Charge ordering in amorphous WOx films

Article abstract of DOI:10.1016/j.physleta.2007.04.046

We report on the observation of highly anisotropic viscous electronic conducting phase in amorphous WO_1.55 films that occurs below a current (I)- and frequency (f)-dependent temperature T^* (I, f). At T < T^* (I, f) the rotational symmetry of randomly disordered electronic background is broken leading to the appearance of mutually perpendicular metallic- and insulating-like states. A rich dynamic behavior of the electronic matter occurring at T < T^* (I, f) provides evidence for an interplay between pinning effects and electron-electron interactions. The results suggest a dynamic crystallization of the disordered electronic matter, viz. formation of sliding Wigner crystal, as well as the occurrence of quantum liquid-like crystal or stripe phase at low drives.

Full text of DOI:10.1016/j.physleta.2007.04.046

Physics Letters A 368 (2007) 419–422
www.elsevier.com/locate/pla
Charge ordering in amorphous WOx films
Yakov Kopelevich a,∗, Robson R. da Silva a, Aline Rougier b, Igor A. Luk’yanchuk c,d
a
Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
b
Laboratoire de Réactivité et Chimie des Solides, Université de Picardie Jules Verne, Amiens 80039, France
c
Laboratoire de Physique de Matière Condensée, Université de Picardie Jules Verne, Amiens 80039, France
d
L.D. Landau Institute for Theoretical Physics, Moscow, Russia
Received 11 April 2007; accepted 15 April 2007
Available online 19 April 2007
Communicated by V.M. Agranovich
Abstract
We report on the observation of highly anisotropic viscous electronic conducting phase in amorphous WO
films that occurs below a current
1.55
∗
∗
(I)- and frequency (f )-dependent temperature T (I, f ). At T < T (I, f ) the rotational symmetry of randomly disordered electronic background
is broken leading to the appearance of mutually perpendicular metallic- and insulating-like states. A rich dynamic behavior of the electronic matter
∗
occurring at T < T (I, f ) provides evidence for an interplay between pinning effects and electron–electron interactions. The results suggest a
dynamic crystallization of the disordered electronic matter, viz. formation of sliding Wigner crystal, as well as the occurrence of quantum liquid-
like crystal or stripe phase at low drives.
© 2007 Elsevier B.V. All rights reserved.
PACS: 71.27.+a; 71.30.+h; 71.45.Lr; 74.20.Mn
Transition-metal oxides (TMO) attract a broad scientific
interest due to their extraordinary physical properties such
as, e.g., high temperature superconductivity [1] and colossal
magnetoresistance [2]. The interplay between different ground
states of the electronic matter is one of the central issues of the
TMO physics. In particular, a profound relationship between
the above phenomena and quantum dynamics of quasi-one-
dimensional electronic stripes is expected [1–3]. The theory
of quantum electronic liquid crystals [3,4] predicts the occur-
rence of either superconducting or non-Fermi-liquid ground
states associated with dynamics of charge-ordered phases. Ex-
periments revealed the charge ordering in various TMO, indeed
[1,2]. However, all the studies were performed on crystalline
TMO compounds, where the atomic (ionic) long-range order
inevitably affects, or perhaps governs the stripe formation.
In this Letter we report on the observation of anisotropic
charge-ordered electronic phase in amorphous WOx (x ∼ 1.55)
films, characte∗rized by broken rotation symmetry below the
temperature T (I, f ) of the order of ∼10 K that is current
(I) and frequency (f ) dependent. Measurements of anisotropic
low-frequency resistance and current–voltage (I–V ) character-
istics at T < T ∗ revealed generic features of moving many-
body interacting systems such as Wigner crystals (WC), Wigner
glasses or smectics [5,6], electronic stripe phases [7], and
Abrikosov vortex matter [8–10].
Tungsten trioxides WO3 can be described as a network of
corner-linked WO6 octahedra resulting in the occurrence of
several crystallographic phases ranging from triclinic or mono-
clinic phases to the tetragonal one [11]. Tungsten dioxide WO2
possesses even more complicated monoclinically distorted ru-
tile structure [12]. The stoichiometric WO3 is an insulator
because all six (6s26d4) valence electrons of tungsten W6+
are captured by surrounded oxygen O2−. Experimentally, the
low-temperature activation energy for the electron conduction
Δ = 0.3 or 0.23 eV has been reported for WO3 amorphous
films [13] and the bulk crystal [14], respectively. Doping of
WO3 with electropositive donors M (H, Na, K, Rb, Cs, In,
Ta) leads to a metallic or even superconducting MxWO3 com-
*
Corresponding author.
E-mail address: kopel@ifi.unicamp.br (Y. Kopelevich).
0375-9601/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2007.04.046

420
Y. Kopelevich et al. / Physics Letters A 368 (2007) 419–422
pounds [15], typically having transition temperature Tc < 4 K.
Noting, however, observations of possible high temperature sur-
face superconductivity in Na-doped WO3 with Tc = 91 K [16].
On the other hand, the superconductivity below Tc = 3 K was
observed in twin walls of reduced WO3−δ crystals [17].
Here we explored the possibility of a conductivity enhance-
ment in reduced amorphous WOx films. The studied WOx films
were grown on glass substrates from WO3 target under vac-
uum P ≈ (5–8) × 10−4 Pa or oxygen pressure PO2 ≈ 1 Pa at
room temperature by pulsed laser deposition using a KrF ex-
cimer laser (Lambda Physik, Compex 102, λ = 248 nm) with a
laser pulse energy of 180 mJ and a rate frequency of 3 Hz [18].
The film thickness 400 nm < d < 500 nm was measured by a
DEKTAK profilometer. The Rutherford Backscattering Spec-
troscopy analysis revealed WO1.55 and WO2.33 homogeneous
films obtained under vacuum (WO1.55) and 1 Pa oxygen pres-
sure (WO2.33). Featureless X-ray diffraction patterns measured
for all studied films provide evidence for the film amorphiza-
tion.
Fig. 1. Temperature dependence of the resistance R(T ) measured for sample
F1 with I = 0.1 mA, f = 1 Hz for zero (B = 0) and applied magnetic field
−1
B = 5 T. Dashed line corresponds to Eq. (1) with parameters A = 0.0346 ꢀ
−1 −0.85
(see text).
max
,
Van der Pauw-type measurements of the longitudinal R(T,
f, I, B) resistance vs. temperature (T ), frequency (f ), applied
electrical current (I) and magnetic field (B) have been per-
formed on several amorphous WOx films for 2 K ꢀ T ꢀ 300 K,
1 Hz ꢀ f ꢀ 1 kHz, 10 µA ꢀ I ꢀ 1 mA, and 0 ꢀ B ꢀ 9 T by
means of PPMS (Quantum Design) and Janis 9 T-magnet He-
cryostats. Four Pt point-like contacts were patterned at corners
B = 0.000525 ꢀ
K
; charge ordering takes place at T ꢀ T
The inset shows R(T ) measured for the film F2 at f = 1 Hz, B = 0; solid and
dashed lines are obtained from Eq. (2) and Eq. (3) respectively; T = 400 K,
M
R
M
= 25 ꢀ, T = 40 K, R = 110 ꢀ.
ES
ES
of square- or rectangular-shaped films. The resistances R14,23
=
V23/I14 and R12,34 = V34/I12 were measured as shown in the
inset of Fig. 3(a) and Fig. 3(b) respectively.
All studied WO1.55 films with dimensions 0.72 × 0.38 ×
0.0004 mm3 (samples F1 and F3), and 0.84×0.8×0.0004 mm3
(sample F4) have the resistivity ρ(300 K) = 5.0 0.2 mꢀcm.
Dimensions and resistivity of the WO2.33 film, labeled here
as F2, are 0.8 × 0.75 × 0.00049 mm3 and ρ(300 K) = 45
5 mꢀcm, respectively.
Fig. 1 presents R(T ) ≡ R14,23(T ) measured for the sam-
ple F1 with I = 0.1 mA, f = 1 Hz, for B = 0 and B = 5 T.
The prominent feature of given in Fig. 1 R(T )∗curves is the
resistance drop that occurs at T < Tmax(I) ≡ T (I) ∼ 6.5 K,
insensitive to the applied magnetic field.1 Fig. 1 illustrates also
that for T > Tmax, R(T ) can be well described by the equation
1
Fig. 2. Temperature dependencies of the resistance R(T ) obtained for film F1
using various measuring currents, f = 1 Hz, and B = 0. T
(I) increases
(see inset).
max
2.6
with the applied current according to the power law I ∼ (T
)
max
R(T ) =
,
(1)
A + BT α
where α = 0.85. Similar R vs. T behavior with α = 1.00 0.15
was found for all measured WO1.55 films. On the other hand,
R(T ) obtained for the film F2, WO2.33 diverges (see inset in
Fig. 1) with the temperature lowering as
[19,20] or Efros–Shklovskii (ES) law that implies a Coulomb
gap existence in the VRH regime [21].
Fig. 2 shows R(T ) obtained for the film F1 with various
measuring currents and f = 1 Hz. Fig. 2 demonstrates that
R(I, T = const) is a decreasing function of I, as well as that
ꢀ
ꢁ
R(T ) = RM exp (TM/T )1/3
,
(2)
or
Tmax(I) increases with the applied current. The best fitting to
ꢀ
ꢁ
β
R(T ) = RES exp (TES/T )1/2
i.e. R(T ) obeys the Mott’s (M) law for variable range hopping
,
(3)
the data (dashed line in the inset of Fig. 2) gives I ∼ (Tmax
)
where β = 2.6.
Shown in Figs. 3–5 results further characterize the intriguing
low-temperature resistance behavior revealed in WO1.55 films.
Fig. 3 (a, b) presents low-temperature portions of R12,34(T )
and R14,23(T ) obtained for the film F3 at various frequen-
cies and measuring current I = 10 µA. As can be seen form
(VRH) of localized electrons in two-dimensional (2D) systems
1
Negative magnetoresistance ꢁR/R = −[R(5T ) − R(0)]/R(0) ∼ 2% has
been measured for this sample at T = 2 K.

Y. Kopelevich et al. / Physics Letters A 368 (2007) 419–422
421
Fig. 5. Temperature dependencies of resistance R (T ) in “hard” di-
h
rection for sample F4 at B = 0, I = 10 µA and frequencies f =
50, 100, 200, 300, 400, 600, 1000 Hz (from bottom to the top). The inset shows
R (T ) measured for the same sample at B = 0, f = 1 kHz, and currents
h
Fig. 3. Temperature dependencies of resistances measured for the film F3
I = 20, 30, 40, 60, 70, 80, 90, 100, 150, 200, 300, 400 µA (from top to the bot-
in “easy” R = V /I , inset in (a), and “hard” R = V /I , upper in-
e
34 12
h
23 14
tom). Arrows mark T
and T
(see text).
max
min
set in (b), directions for B = 0, I = I = 10 µA and frequencies (a)
12
14
f = 10, 100, 200, 500, 1000 Hz; (b) f = 10, 25, 50, 100, 200, 500, 1000 Hz,
from top to bottom. Lower inset in (b) shows variation of T with frequency;
max
0.003, and C = 12[K1/2]. This Rh/Re vs. T behavior suggests
the formation of an ideal metal in the “easy” (more conductive)
direction or/and an insulator—in the “hard” (less conductive)
direction ground states (A1 > 1 originates from the sample geo-
metrical factor). At the same time, for our highest measuring
frequency (f = 1 kHz) the resistance drops below Tmax by two
2.7
dotted line corresponds to the power law f ∼ (T
)
.
max
orders of magnitude, independently of the applied current di-
γ
rection. As the low inset in Fig. 3(b) illustrates, f ∼ (Tmax
)
where γ = 2.7. Noting, f (Tmax) can be approximated by the
Arrhenius-type law expected for a simple thermally-activated
process only at T > 4 K.
Thus, Figs. 2 and 3 provide evidence that the increase of
either current amplitude or its frequency reduces the resistance
and its anisotropy at T < Tmax(I, f ). Because I ∼ (Tmax)β and
γ
f ∼ (Tmax
)
correspond to the same power law (β ≈ γ ), it is
reasonable to assume a similar physical mechanism behind of
the non-linear and frequency-dependent resistance.
Fig. 4 exemplifies current–voltage I(V ) characteristics mea-
sured at T ꢀ Tmax and f = 60 Hz for the film F4 with current
flowing in both “hard” (curve 1) and “easy” (curve 2) direc-
tions. The I(V ) measured for the film F3 in “hard” direction
(curve 3) is also shown. Inset in Fig. 4 gives differential con-
ductance G ≡ dI/dV vs. V dependencies derived from I(V )
curves presented in Fig. 4.
Shown in Fig. 4, I(V ) and G(V ) dependencies resemble
very much the curves measured for various driven macroscopic
elastic objects interacting with a quenched disorder [5–10],
such as e.g. Abrikosov vortex lattices and charge-ordered elec-
tronic systems, where an interplay between inter-particle (vor-
tices or electrons) and particle-quenched disorder interactions
plays a crucial role. In these systems, an effective strength of
the interactions can be controlled by the applied driving force.
At low drives the particle motion is dominated by the quenched
disorder (pinning) effects, leading to the plastic (channel-like)
Fig. 4. Current–voltage I(V ) characteristics measured at T = 2 K, B = 0
and f = 60 Hz for the film F4 with current flowing in both “hard” (curve
1) and “easy” (curve 2) directions; curve 3 is I(V ) measured for the film F3
(T = 5 K, B = 0, f = 60 Hz) in “hard” direction. The inset shows differen-
tial conductance G ≡ dI/dV vs. V dependencies (1, 2, and 3) derived from the
corresponding I(V ) curves; V marks the maximum in G(V ).
p
this figure, for temperatures below ∼10 K, R12,34(T ) and
R14,23(T ) demonstrate a pronounced frequency dependence. At
low enough frequencies and down to T = 2 K, dR14,23/dT < 0
and dR12,34/dT > 0, such that the ratio R14,23/R12,34 diverges
(not shown) with temperature lowering according to the for-
mula Rh/Re = A1 + B1 exp(C/T 1/2), with A1 = 1.5, B1 =

422
Y. Kopelevich et al. / Physics Letters A 368 (2007) 419–422
motion of some regions of the elastic medium with respect to
other temporarily pinned regions. With increasing the driving
force, (re)ordering or dynamic crystallization of the elastic
medium takes place [7,10]. Whereas our results revealed no
signature for the superconductivity and hence vortices, WC,
electronic stripe or other many-electron phase formation are
plausible scenarios.2
phase in WO1.55 films is also supported by the striking simi-
larity of our results with observations of WC in other systems.
Thus, the resistance drop at T ꢀ TWC, the peak in G(V ) and
its similar frequency dependence, all have been observed in 2D
4
WC formed on a surface of superfluid He [5]. Besides, our
data suggest the opening of a Coulomb gap in the sample F2
(WO2.33), see inset in Fig. 1, that can be considered as a precur-
sor of WC [36].
According to theoretical models [7], the peak in G(V ) at
V ≡ Vp, see the inset in Fig. 4, is expected when the disor-
dered electronic matter becomes dynamically more ordered,
forming WC or other ordered electronic phases. Because Vp
in the film F3 exceeds that in the F4 sample, one concludes that
pinning in the sample F3 is stronger. Considering a combined
effect of quenched disorder and electron–electron interactions,
R vs. f behavior shown in Fig. 3 can be accounted for by
the frequency-induced depinning of the elastic electronic me-
dia, in a close analogy with the vortex depinning [25,26]. The
frequency-induced resistance drop is also expected for pinned
WC at f < fp, where fp is the characteristic de(pinning) fre-
quency, see e.g. Ref. [27]. In the opposite limit, i.e. for f > fp,
R is an increasing function of the frequency [27]. Fig. 5 il-
lustrates such an “inverse” R(f ) dependence measured for
the film F4 which possesses a weaker pinning. The inset in
Fig. 5 presents Rh(T ) for the same sample F4 measured with
f = 1 kHz and 20 µA ꢀ I ꢀ 400 µA. We stress, that while in
the low-frequency, large-current limit, R grows monotonically
with the temperature increase, the non-monotonic R(T ) takes
place for low currents and high enough frequencies (Fig. 5).
The minima in R(T ), which develop at higher resistance level,
may result from a competition between pinning effects and
electron-electron interactions. As temperature increases up to
T ≈ Tmin, see Fig. 5, inter-electron interactions dominate, and
a more ordered state characterized by the lower resistance can
be formed. At yet higher temperatures, the crystal melts and the
resistance increases once again. If our interpretation is correct,
this “dip effect” may well be related to the temperature-induced
crystallization also reported for vortex [28–30] and polymeric
[31] systems.
Summing up, we observed the anomalous metallic phase in
amorphous WO1.55 films that demonstrates characteristic fea-
tures of moving many-body interacting electron systems. The
origin of anisotropic conducting state with a broken rotation
symmetry at low drives remains to be elucidated.
Acknowledgements
One of us (Y. K.) thanks Zvi Ovadyahu for useful comments.
This work was supported by FAPESP, CNPq, CAPES, COFE-
CUB, and MULTICERAL project.
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To get more insight on the origin of the possible collec-
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by Eq. (1), see Fig. 1, is expected for systems in the vicin-
ity of a metal–insulator transition (MIT), characterized by the
incoherent electronic transport [32]. The resistance drop at
T < Tmax indicates the opening of an additional coherent chan-
nel. Taking kF l ∼ 1 at MIT and σ(Tmax) = (e2/3π2h)k2 l ∼
¯
F
100 ꢀ−1 cm−1, one gets kF ∼ 107 cm−1 that translates to the
carrier density n = (kF )3/3π2 ∼ 1018 cm−3. For such n, WC
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WC occurrence were reported for various strongly correlated electron systems
[22,23], including TMO [24].
3
Noting, the Hall voltage could not be detected in our films, being in agree-
B.I. Shklovskii, Phys. Rev. B 69 (2004) 035413.
ment with expectedly low Hall mobility in the vicinity of MIT [34,35].