate voltage
sweeps between 3 and 23 V or vice-versa. One of these sheet conductance vs. gate voltage VG curves is reported in Figure 1c for a 4LG
device. Up to VG, 6 1 V (with respect to the neutrality point) the
curve is symmetric, but at a higher gate voltage a pronounced asymmetry is observed, together with a broad depression at about VG 5
1.5 V. Similar features have been observed in 3LG where the depression has been related to the crossing of a VHS when the Fermi level
reaches the split band T2g29.

results with the calculated ratio of their quantum capacitance Cq37.

A further consistency check of the results shown in Fig. 2 is possible In fact it is well known that in case of gating of a 2D material the

reaches the split band T2g29.

The determination of the induced charge density is particularly
important in these experiments. We used three different methods for
accessing this quantity. The first one consists in the classic Hall-effect
measurements that we performed at room temperature by using a
calibrated variable-gap magnet made with permanent magnets and
able to apply magnetic fields up to 0.7 T at the sample surface. The
second method is a typical electrochemical technique well described
in literature 36 and known as double-step chronocoulometry (DSCC).
It consists in the successive application and removal of the gate
voltage in the form of a step-wise function while measuring the small
current (of the order of few nA) that flows between the gate electrode
and the device (gate current IG). The time dependence of this current
shows a fast exponential component connected to the formation of
the EDL and a slower minor one that pertains to electrochemical
reactions possibly occurring between the PES and the sample. The
inset of Fig. 2 shows a typical time dependence of IG under removal of
a 3 V gate voltage in a 4LG device. By fitting with the proper electrochemical model 36 the IG vs. time curves it is possible to determine
the charge that forms the double layer and, dividing by the gated area,
to obtain the induced surface charge density n2D34,35. The main panel

to obtain the induced surface charge density n2D34,35. The main panel

of Fig. 2 shows a comparison between the n2D values determined by
Hall effect measurements in 4LG (orange diamonds) and the ones
obtained from DSCC (black, red and blue circles). The induced
charge density was measured in 3LG (black circles) and then the
values for 4LG and 5LG have been obtained by scaling the 3LG
results with the calculated ratio of their quantum capacitance Cq37.

Figure 1 | a) Micrograph of one of the FLG devices where the exposed pads for wire bonding and the photoresist (PR) protection layer are clearly seen.
The inset shows a closer view into the region of the Hall-bar shaped FLG flake and the PR window; b) Schematic of the complete device with the
PES drop casted over the PR window and the electrical connections for the 4-wire sheet resistance and Hall voltage measurements. The gate voltage VG is
applied between a platinum wire immersed in the PES and the ground electrode; c) An example of a Dirac curve, i.e. a sheet conductance vs. VG curve
recorded between 13 V and 23 V in a 4LG device.

EDL plus the 2D electron-liquid system can be modeled by a series of
two specific capacitances: the geometric one Cg, which describes the
EDL, and the quantum one, Cq, that essentially describes the screening properties of the 2D conductor. As a consequence 1/CEDL 5 1/Cg
1 1/Cq. The geometrical capacitance Cg depends on the properties of
the PES and on VG and can be determined from our gating experiments in Au thin films 34 where, of course, Cq R ‘. At VG 5 4 V it
turns out to be in the range 50–140 mF/cm 2 depending on the ‘‘freshness’’ of the PES 35 . The quantum capacitance Cq of our devices can be
estimated from tight-binding and ab-initio DFT calculations (jellium
model) of the effective electron mass m* of the FLG flakes at the
different charge dopings by using the original definition of Cq derived
by Luryi 38 :

Cq~ gvm�e2 ð1Þ

p�h 2

where gv is the valley degeneracy factor. At VG 5 4 V, for example, we
estimate Cq 5 24 6 7 and 27 6 8 mF/cm 2 for 4LG and 5LG, respectively, in good agreement with the values measured in 3LG at high
charge doping 29 . From the above values of Cg and Cq we can calculate
CEDL and, consequently, n2D for 4LG and 5LG at VG 5 4 V. The
obtained ranges of values (including only the variability of Cg) are
shown in Fig. 2 as dashed bands (red for 4LG and blue for 5LG). By
comparing the carrier density determined by Hall measurements
with that obtained by DSCC it is possible to notice that the Hall
values are somewhat larger especially at larger gate voltages. We
think that the reason for this behavior is related to the low values
of the magnetic field we used in the Hall measurements. There are
strong non-linearities in the Hall voltage at low field mainly due to
inhomogeneities and differences in the mobility of the sample that

introduce a large uncertainty in the measure (see error bars in Fig. 2).
More precise Hall values of the average charge density can be
obtained at fields of the order of 5 T that are not available in our
cryo-cooler experimental setup. In the range where the comparison
of the three methods of n2D determination is possible (VG # 2 V) the
average n2D value coincides with the one obtained from DSCC and
thus we conservatively decided to use these DSCC values in the whole
VG range including the proper error (of the order of 630% at high
doping) in the n2D evaluation. Please note that, even if the redox
potential of Li 1 is 3.04 V, we have experimentally observed by
long-term monitoring the device resistance and the gate current at
room temperature that a VG up to 14 V can be safely applied without any evidence of electrochemical reactions at the interface.

Figure 3 shows the sheet resistances as a function of temperature
obtained at different induced charge densities (indicated in the
legends) in 3LG, 4LG and 5LG devices. The curves show some common features. The sheet resistances R% of 3LG and 4LG devices
(panels a, b and c) exhibit a metallic behavior even at the lowest
doping (VG 5 0 and n2D slightly negative), while the R% of 5LG in
the same conditions (panel d) is increasing at the decrease of temperature showing a typical localization-regime behavior. This particular behavior of the 5LG device needs to be fully clarified, but it
could be due to the presence of a large number of defects and impurities at the channel surface able to introduce a strong scattering
responsible for the localization at low n2D. However, the increase
of the charge density (both positive and negative) produces a strong
decrease of the sheet resistances and, in the 5LG device, leads to a
crossover from localization to a metallic regime at VG . 1 V, i.e. n2D
. 4.3?10 13 cm 22 . A similar behavior has been recently observed in
liquid gated 3LG devices 30

Figure 2 | The induced charge density n2D as function of the gate voltage
measured by different techniques in 3LG, 4LG and 5LG devices. The results
of Hall effect (orange diamonds) and double-step chronocoulometry
(DSCC) measurements (black, red and blue circles) are compared. The
range of n2D values estimated at VG 5 4 V for 4LG and 5LG from an abinitio evaluation of the quantum capacitance of the devices is also shown
(red and blue hatched regions). The inset shows an example of the
measured gate current (red line) at the step removal of gate voltage (black
line) in a 4LG device. This is a part of the procedure for the determination
of n2D by DSCC (see text for details).

No sign of superconducting transition can be seen at the lowest
temperature reached in the experiments, i.e. 3.5 K, but a logarithmic
upturn of the sheet resistance is present at T, 15 K in all the FLG
devices. This behavior will be analyzed and discussed in detail in a
forthcoming paper.

Let us focus here on the range of higher temperatures, i.e. when
T . 20 K. When the resistances are in the complete metallic regime
(any VG for 3LG and 4LG, VG $ 2 V, i.e. n2D $ 1.85?10 14 cm 22 for
5LG) they show a linear behavior as a function of temperature in the
range between about 100 K and 270 K. The slope of this hightemperature linear-T dependence practically does not change at
the increase of the charge density n2D (both positive and negative)
as it can be seen from the curves of Fig. 3 and has been already
observed in SLG 8,28 . Below,100 K the curves change behavior
assuming a steeper T dependence that is appreciable in the curves
of Fig. 3a, b and c, but is also present (even if not visible due to the
different scale) in the curves of Fig. 3d.

The standard way to get more information on the temperature
dependence of the resistance curves is to plot them in a double
logarithmic scale. Figure 4 shows an example of these log (R%–R%

min ) vs. log T curves in the case of the 4LG device and in the tem-
perature range 20–280 K for both positive (panel a) and negative
(panel b) charge induction. Here R% min is the minimum of the sheet
resistance (at T, 0 K) obtained by fitting the temperature dependency in the range 20–90 K (see below). In both cases a linear T
dependence is observed at T *> 100 K. Below,80 K the temperature
dependence becomes steeper, showing a dominant T 2 component
(see Fig. 4b). In the intermediate temperature range (70 K # T #
100 K) we see a rather sharp (at least for positive gating, i.e. electron
doping) crossover between the two regimes. These results are confirmed by the temperature dependence of the carrier mobility that is
shown in Fig. 5 for the 4LG device both for positive (panel a) and
negative (panel b) charge induction. Also in this graph the crossover
around 100 K toward a steeper low-temperature dependence and the
progressive reduction of the slope of the mobility below 30–40 K can

Figure 3 | The experimental sheet resistances as function of temperature measured at different gating-induced surface charge densities (reported in the
legends) in a) a 3LG device for positive gating (electron doping); b) a 4LG device for positive gating; c) the same as in b) but for negative gating
(hole doping); d) a 5LG device for positive and negative gating

Figure 4 | Log-log plot of the increase of the sheet resistance in the range 20–280 K for a 4LG device at different surface charge densities induced by a)
positive gating (electron doping) and b) negative gating (hole doping). Dotted lines that represent the linear, quadratic and quartic T dependences
are also shown for comparison. Dash-dotted lines are the generalized Bloch-Gru¨neisen fits of the curves at (a) VG 5 2 V, i.e. n2D 5 1.73?10 14 cm 22 and (b)
VG 5 23 V, i.e. n2D 5 21.75?10 14 cm 22 .

be seen in the curves at lower charge doping. These results have been
reproducibly observed also in the 3LG and 5LG devices.

A ‘‘classic’’ small-angle electron-phonon scattering should dominate the sheet resistance below the Bloch-Gru¨neisen temperature
HBG in a low-density electron system. This should lead to the wellknown T 5 dependence in the 3D case and to a T 4 dependence in the
2D one, as theoretically predicted 39 and experimentally observed in
SLG 28 . However, in our case, it is clearly impossible to fit the experimental data with a T 4 dependence (shown, as reference, in both the
panels of Fig. 4). As a consequence, this weaker fall-off of the sheet
resistance with decreasing T in the gated few-layer graphene samples
compared to single-layer-graphene (Ref. 28) is certainly somewhat
unexpected, even if previously observed and discussed in SLG
devices 40 . As we have already pointed out, the geometric capacitance
of the EDL strongly depends on the composition of the PES and its
preparation and, therefore, also the carrier transport in the channel
could be sensitive to this composition. One could argue that the
difference in the low-temperature behavior of SLG and FLG is due
to the different PES used in the two experiments. This is not the case.
In Fig. 5c we show the log-log plot of the temperature dependence of
the sheet resistance measured in a 3LG and in a 4LG device before
drop casting the PES. It is quite evident that the T 2 dependence and
the crossover to the linear-T behavior at about 100 K are present in
our devices even when the PES is not put over the channel. In our
experiments we always observed that, apart from a small change in
the charge density (indicated by a shift in the sheet resistance), the
presence of the PES (at VG 5 0) does not generate any ‘‘discontinuity’’ in the behavior of the resistance curves as a function of temperature. As a consequence the peculiar T 2 dependence of these FLG
devices cannot be attributed to the gating and to the large carrier
density it introduces, but is likely due to the multiband nature of their
electronic spectrum or, less likely, to extrinsic effects related to the
fabrication of the devices.

The most straightforward explanation for the T 2 dependence of
the resistance below,80 K that progressively turns to a T dependence below 25–30 K (see Fig. 4a and, especially, Fig. 5c) is that in
our devices the intermediate- and low-temperature sheet resistance is dominated by electron-electron collisions with both small
momentum transfer (Nyquist term, R% / T) and with large
momentum transfer (direct ballistic term, R% / T 2 ). A very similar
low-T behavior has been already observed in SLG, but not discussed
at T . 60 K 40 . In order to quantitatively confirm this observation we
fitted the sheet resistances of all our devices in the temperature range
20–90 K by the function: R% min 1 aT 1 bT 2 where R% min, a and b
are fitting parameters and the quadratic term is always more or less

dominant at T *> 30 K. Figure 6a shows two very good examples of
these best fits (black dashed lines) in the case of the 4LG device at two
different gating levels, VG 5 3 V (green continuous line) and 4 V
(orange continuous line). The weight of the quadratic component
varies with the number of graphene layers and the sign of doping,
but, in any case, it becomes small at T, 20–30 K and the Nyquist
term finally becomes dominant at lower temperatures.

As far as the crossover to the high-temperature linear T dependence is concerned we can simply note that, independently of the
value and the sign of the induced charge density (for example from
0.39?10 14 cm 22 to 6.19?10 14 cm 22 as shown in Fig. 4a), it always
occurs at a temperature of 90–120 K. This temperature is very close
to the one where a similar crossover (but from a T 4 to a T behavior)
has been observed in SLG at n2D . 4.65?10 13 cm 22 (see Fig. 2 of Ref.
28). This temperature cannot be associated to the Debye temperature
HD of the material since it should be higher than 2000 K (HD <
2300 K in SLG 28 and HD < 2500 K for in-plane phonon modes of
graphite) thus potentially leading to a crossover at T . 400 K (,0.2
HD).

Following Ref. 28 it is thus tempting to interpret also in our case
this crossover temperature as related to the Bloch-Gru¨neisen temperature HBG of the FLGs at our high doping levels. In a simple,
single-band and free-electron-like picture HBG is the temperature
at which the maximum momentum of acoustic phonons equals twice
the Fermi momentum and is therefore able to completely span the
Fermi surface. In this ideal case HBG is given by:

where A, m and HBG are free parameters. Two examples of these fits,
corresponding to the electron densities n2D 5 1.73?10 14 cm 22 and
n 5 21 75?10 14 cm 22 are shown as dash dot curves in Fig 4a and

HBG~ 2�hkFvs

ð2Þ

where kF is the Fermi wave vector of the spherical (or cylindrical)
Fermi surface and vs is the sound velocity. Of course we can anticipate right now that this simplified expression will not be adequate to
describe our FLG multiband devices.

We fitted our sheet resistance curves by using a generalized BlochGru¨neisen model similar to the one introduced in Ref. 40, but with
the low-T exponent left as a parameter, i.e. by the function:

DR%ðTÞ~R%ðTÞ{R% min

�HTBG xm pf1 f i f{ f i f f i f f i fx f i 2 f eHTBG x ���e

- HBG �2

e T x {1 dx

HBG

ð3Þ

~A :

ð1

HBG

BG pf f i f f i f f i f f i f f i f

T xm 1{x 2

HBG

Figure 5 | Carrier mobility as a function of temperature in a 4LG device under electron (a) and hole (b) doping regimes. The mobility is suppressed by an
increase in both charge density and temperature. A crossover in the temperature dependence of the mobility is evident around 100 K in all the
curves; (c) Longitudinal resistance as a function of temperature for 3LG and 4LG devices before PES drop-casting. Even if the PES is not over the channel
we can see the same crossover from a linear to a quadratic temperature dependence around 100 K observed in the gated devices.

4b, respectively. In the fits of all the curves of Fig. 4a and b (not shown
here for clarity) the m parameter is 1.85 for electron doping (Fig. 4a)
and ranges between 2.1 and 2.5 for hole doping (Fig. 4b), while HBG
values range between 350 and 400 K for electron doping and between
350 and 430 K for hole doping. In Fig. 6b the parameters HBG and m
obtained from the fit of the resistances of 4LG and 5LG devices using
the model of Eq. 3 are plotted as function of the charge density n2D.
This figure clearly show that, apart from an increase of about 100 K
of the average value passing from 4LG to 5LG, HBG doesn’t show any
specific trend as a function of n2D.

Summarizing up to now, the comparison of our present results
with those previously reported in literature leads to the following
conclusions: i) in 3LG, 4LG and 5LG we were able to induce a charge
density quite higher than that observed in SLG and 2LG 27–29 and
similar to the one recently obtained by liquid gating in 3LG 30 ; ii) as
in the few previous low-temperature experiments in SLG 27,28 and
3LG 30 no superconducting transition has been observed down to
,3.5 K; iii) in contrast with some of the results in SLG 28, but in
agreement with others 40 the dominant scattering mechanism in the
range 20–90 K appears to be the direct electron-electron scattering
(quadratic dependence of the temperature behavior of the sheet resistance); iv) in contrast with what theoretically predicted 39 and measured in SLG 28 the observed crossover from the low-temperature T 2

behavior to the standard linear-T dependence at T > 100 K (and the
related HBG obtained by the fit of the sheet resistance using Eq. 3) is
independent of the doping up to the maximum induced charge in
3LG, 4LG and 5LG.
At a first and superficial analysis in the framework of Eq. 2, since
any kF in FLGs increases at the increase of doping (even if not pro-pf f i f f i f f i ffi
portionally to n2D as in SLG), the absence of HBG tuning with the
Fermi energy could be related to a reduction of the sound velocity
produced by the strong charge doping. As a matter of fact a similar
effect of tuning of the phonon dispersion relations with a decrease of
the sound velocity of some acoustic modes (and consequent softening of the corresponding part of the phonon spectrum) has been
already predicted in SLG at a very high level of charge doping 16 . Even
though this effect could be present in FLGs, the situation here is quite
more complex. First of all the FLG flakes with Bernal stacking are
always a multiband electron system. For example, even at low electron doping (when EF is tens of meV above the neutrality point) the
4LG is a two-band material with a Fermi surface made of two sheets
and with two Fermi wave vectors that strongly depend on the direction in the k space. The situation becomes even more complex at
the increase of the electron charge density. When EF, 230 meV a
third band crosses the Fermi level and a fourth does the same at EF,
600 meV. These Fermi energy shifts are certainly compatible with

Figure 6 | (a) Longitudinal sheet resistance as a function of temperature between 15 and 90 K for the 4LG device at two different gating levels
corresponding to VG 5 3 V (green line) and VG 5 4 V (orange line). Black dashed lines are the best fits obtained by using the fitting function: R% min 1 aT
1 bT 2 (see text). They show a remarkable agreement with the experimental data; (b) The Bloch-Gru¨neisen temperature HBG and the m exponent of the
Bloch-Gru¨neisen model (Eq. 3) versus the charge density n2D for 4LG and 5LG devices. While the average values of HBG in 4LG and 5LG are remarkably
different no significant doping dependence of HBG can be appreciated in these curves

the large electron densities obtained with our PES gating. In addition,
in the presence of several bands, not only intraband scattering processes but also interband ones are possible, thus considerably complicating the picture. As a consequence, in contrast with the case of
SLG, in FLGs Eq. 2 cannot be used anymore as a definition of HBG. In
this case, the constancy of the crossover temperature might arise
from the interplay between the increase of the number and of the
overall size of the FLG Fermi surfaces (at the increase of electron
doping) and the presence of interband scattering processes. A quite
similar situation can occur in the presence of a large hole doping.
Only first-principles DFT calculations of the electron-phonon interaction accompanied by a semi-analytical solution of the Boltzmann
equation in FLGs (as the one recently appeared in literature for
SLG 41 ) will clarify the causes of this crossover invariance.

In conclusion, by gating with a novel PES of enhanced chargeinduction capability, we were able to dope 3-, 4- and 5-layer graphene
devices at charge density levels that, we believe, are close to the
intrinsic maxima fixed by the quantum capacitance of the devices,
and to measure their sheet resistance down to 3.5 K. No traces of
superconducting transition have been observed, but the temperature
dependence of the resistance showed a crossover from a low-T
regime dominated by electron-electron scattering and a regime at

-     higher T *>100 K where only the standard high-temperature electron-phonon scattering exists. The crossover temperature can be
associated to the Bloch-Gru¨neisen temperature of the material, but
it does not show any dependence on the Fermi energy, pointing to
important differences in the electric transport properties of FLGs and
SLG at the large charge densities induced by PES gating. Further abinitio theoretical calculations of the electron and phonon properties
of these materials in presence of a huge induced charge density, as
well as further experiments under PES gating able to provide direct
information on these properties, could shed light on these differences
and their origin.

Methods
Device fabrication. Few layers graphene (FLG) flakes are deposited on a 285 nm
thick SiO2 on Si substrates by adhesive tape exfoliation of natural graphite. Then, the
samples are analyzed by optical microscopy 31, in order to estimate the number of
graphene layers composing the deposited thin flake and by Raman spectroscopy for
the determination of their stacking sequence 32,33 . Only FLG flakes with Bernal
stacking have been used in our transport measurements.

The geometry of the contacts is defined using photolithography followed by Cr/Au
(5 nm/60 nm) thermal evaporation and lift-off. The Hall bar geometry is defined by
creating a photoresist (PR) mask by photo-lithography and etching the uncovered
portion of the film by O2/Ar reactive ion etching. A further layer of PR is then spun on
the sample. Windows are open by photolithography in this layer only on the FLG
channel and on the contact pads for device wire bonding and mounting (see Fig. 1a).
The PR mask is then hard-baked at 145uC for 5 minutes in order to improve its
chemical stability.

PES composition and preparation. The reactive liquid formulation for the
preparation of PES is made of a dimethacrylate oligomer, i.e. bisphenol A
ethoxylatedimethacrylate (average Mw, 1700 daltons, Sigma Aldrich) and a
mono methacrylate based reactive diluent, i.e. poly(ethylene glycol) monomethyl
ether monomethacrylate (average Mw, 500 daltons, Sigma Aldrich) in 753 ratio
along with 10 wt % of lithium bistrifluoromethanesulfonimidate salt (LiTFSI) and
3 wt % of free radical photo initiator (Darocur 1173). The components are
thoroughly mixed at ambient temperature to obtain a homogeneous transparent
viscous solution which is drop casted over the device 42 with the help of an optical
microscope. Once the deposition is done, the whole device is exposed to UV light
(light intensity 35 mWcm 22 ). Under UV exposure, the initiator decomposes into
free radicals and reacts with the monomers and oligomers to form a soft threedimensional network. The complete conversion of the reactive liquid to the
polymer electrolyte takes around 180 seconds. The final solid polymer electrolyte
is a soft material with a glass transition below 230 K and a thermal stability up to
430 K. It may conduct Li 1 ions through segmental motion in the network, where
the mobility of ions is facilitated by the pendant ethoxy group of the reactive
diluent. The whole process, comprising mixing, casting and polymerization, is
carried out in an environmentally controlled dry-room (10 m 2, R.H., 2% 6 1 at
20uC) produced by SOIMAR (Caluso, Italy) to avoid the contamination of water
molecules and other substances that may influence the performance of the
polymeric system

Hall effect and double-step chronocoulometry measurements. Hall effect
measurements were performed by supplying a small DC current of a few mA at the two
current contacts of the patterned devices via a low-noise Keithley 6221 current source
and measuring the transverse voltage Vxy on two opposite voltage contacts via a lownoise Keithley 2182 nanovoltmeter. The magnetic field was supplied by a calibrated
variable-gap magnet made with permanent magnets and able to apply magnetic fields
up to 0.7 T at the sample surface. For each gate voltage, Vxy was recorded inverting the
direction of both the current and the magnetic field and then averaged in order to
eliminate any background contribution. Chronocoulometry measurements were
performed by applying and then removing a potential step perturbation between the
platinum wire (gate electrode) and the negative current contact of the device (working
electrode). The small gate current flowing through the electrolyte was measured
between the same contacts. The potential step was removed after the current had
reached less than one percent of its peak value. Both voltage sourcing and current
measurements were performed together via a low-noise Keithley 2400 source
measure unit. The measured charge and discharge current curves were fitted
separately according to the formulas in Ref. 36. Both Hall effect and
chronocoulometry measurements were performed at ambient pressure and room
temperature conditions.

Low-temperature transport experiments. Temperature-dependent sheet resistance
measurements were performed by supplying a small DC current of a few mA at the two
current contacts of the patterned devices via a low-noise Keithley 6221 current source
and measuring the longitudinal voltage Vxx on two adjacent voltage contacts via a
low-noise Keithley 2182 nanovoltmeter. Each voltage value was measured with both
directions of the sourced current and then averaged in order to eliminate
thermoelectric voltages present along the voltage leads. Gate voltage was applied at
room temperature via a low-noise Keithley 2400 source measure unit and kept
constant throughout the entire measurement. Samples were hosted on the cold finger
of a Cryomech ST-403 3 K pulse-tube cryocooler which also provided the
temperature control; the cryostat chamber was evacuated to high vacuum in order to
prevent vapor liquefaction on the samples during cool down via an Agilent MiniTASK Turbo Pumping System. Thermal cycles were performed at the slowest
obtainable speed in order to minimize the possibility of thermal shock to the samples,
i.e., cool down was performed at the maximum power of the in-built Joule heater,
while heat up was performed only through the residual thermal conductance of the
chamber to the outside environment. The heat up process up to room temperature
usually takes more than ten hours during which more than ten thousand resistance
values are recorded.

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Acknowledgments
The authors acknowledge the support from the EU Graphene Flagship. Many thanks are
due to D. Daghero and G. Profeta for perusing the manuscript and to M. Calandra and F.
Dolcini for the useful comments and suggestions on the interpretation of experimental data.
We are grateful to E. Cappelluti and S. Galasso for tight-binding and ab-initio DFT
calculations.

Author contributions
R.S.G. conceived and planned the experiments. M.B., S.B. and E.P. realized the FLG devices.
J.R.N. and C.G. formulate the PES composition and prepared it. F.P., A.S., M.T. and M.B.
performed the transport measurements. E.P., R.S.G. and K.S. analyzed the experimental
results. R.S.G. and E.P. wrote the manuscript.

Additional information
Competing financial interests: The authors declare no competing financial interests.

How to cite this article: Gonnelli, R.S. et al. Temperature Dependence of Electric Transport
in Few-layer Graphene under Large Charge Doping Induced by Electrochemical Gating.
Sci. Rep. 5, 9554; DOI:10.1038/srep09554 (2015).

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