APPLIED PHYSICS LETTERS
VOLUME 74, NUMBER 9
1 MARCH 1999
Observation of supercurrent distribution in YBa2Cu3O72d thin films
using THz radiation excited with femtosecond laser pulses
S. Shikii, T. Kondo, M. Yamashita, M. Tonouchi,a) and M. Hangyob)
Research Center for Superconducting Materials and Electronics, Osaka University, 2-1 Yamadaoka, Suita,
Osaka 565-0871, Japan
M. Tani and K. Sakai
Kansai Advanced Research Center, Communications Research Laboratory, 588-2 Iwaoka, Nishi-ku,
Kobe 651-2401, Japan
~Received 20 July 1998; accepted for publication 6 January 1999!
We have demonstrated that the supercurrent distribution in current-biased YBa2Cu3O72d thin films
can be obtained by measuring the radiation power of THz electromagnetic pulses excited with
femtosecond laser pulses. As the radiation power is proportional to the square of the bias current
density at the laser spot position, the two-dimensional current distribution can be obtained from the
intensity distribution of THz radiation by scanning the laser spot. The characteristic supercurrent
distribution is analyzed by using the critical-state model. © 1999 American Institute of Physics.
@S0003-6951~99!04609-4#
High-T c superconductors ~HTSCs! are good optoelectronic materials for their ultrafast optical response.1 Previously, we reported that ultrashort electromagnetic ~EM!
pulses are radiated into free space from current-biased
YBa2Cu3O72d ~YBCO! thin films by femtosecond ~fs! laser
pulse irradiation.2–4 As the Fourier component of the radiated pulses extends up to ;3 THz, they are referred to as
THz radiation. The radiation mechanism is explained in
terms of the ultrafast modulation of the supercurrent associated with the Cooper pair breaking by the laser pulse irradiation and the subsequent quasiparticle recombination.5 The
THz radiation from YBCO has also been reported by Jaekel
et al.6 The THz radiation has also been emitted under external magnetic fields and magnetic-flux trapped states without
a bias current.7,8
According to the classical electromagnetic dynamics, the
electric-field E observed in the far field is proportional to
dJ/dt, where J is a current. The supercurrent is expressed as
J5e * n s y , where e * , n s , and y are the charge, number, and
velocity of supercarriers, respectively, under a dc bias current. If the transient change of the supercarrier number induced by the optical excitation is Dn s , the transient change
of the supercurrent is expressed as DJ5e * Dn s y
5JDn s /n s . This means that E is proportional to J, and the
radiation power, which is proportional to E 2 , is proportional
to J 2 . This relation is confirmed experimentally when the
bias current is below the critical current.3
On the other hand, because of the importance of the
magnetic-flux penetration into superconductors for various
applications, there is considerable interest in the magnetic
flux and supercurrent distribution in superconductors. Several experimental methods have been developed to measure
the magnetic and supercurrent distribution in superconductors. For example, magneto-optic ~MO! imaging,9,10 scanning
Hall microprobe,11,12 and scanning superconducting quantum
interference device microprobe13 methods have been used
for this purpose.
In this letter, we demonstrate a direct observation
method of the supercurrent distribution by measuring the
FIG. 1. ~a! Schematic structure of the sample. ~b! Two-dimensional plot of
the square root of the THz radiation intensity near the bridge of the sample.
The vertical solid line indicates the cross section corresponding to Fig. 2.
Also at: CREST, Japan Science and Technology Corporation ~JST!.
b!
Electronic mail: hangyo@rcsuper.osaka-u.ac.jp
a!
0003-6951/99/74(9)/1317/3/$15.00
1317
© 1999 American Institute of Physics
1318
Shikii et al.
Appl. Phys. Lett., Vol. 74, No. 9, 1 March 1999
FIG. 2. Current distribution corresponding to the Bean
model for ~a! I B 5100 mA and ~c! I B 5200 mA. Closed
circles in ~b! and ~d! indicate the square root of the experimental THz intensity along the cross section shown in
~b! for I B 5100 mA and I B 5200 mA, respectively. Solid
curves show the convolution of the current distribution
and the laser beam profile function.
THz radiation from YBCO thin films excited by fs laser
pulses. Since the THz radiation power is proportional to the
square of the bias current density at the laser spot position,
two-dimensional mapping of the current distribution is possible by measuring the THz radiation power with scanning
the laser spot. Based on this idea, we carried out the supercurrent mapping in superconducting YBCO films under a
bias current. A similar static electric-field mapping in a lowtemperature-grown GaAs photoconductive switch using THz
radiation has already been reported by Brener et al.14
YBCO films were deposited on 0.5 mm thick MgO substrates 10310 mm2 in area and patterned into a bow-tie antenna structure having a 1003200 m m2 bridge at the center.
The films were c-axis oriented and had a typical thickness of
110 nm. The transition temperature T c was 86.7 K after patterning into the antenna structure and the critical current I c
of this YBCO antenna was 220 mA at 16 K ~100 mV criterion across the bridge!. The sample was mounted on a
sample holder of a closed-cycle He refrigerator. The sample
holder was connected to a cold base of the refrigerator using
a metal mesh to avoid the mechanical vibration and translated two-dimensionally by a computer-controlled X – Z
stage, which supported the sample holder with a thermally
insulating polyethylene rod. A mode-locked Ti:sapphire laser
operating at a repetition rate of 82 MHz was used to generate
about a 50 fs full width at half maximum ~FWHM! pulses
with a center wavelength of about 790 nm. The laser beam
was focused onto a spot of the YBCO films with a diameter
of about 30 mm. The THz radiation was transmitted into free
space through the MgO substrate. A MgO hemispherical lens
with a diameter of 3 mm was attached to the backside of the
substrate in order to enhance the collection efficiency of the
THz radiation. Since the center of the MgO lens was located
at the center of the bridge, the collection efficiency of the
THz radiation in the center region of ;100 mm radius of the
bridge was enhanced. The experimental setup was similar to
that reported elsewhere2,3 except that an InSb hot-electron
bolometer was used instead of a photoconductive antenna
made of low-temperature-grown GaAs films.
Figure 1~a! shows the schematic structure of the sample
and Fig. 1~b! shows the two-dimensional image of the square
root of the radiation power, which is proportional to the amplitude of the THz EM pulses, obtained at T516 K by applying a bias current of I B 5100 mA. The average power of
the excitation laser beam is 30 mW. This image contains
80340 pixels with one pixel of 10 mm310 mm and the sampling rate is 2 pixels/s. The radiation power is large along the
edge of the bridge, and this indicates that the transport current flows along the sample edge mainly in this condition.
The characteristics of the transport current distribution
can be discussed in terms of the critical-state model.15 In the
critical-state model, when the self-magnetic field at the surface exceeds the lower critical-field H c1 , vortices penetrate
into the sample to a depth that is determined by the strength
of the pinning, which is in turn characterized by the critical
current density J c . According to the Bean model, the current
density distribution J s (x) in a slab is given by
J s~ x ! 5
H
0, 2a,x,a,
J c , a< u x u ,w.
~1!
Here, we assumed that the current density is constant
throughout the thickness d of the film as the thickness 110
nm is less than the London penetration depth l.16 The value
2w5100 m m is the width of the bridge and a is determined
geometrically by
a5w ~ 12I B /I c ! .
~2!
Here, I B is the applied transport current and I c 52wJ c d. Figures 2~a! and 2~c! show the current density distributions calculated from Eqs. ~1! and ~2! for the bias currents of I B
5100 and 200 mA, respectively, with I c 5220 mA. We estimated the distribution of the THz amplitude across the
bridge assuming a Gauss function with a FWHM of 30 mm
for the excitation pulses and taking the convolution with the
calculated supercurrent distribution shown in Figs. 2~a! and
2~c!. The result is shown in Figs. 2~b! and 2~d! by solid lines.
In Figs. 2~b! and 2~d!, the observed supercurrent distributions along the cross section depicted in Fig. 1~b! are also
plotted for I B 5100 and 200 mA, respectively. It is seen that
the measured current distribution is close to that calculated
Shikii et al.
Appl. Phys. Lett., Vol. 74, No. 9, 1 March 1999
1319
tal and calculated results in Fig. 3~b! may be partly due to the
relatively large laser spot size and partly due to the movement of magnetic flux induced by the laser heating. Experiments on the effect of the laser intensity on the supercurrent
distribution is now in progress.
In summary, we have demonstrated that the supercurrent
distribution can be obtained by measuring the THz radiation
with the spatial resolution determined by the laser spot size
~30 mm!. The transport current flows mainly along the
sample edge. Under the higher bias current, the supercurrent
flows rather uniformly across the bridge. The characteristics
of the supercurrent distribution is semiquantitatively understood by the critical-state model. The spatial resolution of
;30 mm limited by the present focusing optics of the exciting laser beam can be reduced to ;1 mm by improving the
focusing optics. The present result gives a method of noncontact evaluation of current distribution in superconducting
films.
FIG. 3. ~a! Current distribution corresponding to the Zeldov model. ~b!
Closed circles indicate the square root of the experimental THz intensity and
a solid curve shows the convolution of the current distribution shown in ~a!
and the laser beam profile function.
from the Bean model. The supercurrent distribution
progresses toward the inside of the bridge with increasing the
bias current.
The calculated value of the current density is less than
the measured values around the center of the bridge for I B
5100 mA. The current distribution based on the Bean model
for the slabs is not sufficiently correct for the films. Zeldov
et al.17 obtained the accurate supercurrent distribution in thin
films assuming the critical state as
J s~ x ! 5
H
A
2J c
arctan
p
Jc ,
w 2 2a 2
,
a 2 2x 2
2a,x,a,
~3!
a< u x u ,w,
where a is determined from
a5w A12 ~ I B /I c ! 2 .
~4!
Figure 3~a! shows the current density distribution calculated
from Eqs. ~3! and ~4! for the case of I B 5100 mA, and Fig.
3~b! shows the convolution with the Gauss function assumed
before. In contrast to the Bean model for the slabs, the calculated value is considerably greater than the experimental
value around the center of the bridge. It has been reported
that the behavior of the magnetic-flux penetration into thin
films of YBCO is well explained by the critical-state model
for thin films.9,18 The disagreement between the experimen-
This work was partly supported by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Science,
Sports, and Culture, Japan. This work was also partly supported by the public participation program for the promotion
of creative infocommunications technology R&D of the
Telecommunications Advancement Organization of Japan
~TAO!.
1
F. A. Hegmann, D. Jacobs-Perkins, C.-C. Wang, S. H. Moffat, R. A.
Hughes, J. S. Preston, M. Currie, P. M. Fauchet, T. Y. Hsiang, and R.
Sobolewski, Appl. Phys. Lett. 67, 285 ~1995!.
2
M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z.
Wang, K. Sakai, and S. Nakashima, Appl. Phys. Lett. 69, 2122 ~1996!.
3
M. Tonouchi, M. Tani, Z. Wang, K. Sakai, S. Tomozawa, M. Hangyo, Y.
Murakami, and S. Nakashima, Jpn. J. Appl. Phys., Part 1 35, 2624 ~1996!.
4
M. Hangyo, N. Wada, M. Tonouchi, M. Tani, and K. Sakai, IEICE Trans.
Electron. E80-C, 1282 ~1997!.
5
M. Tonouchi, M. Tani, Z. Wang, K. Sakai, N. Wada, and M. Hangyo, Jpn.
J. Appl. Phys., Part 2 35, L1578 ~1996!.
6
C. Jaekel, H. G. Roskos, and H. Kurz, Phys. Rev. B 54, R6889 ~1996!.
7
M. Tonouchi, M. Tani, Z. Wang, K. Sakai, N. Wada, and M. Hangyo, Jpn.
J. Appl. Phys., Part 2 36, L93 ~1997!.
8
M. Tonouchi, N. Wada, M. Hangyo, M. Tani, and K. Sakai, Appl. Phys.
Lett. 71, 2364 ~1997!.
9
T. H. Johansen, M. Baziljevich, H. Bratsberg, Y. Galperin, P. E. Lindelof,
Y. Shen, and P. Vase, Phys. Rev. B 54, 16246 ~1996!.
10
Ch. Jooss, A. Forkl, R. Warthmann, H.-U. Habermeier, B. Leibold, and H.
Kronmüller, Physica C 266, 235 ~1996!.
11
D. A. Brawner and N. P. Ong, J. Appl. Phys. 73, 3890 ~1993!.
12
W. Xing, B. Heinrich, H. Zhou, A. A. Fife, and A. R. Cragg, J. Appl.
Phys. 76, 4244 ~1994!.
13
L. N. Vu, M. S. Wistron, and D. J. Van Harlingen, Appl. Phys. Lett. 63,
1693 ~1993!.
14
I. Brener, D. Dykaar, A. Frommer, L. N. Pfeiffer, J. Lopata, J. Wynn, K.
West, and M. C. Nuss, Opt. Lett. 21, 1924 ~1996!.
15
C. P. Poole, Jr., H. A. Farach, and R. J. Creswick, Superconductivity
~Academic, San Diego, 1995!.
16
A. T. Fiory, A. F. Hebard, P. M. Mankiewich, and R. E. Howard, Phys.
Rev. Lett. 61, 1419 ~1988!.
17
E. Zeldov, J. R. Clem, M. McElfresh, and M. Darwin, Phys. Rev. B 49,
9802 ~1994!.
18
R. Knorpp, A. Forkl, H.-U. Habermeier, and H. Kronmüller, Physica C
230, 128 ~1994!.