Field-induced carrier delocalization in the strain-induced mott insulating state of an organic superconductor.

Abstract

We report the influence of the field effect on the dc resistance and Hall coefficient in the strain-induced Mott insulating state of an organic superconductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br. Conductivity obeys the formula for an activated transport sigma(square)=sigma(0)exp(-W/k(B)T), where sigma(0) is a constant and W depends on the gate voltage. The gate-voltage dependence of the Hall coefficient shows that, unlike in conventional field-effect transistors, the effective mobility of dense hole carriers ( approximately 1.6x10(14) cm(-2)) is enhanced by a positive gate voltage. This implies that carrier doping involves delocalization of intrinsic carriers that were initially localized due to electron correlation.

Full text

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arXiv:0908.0047v2 [cond-mat.str-el] 21 Sep 2009
Field-induced carrier delocalization in the strain-induced Mott insulating state of an
organic superconductor
Yoshitaka Kawasugi,1,2, ∗Hiroshi M. Yamamoto,2, †Naoya Tajima,2
Takeo Fukunaga,2Kazuhito Tsukagoshi,3and Reizo Kato1,2
1Saitama University, Saitama, Saitama 338-8570, Japan
2RIKEN, Hirosawa, Wako, Saitama 351-0198, Japan
3MANA, NIMS, Tsukuba, Ibaraki 305-0044, Japan
We report the influence of the field effect on the dc resistance and Hall coefficient in the strain-
induced Mott insulating state of an organic superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br. Con-
ductivity obeys the formula for activated transport σ2 = σ0exp(−W/kBT), where σ0 is a constant
and W depends on the gate voltage. The gate voltage dependence of the Hall coefficient shows
that, unlike in conventional FETs, the effective mobility of dense hole carriers (∼ 1.6 × 1014cm−2)
is enhanced by a positive gate voltage. This implies that carrier doping involves delocalization of
intrinsic carriers that were initially localized due to electron correlation.
Electrostatic carrier doping (ESD) into novel materi-
als using the field-effect transistor (FET) principle has
recently attracted considerable interest [1]. One reason
for this interest is that ESD could be used to achieve con-
tinuous carrier density tuning in materials with minimal
disturbance of their underlying lattices [2]. One fascinat-
ing material for ESD is Mott insulators associated with
the effect of chemical doping by which unconventional
superconductivity can be achieved [3, 4].
Recently,
gle
(BEDT-TTF)2Cu[N(CN)2]Br
bis(ethylenedithio)tetrathiafulvalene,
κ-Br) [5, 6] adhered to a Si substrate becomes a Mott
insulator due to the negative pressure exerted through
the incompressible Si substrate. In addition, we found
that the insulating state exhibits a field effect in which
the conductivity enhancement exceeds seven orders
of magnitude [7].The series κ-(BEDT-TTF)2X (X:
monoanion) consists of conducting layers of BEDT-TTF
and insulating anion layers. It belongs to the mother
system of unconventional superconductivity and have
been investigated in terms of the bandwidth-controlled
Mott transition [8]. In addition, this material group also
contains a doped superconductor [9, 10]. On the basis
of the generic bandwidth-bandfilling phase diagrams
[11, 12, 13], the ground state of strained κ-Br is consid-
ered to be located near the tip of the Mott insulating
phase. Consequently, the field effect in a κ-Br FET is a
result of carrier doping in the Mott insulating state, in
which dense carriers are present but are localized due to
the strong electron correlation.
we
of
reported
an
thatathin-filmsin-
κ-crystalorganicsuperconductor
(BEDT-TTF
abbreviated
=
as
In typical FET devices, the field effect originates from
the control of the Fermi energy in the rigid band struc-
ture.By contrast, in a Mott insulator, doped carri-
ers increase screening of Coulomb interaction, resulting
in reduction of the effective Coulomb repulsion energy
[14, 15]. The energy dependence of the density of state is
hence coordinated with the doping concentration so that
the charge gap collapses as the bandfilling deviates from
1/2. In the first part of this letter, we discuss influence of
the field effect on the conductivity. We then discuss the
gate voltage dependence of the Hall effect in the second
part of this letter.
We constructed a bottom-gate FET configuration by
laminating electrochemically synthesized thin single crys-
tals of κ-Br onto a p-doped Si substrate (used as the
gate electrode) with a 200 nm thick SiO2layer on which
Au source-drain electrodes were evaporated. The crystal
transfer was carried out in ethanol so that the crystal was
fixed when the ethanol was evaporated. Subsequently,
the crystal was shaped into a Hall bar geometry using
pulsed laser radiation [16]. Details about sample fab-
rication and the strain effect have been described in a
previous report by us [7]. We employed a conventional
five-probe dc method using the standard Hall bar config-
uration with a current of 1 µA. The temperature and the
magnetic field normal to the films were controlled using
a Quantum Design Physical Property Measurement Sys-
tem. The unlabeled data are from the same sample (sam-
ple A), which had dimensions of 300 µm×100 µm×130
nm (width, length, thickness). For the Hall measure-
ments, data from another sample (sample B), which had
dimensions 100 µm×50 µm×170 nm), are also shown.
Figure 1 shows the field effect on the conductivity. The
variation in the four-probe conductivity with gate voltage
Vg (Fig. 1(a)) is reversible and the field-effect mobility
µFE≡ (1/Ci)(∂σ2/∂Vg) (Ci: capacitance per unit area
of the SiO2film) is around 30 cm2/Vs in the linear re-
gion for this sample (Fig. 1(b)). The value of µFE at
the highest gate voltage increases on cooling to 2 K. The
channel conduction is almost ohmic in the range applied
here and exhibits no noticeable hysteresis. The field ef-
fect is reproducible, although the threshold voltage Vth
is sample dependent. We observed the ambipolar field
effect in samples with relatively high Vth. This indicates
that the present device is ambipolar, as expected for Mott
insulators. However, the threshold shifts depend on the

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2
(b)
-50050 100
10-1
100
101
Vg (V)
FE (cm2/Vs)
20 K
10 K
5 K
2 K
(a)
-1000100
0
10
20
30
40
50
Vg (V)
(µS)
??
00.1 0.20.3
105
106
(Ω)
1/T (K-1)
(c)
??
Vg = 120 (V)
100
80
60
0
050100
0
5
10
Vg (V)
W (meV)
40
40 K
35 K
20 K
2 K
FIG. 1: (a) The sheet conductance variation through gate
voltage cycles between ±120 V, at 40, 35, 20, and 2 K. Both
the forward and backward data are shown. (b) The field-
effect mobilities plotted on a logarithmic scale. (c) Arrhenius
plots for the sheet resistance for various gate voltages. The
solid lines represent the data for Vg=120, 100, 80, 60, 40, 0
V in ascending order. The dashed line shows the data for
0 V multiplied by the number of conducting layers. The Vg
dependence of W is shown in the inset.
fabrication process used and the surface conditions of the
samples. Most of the samples exhibit n-type behavior.
Figure 1(c) shows the four-probe sheet resistance in
activation plots for different gate voltages. The activa-
tion plot at Vg = 0 V gives a charge gap of 25 meV
for the ungated film (i.e., bulk), whereas the activation
energy monotonically decreases with an increase in the
gate voltage. The gated resistance at low temperature
can also be fitted to the activation plots. The bends at
the intermediate temperature are therefore attributed to
the shifts from the bulk conductance regime (high tem-
perature) to the field-induced conductance regime (low
temperature). At Vg = 120 V, the activation energy is
reduced to about 0.3 meV (3.5 K). Extrapolations of the
field-induced conductance intersect at the high tempera-
ture limit at which σ0= 2.4×10−5S ∼ 0.1 e2/¯ h for this
sample. One finds,
σ2= σ0e−W/kBT
(1)
where σ0 is a constant and W is the activation energy,
which depends on the gate voltage.Thus, the gated
transport is basically an activation type. In FETs with
a high density of deep trap states, the activation plots
of the conductivity intersect at a finite temperature so
that σ0 decreases with increasing Vg (the Meyer-Neldel
rule [17]).On the other hand, in Si-MOSFETs with
long-range potential fluctuations, σ0 increases as Vg is
increased due to their macroscopic inhomogeneity [18].
Therefore, σ0in the present system indicates that neither
deep trap states nor macroscopic inhomogeneity govern
the transport properties. At the high temperature limit,
the bulk conductivity (Vg = 0 V) divided by the num-
ber of conducting layers is almost σ0, suggesting that
the field-induced conducting layer is confined within the
half of the unit cell containing a pair of BEDT-TTF and
anion layers (1.5 nm).
Let us consider the mechanism for the change in the
activation energy in the present system. In typical FET
devices such as Si-MOSFETs, the insulating state is un-
derstood in terms of strong Anderson localization [19]
where W = EC− EF (EC: mobility edge, EF: Fermi
energy). Application of a gate voltage changes EF, re-
sulting in the variation in W. In most of FET devices
including this type, the gate voltage does not alter the
energy dependence of the density of states (rigid band
model). On the other hand, a sufficient shift of the chem-
ical potential (bandfilling) reduces the effective Coulomb
repulsion energy in a Mott insulator. Realistic theories
and experiments predict that the shift in the chemical
potential of a Mott insulator modifies the profile of the
density of states so that the charge gap collapses [11].
We investigated the Hall effect in the present system to
ascertain the nature of the field-induced carriers. The
conductivity can be separated into two components: the
carrier density and mobility.
In general, the Hall coefficient is related to the carrier
density by RH = 1/en (RH: Hall coefficient n: carrier
density). The electron density is expected to increase
linearly with the gate voltage in an ideal n-type FET.
We employed two methods, magnetic-field sweeping (B-
sweeping) and gate-voltage sweeping (Vg-sweeping) at
fixed temperatures. In B-sweeping, the magnetic field
varied between ±8.5 T by 100 G/s at fixed gate voltages.
In Vg-sweeping, the gate voltage cycled between ±120
V under stationary magnetic fields of ±8.5 T. The for-
ward and backward data in the reciprocation cycles were
confirmed to be consistent for both methods.
First, the Hall effect without a gate voltage was mea-
sured to confirm the property of the bulk (about 90 con-
ducting BEDT-TTF layers). κ-Br has a single folded
Fermi surface giving a hole density of 1/eRH, which cor-
responds to almost 100% of the first Brillouin zone at
high temperatures. At room temperature, we obtained
a hole density of n = 1.14 × 1021cm−3(Fig.
which corresponds to 95% of the active hole density esti-
mated from the lattice parameters and the Hall mobility
µH≡ RHσ = 0.12 cm2/Vs. The values obtained are con-
2(a)),

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3
02468
0
10
20
30
40
B (T)
Rxy (Ω)
0 10 2030
1
10
5
T (K)
RH ( /T)
(a)
40 K
20 K
5 K
Ω
Sample A
0 V
80 V
120 V
Sample B
130 V
0.5
(c)
20 K
120 V
100 V
80 V
60 V
40 V
0
10
20
30
Rxy (Ω)
02468
B (T)
(d)
0
0.1
0.2
0.3
295 K
Vg = 0 V
1.14?1021 /cm3
hole
Rxy (Ω)
02468
B (T)
120 V
(b)
FIG. 2: (a) The Hall resistance vs magnetic field at room
temperature, (b) for Vg=120 V at 40, 20, and 5 K, (c) at 20 K
for different gate voltages. (d) The temperature dependence
of RH.
sistent with the reported values for a related material [20]
because the strain effect is absent at room temperature.
The Hall mobility increased slightly on cooling to about
150 K, after which it started to decrease moderately as
the temperature was further reduced. The carrier density
and Hall mobility at 20 K are n = 1.7 × 1018cm−3and
µH = 0.09 cm2/Vs. Therefore, the temperature depen-
dence of the bulk conductivity is almost entirely due to
the variation in the carrier density down to intermediate
temperatures.
The Hall effect when a gate voltage is applied is found
to be anomalous. The Hall resistances at Vg = 120 V
are plotted in Fig.2(b).
ficients are clearly positive despite the positive applied
gate voltage. Using n = 1/eRH, we obtain a hole density
of 1.6 × 1014cm−2, which exceeds the surface electron
density of 7×1012cm−2estimated from a typical capac-
itance model n = Ci(Vg−Vth)/e (Vth: threshold voltage
estimated from Fig. 1(a)). The hole density is close to
the hole density per conducting layer expected at room
temperature, n = 1.8×1014cm−2. At low temperatures,
RH appears to be almost independent of temperature
(Fig. 2(d)), namely, µH rather than n is thermally ac-
tivated. This is in contrast with the behavior of µFEin
the same region, which increases slightly with decreas-
ing temperature. Note that the decrease in RH at tem-
peratures above 25 K in sample A is attributed to the
contribution of thermally activated holes in the bulk.
In Vg-sweeping, we observed a shift in RHbetween the
bulk and field-induced interface (Fig. 3(a)). The RH
Surprisingly, the Hall coef-
values are almost constant at Vg < 0 and they repre-
sent the carrier density in the bulk. Applying a positive
gate voltage reduces RH to a temperature independent
value of approximately 4 Ω/T. According to the classical
expression for a two-carrier system, RH is given by
RH=
µ2
hnh− µ2
e(µhnh+ µene)2
ene
(2)
where µh(µe) and nh(ne) denote the mobility and den-
sity of holes (electrons), respectively. µhand nhare re-
spectively set to the mobility and carrier density of ther-
mally activated bulk holes. In the case of a conventional
FET, µe is replaced with the measured µFE and ne is
estimated from ne= Ci(Vg− Vth)/e. RHshould be neg-
ative at Vg > Vth and then vary almost proportionally
with 1/(Vg− Vth) (inset of Fig. 3(a)). However, no sign
reversal was observed between the bulk and field-induced
carriers over the entire temperature range. The conven-
tional capacitance model, ne = Ci(Vg− Vth)/e, is not
valid for the present system.
In order to understand the effect of the gate voltage
in this system, we performed a simple simulation of RH
by making the following assumptions. The first assump-
tion is that electron carriers can be ignored in the system
so that µe and ne in Eq. (2) can be replaced with the
values for the surface hole carriers (the negative sign in
the numerator becomes positive for hole carriers). The
second assumption is that the surface hole density is con-
stant (n = 1.6 × 1014cm−2) so that the mobility is en-
hanced by increasing Vg. The surface hole mobility ex-
hibits the same Vg dependence as the conductivity be-
cause σ = enµ. This delocalized hole model reproduces
the experimental data well, as shown in the inset of Fig.
3(a). Thus, the straightforward interpretation is that a
positive Vg activates the mobility of hole carriers. The
hole density is around n = 1.6×1014cm−2corresponding
to 90% of the first Brillouin zone in a single conducting
layer of κ-Br. The effective mobility (but not the con-
centration) of the field-induced carriers increases with an
increase in the gate voltage (Fig. 3(b)).
Below, we summarize the observed characteristics of
the field effect. (i) The conductivity obeys the formula
σ2= σ0exp(−W/kBT), where σ0 is a constant and W
depends on Vg. (ii) 1/eRHincreases when a positive gate
voltage is applied, but its sign remains positive. (iii) In
the Vgvs RHplot, RHappears to alternate between the
bulk and surface values. The value of 1/eRHat high Vg
gives a hole density of about n = 1.6 × 1014cm−2corre-
sponding to 90% of the first Brillouin zone in a single con-
ducting layer. (iv) When the temperature is varied, RH
remains almost constant at the gated surface, indicating
that the Hall mobility, rather than the concentration, of
the field-induced carrier is thermally excited.
The constant σ0 indicates that the macroscopic
phase separation, which is observed in the bandwidth-
controlled Mott transition of κ-Br [21], does not occur by

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4
10
RH (Ω/T)
µH (cm2/Vs)
Vg (V)
0
50-50
100
10-1
100
sample B
30 K
sample A
20 K
20 K
5 K
(a)
(b)
n~1.6 10 cm
?
14 -2
5
50
0 50100
5
10
15
20
-500
0
delocalization

injection
RH(Ω/T)
RH
FIG. 3: (a) Vg dependence of RH. The blue squares and open
diamonds are from B-sweeping. Other data points are ob-
tained by Vg-sweeping; both the forward and backward data
are shown. The inset shows simulations for electron injection
and hole delocalization (see the text) plotted on a linear scale.
(b) The Vg dependence of µH.
a gate voltage. Since increasing the chemical potential by
applying a positive gate voltage should inject only elec-
tron carriers into a band insulator, (ii) and (iii) indicate
that the suppression of the activation energy is due to
the collapse of the charge gap in strained κ-Br. In other
words, the hole carriers that are initially localized due to
the electron correlation become delocalized when a gate
voltage is applied. These results are consistent with the
continuous character of the bandfilling-controlled Mott
transition in which the charge mass diverges with ap-
proaching half-filling [22].
The temperature and gate voltage independence of RH
(at high Vg) shown in (iii) and (iv) implies hopping trans-
port without excitation in the carrier density, conflicting
with the mobility edge model proposed for the insulating
region of Si-MOSFETs [19]. In the future, we intend to
investigate the transport mechanism when a gate voltage
is applied in more detail by performing additional exper-
iments at lower temperatures. Furthermore, it will be
important to investigate the capacitance and the mag-
netic properties.
As far as we know, the present experiment is the first
continuous observation of RHfor a FET structure using a
Mott insulator. The results reveal the clear difference be-
tween this device and conventional FET devices, namely
that the intrinsic localized carriers have a finite mobility
when a gate electric field is applied. Electrostatic tuning
is a powerful tool for investigating the physics of Mott
insulators. Organic π electron systems are particularly
suitable for this method because of their high purities,
low carrier concentrations and simple electronic struc-
tures.
We would like to acknowledge Drs. H. Taniguchi, T.
Minari, Y. Nishio and K. Kajita for valuable discussions,
Dr. K. Kubo for helpful advice on crystal preparation,
and Drs. S. Niitaka and H. Katori for assistance with
using the instrument. This work was partially supported
by Grants-in-Aid for Scientific Research (Nos. 16GS0219
and 20681014) from the Ministry of Education, Culture,
Sports, Science and Technology of Japan.
∗Electronic address: kawasugi@riken.jp
†Electronic address: yhiroshi@riken.jp
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