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: [email protected] 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. 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