VOLUME 80, NUMBER 18
PHYSICAL REVIEW LETTERS
4 MAY 1998
Nonlocal In-Plane Resistance due to Vortex-Antivortex Dynamics
in High-Tc Superconducting Films
Y. Kopelevich,* F. Ciovacco, and P. Esquinazi
Abteilung Supraleitung und Magnetismus, Universität Leipzig, Linnéstrasse 5, D-04103 Leipzig, Germany
M. Lorenz
Abteilung Halbleiterphysik, Universität Leipzig, Linnéstrasse 5, D-04103 Leipzig, Germany
(Received 1 October 1997)
In high-Tc superconducting YBa2 Cu3 O72d films and at no applied magnetic field we found both
positive and negative in-plane nonlocal resistance in the vicinity of a vortex-antivortex unbinding
transition, as it was predicted recently. The sign of the nonlocal resistance depends on the probed
region in the current-temperature diagram. Our results indicate that a negative nonlocal resistance is
due to the motion of unbounded vortex-antivortex ( V-A), whereas a positive sign is attributed to the
motion of a 2D V-A ordered lattice. [S0031-9007(98)06036-0]
PACS numbers: 74.76.Bz, 74.40. + k, 74.60.Ge
increasing and decreasing current or temperature and at
different sweep rates, inverting the current polarity, as well
as using an appropriate combination of current-voltage
electrodes (I36 , V45 , V12 ). No difference between the
results has been observed [5].
Figure 2(a) presents the “secondary” voltage V56 vs
current I14 measured in sample 1 at various temperatures.
At low enough temperatures V56 is positive, monotonically increasing with current. At higher temperatures,
however, V56 shows a complex nonmonotonic behavior.
In a certain temperature interval we define three characlow
sT d, where V56 becomes negative in
teristic currents: I2
the low-current region, I1 sT d where V56 again becomes
high
positive, and I2
sTd, where V56 again becomes negative
at high currents; see inset in Fig. 2(a). Thus, one can define the current-temperature I-T diagram with alternating
domains of positive and negative nonlocal resistance as
shown in Fig. 3(a).
The appearance of a negative nonlocal resistance is
expected for a state of unbinding V-A pairs due to the
motion of the antivortex dragged by the moving vortex in
In conventional resistance measurements the voltage
contacts are within the electrical current path. In this
work, however, we study the in-plane resistance in highTc superconducting YBa2 Cu3 O72d (Y123) films that
arises outside the region in which the current flows.
Our results obtained in zero applied magnetic field show
that this nonlocal in-plane resistance can be positive
or negative and is attributed to vortex-antivortex ( V-A)
dynamics in agreement with recently published theoretical
predictions [1,2].
Y123 films were obtained by pulsed laser ablation on
SrTiO3 substrates as described elsewhere [3]. Structural
and superconducting properties of the films were previously characterized by conventional techniques [3,4]; the
films show a critical current density at 77 K and zero magnetic field jc , 106 Aycm2 . Several Y123 films of thickness ,400 nm with slightly different critical temperature
Tc were measured. Here we focus our attention on the data
obtained for three samples: Sample 1 showed a zero-field
resistive midpoint transition temperature Tcmid ­ 91.5 K,
transition width DTfs10 2 90d%g ­ 2 K, and a normal
state resistivity, just above Tc , rn sTc d ­ 110 mV cm.
Sample 2 was obtained by slightly deoxygenating sample
1; it showed Tcmid ­ 90.66 K, DT ­ 1.63 K, and
rn sTc d ­ 115 mV cm.
Sample 3 showed Tcmid ­
88.8 K, DT ­ 0.8 K, and rn sTc d ­ 76 mV cm. Six
low-resistance (,1 mV) gold electrodes were patterned as
shown in Fig. 1 with a separation distance of ,200 mm.
Copper wires were attached to the electrodes using silver
paste. In the experiments the dc current I14 flows between
the current leads 1 and 4, whereas the voltage is monitored
simultaneously in both the applied current part of the
sample V23 and in the currentless part V56 . Measurements
of both isothermal V -I characteristics and temperature
dependence of the voltage (resistance) at various applied
fixed currents up to 100 mA were done. To rule out
systematic errors, the measurements were performed with
FIG. 1. Geometry of the experiment: I14 is the current flowing
between 1 and 4 current leads; V23 and V56 are primary
and secondary voltages, respectively. a . b . 200 mm, w .
1.6 mm.
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© 1998 The American Physical Society
0031-9007y98y80(18)y4048(4)$15.00
VOLUME 80, NUMBER 18
PHYSICAL REVIEW LETTERS
4 MAY 1998
FIG. 3. Current-reduced temperature diagram obtained for
(a) sample 1 and (b) sample 2. spd: Ic std, shd: I2low std,
s±d: I1 std, s3d: Ix std, s1d: If std, and s≤d: I2high std. The shaded
regions correspond to a positive nonlocal resistance. The lines
are only a guide to the eyes.
FIG. 2. (a) Secondary voltage V56 vs I14 measured in
sample 1 at various temperatures near the unbinding transition
temperature Tub . 89 K. The numbers near the data indicate
the following temperatures: 1: 88.5 K, 2: 88.7 K, 3: 88.75 K, 4:
88.9 K, 5: 88.95 K, 6: 89 K, and 7: 89.25 K. The inset shows
V56 sI14 d measured at temperatures where a negative nonlocal
voltage occurs in the high current limit. ( b) Primary voltage
V23 vs current I14 . The numbers at the curves correspond to
the temperatures of (a). Solid lines are obtained from Eq. (1).
Arrows indicate the crossover current Ix sT d above which the
V -I characteristic is described by a power law V ~ I a with
a . 1 above Tub . The inset shows the temperature dependence
of the exponent a near Tub . The solid line is obtained from
asT d ­ 3 1 2fbs1 2 T yTub dg1y2 , with Tub ­ 88.97 K, and
b ­ 23.
the applied current region [1]. Therefore, it is tempting
to search for features in the “primary” voltage V23 vs
I [see Fig. 2(b)] that may provide some hints for a
V-A unbinding transition. We found that at low enough
temperatures V23 sId can be well described by the equation
V ­ csT dIfI 2 Ic sT dgasTd21
(1)
[solid lines in Fig. 2(b)]. This form for V -I characteristics has been suggested in Ref. [6] to describe a
current-induced V-A unbinding in high-Tc superconductors, where the threshold current Ic sTd originates from
a finite Josephson interplane coupling and csT d is a fitting parameter. According to theory, at a V-A unbinding transition temperature Tub the exponent asT d jumps
from a ­ 3 to 1 in the low-current limit. The occurrence of such a jump in the measured film is clear at
T . 89 K [see inset in Fig. 2(b)] which is similar to
the results obtained for Y123 films [7] and Y123 single
crystals [8]. Slightly below this temperature asT d can
be fitted by asT d ­ 3 1 2fbs1 2 T yTub dg1y2 [9], taking
Tub ­ 88.97 K and the nonuniversal parameter b ­ 23.
It is also expected that near Tub the threshold current
Ic sTd becomes very small. A diminishing Ic sT d manifests itself as an apparent disappearance of the negative
curvature on a logsV d 2 logsId plot at temperatures near
Tub ; see Fig. 2(b). We note that the obtained transition
temperature Tub ­ 88.97 K is close to the temperature
T ­ 88.9 K, where the negative secondary voltage first
appears. This strongly suggests an intimate relationship
between a V-A unbinding transition and the occurrence of
the negative nonlocal resistance. We should stress, however, that the here observed V-A unbinding transition may
not be a true Kosterlitz-Thouless transition due to sample
size effects; see Ref. [10] for more details. This issue requires further investigations.
Above some current Ix sT d, marked by arrows in
Fig. 2(b), and at T . Tub , V23 , I a with a . 1, that
corresponds to a regime of bound V-A pairs on the probed
length scale [11]. The temperature dependence of Ix sT d
is shown in Fig. 3(a). As can be seen, Ix sT d and I1 sT d
are very close. This observation, together with the results
obtained at T , Tub , suggests that the positive nonlocal
resistance originates from the motion of bound V-A pairs.
At I . If sT d, the local V -I characteristics become linear [V ~ I, see, e.g., the results for sample 2 in Fig. 4(b);
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VOLUME 80, NUMBER 18
PHYSICAL REVIEW LETTERS
FIG. 4. (a) Secondary voltage V56 vs I14 for sample 2 at the
following various temperatures near the unbinding transition
temperature Tub ­ 88.5 K: 1: 88 K, 2: 89 K, 3: 89.2 K, 4:
89.3 K, 5: 89.5 K, 6: 90 K, 7: 90.5 K, 8: 91 K, and 9: 91.5 K.
( b) Primary voltage V23 vs current I14 . The numbers at the
curves correspond to the temperatures of (a). The inset shows
the hysteretic jump in V23 sId measured at T ­ 89.25 K.
If is the current at which the differential resistance dV ydI
saturates] that means that only dissociated V-A pairs are
present. In this regime one should expect the reentrance
of a negative nonlocal resistance. Indeed, we observed
high
sT d as well as
a negative nonlocal resistance at I . I2
high
the coincidence of I2 sT d and If sT d; see Fig. 3.
Figure 3(b) shows the I-T diagram for sample 2
constructed from the V sId measurements shown in Fig. 4.
As follows from Fig. 3 the I-T diagrams are similar
for both samples 1 and 2. However, for the slightly
deoxygenated sample 2, the threshold current Ic , 0 at
all measured temperatures, reflecting a reduced Josephson
coupling as compared to the virgin film (sample 1).
It is worth noting that the obtained I-T diagrams are
reminiscent of the theoretical predicted I-T phase diagram
proposed for layered superconductors [12].
There is another intriguing feature found in sample 2,
namely, I1 sTd lies just above a hysteretic jump measured
in both primary V23 sI14 d and secondary V56 sI14 d characteristics at temperatures slightly above Tub [see Fig. 4
and inset of Fig. 4(b)]. At higher temperatures the jump
transforms into a minimum in V56 sId measured in both
samples 1 and 2. A similar hysteretic jump in the V -I characteristics has been measured in an applied magnetic field
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in high-Tc [13] and conventional low-Tc superconductors
[14,15]. This was interpreted as a current-induced vortex
crystallization transition [16] or as a current-induced depinning related to the dynamics of an elastic medium [17].
On the other hand, the formation of a V-A crystal has been
recently proposed [18]. Taking into consideration these
results we propose the dynamic crystallization of the V-A
matter at I $ I1 sT d. The motion of the “center of mass”
[2] of the V-A crystal would lead then to a positive nonlocal resistance. Within this scenario the Ohmic (local)
V -I characteristics measured at low currents just above the
unbinding transition would be due to the motion of dissociated V-A pairs in the solid, similar to the thermally
activated plastic motion in a vortex solid with dislocations [16,19].
Next, we compare V23 sTd and V56 sTd measured in
samples 1 [Fig. 5(a)] and 3 [ Fig. 5(b)] with an applied
current I14 ­ 50 mA. V56 sT d of sample 1 shows a pronounced “positive peak” at T ­ 89.8 K as well as “negative peaks” at T . 89 K and . 91 K. However, V56 sTd of
sample 3 shows only a small positive peak at T . 88.4 K.
It is also found that the ratio V56 yV23 at the positive peak
temperature is 300 times smaller in sample 3 as compared to sample 1. The reason for such a difference is
explained as follows. First, the unbinding transition was
not observed in sample 3, which naturally explains the
FIG. 5. Temperature dependent voltages V23 sTd and V56 sTd
measured with a constant current I14 ­ 50 mA in sample 1
(a) and sample 3 ( b). Symbols correspond to measurements
increasing T and lines decreasing. The inset shows the
secondary voltage V56 against reduced temperature TyTc0 ,
where Tc0 is the superconducting transition temperature (onset).
Numbers at the curves correspond to the sample numbers.
VOLUME 80, NUMBER 18
PHYSICAL REVIEW LETTERS
absence of negative peaks in V56 sT d associated with the
motion of unbound V-A pairs. Second, V -I characteristics of sample 3 are described by Eq. (1) up to temperatures
close to Tc . Because Ic originates from a finite Josephson
interplane coupling [6], this would imply that in-plane nonlocal effects are reduced in a strongly coupled system.
Also, the essential reduction of the nonlocal resistance
can be understood assuming stronger vortex pinning in
sample 3. As known from collective pinning theory [20],
the quenched disorder (pinning) destroys the long range
positional order in the vortex lattice beyond a characteristic
length Rc , m3y2 yW (m is the rigidity modulus of the V-A
lattice [18], and W the pinning strength). Thus, in a system with pinning, the nonlocal response due to the motion
of the V-A lattice would vanish at distances R . Rc . This
consideration suggests that Rc (sample 1) ¿ Rc (sample 3).
From Figs. 5(a) and 5(b) and the inset of Fig. 5(b)
one can also see a temperature independent negative
V56 voltage which is equal for these two samples in
the normal state. This nonlocal voltage decays below
the resolution limit at distances much shorter as in the
superconducting state. It is also found that the sign
of the normal state nonlocal voltage oscillates with the
distance between electrodes 4 and 5 (note that this was
not observed in the superconducting state) suggesting its
nontrivial origin, and it will be reported in a future work.
Figure 5 clearly illustrates the fact that both “positive”
and “negative” peaks in V56 sTd are essentially related to
the superconducting state.
Finally, we would like to note that positive nonlocal zero-field c-axis resistance has been measured in
Bi2 Sr2 CaCu2 O8 high-Tc single crystals at T . Tub [21]
and attributed to the Josephson interaction between thermal vortex excitations in adjacent superconducting layers.
Our measurements indicate, however, the importance of
2D V-A dynamics in the occurrence of both positive and
negative in-plane nonlocal resistance.
To conclude, nonlocal in-plane resistance of Y123
superconducting films in the vicinity of a V-A unbinding
transition reveals an I-T phase diagram with alternating
domains of positive and negative nonlocal resistance.
The negative nonlocal resistance is associated with the
motion of unbounded V-A pairs, whereas the positive
nonlocal resistance is attributed to the motion of the
2D vortex-antivortex crystal. These novel phenomena
indicate that nonlocal measurements in “planar” geometry
open new possibilities for the study of vortex dynamics in
superconductors.
One of us (Y. K.) acknowledges the support of the Innovationskolleg “Phänomene an den Miniaturisierungsgrenzen” (DFG IK 24yA1-1) and F. C. the support of
4 MAY 1998
the German-Israeli Foundation for Scientific Research and
Development (Grant No. G-303-114.07y93).
*On leave from Instituto de Fisica, Unicamp, 13083-970
Campinas, Sao Paulo, Brasil.
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