On the origin of photogenerated terahertz radiation from current-biased
superconducting YBa 2 Cu 3 O 7 thin films
Po-Iem Lin, Chih-Wei Luo, Hsin-Shan Liu, Shyh-Feng Chen, Kaung-Hsiung Wu, Jenh-Yih Juang, Tseng-Ming Uen, Yih-Shung Gou, and Jiunn-Yuan Lin
Citation: Journal of Applied Physics 95, 8046 (2004); doi: 10.1063/1.1738537
View online: http://dx.doi.org/10.1063/1.1738537
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/95/12?ver=pdfcov
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On the origin of photogenerated terahertz radiation from current-biased
superconducting YBa
2Cu
3O
7À␦thin films
Po-Iem Lin,a)Chih-Wei Luo, Hsin-Shan Liu, Shyh-Feng Chen, Kaung-Hsiung Wu, Jenh-Yih Juang, Tseng-Ming Uen, and Jenh-Yih-Shung Gou
Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
Jiunn-Yuan Lin
Institute of Physics, National Chiao Tung University, Hsinchu, Taiwan
共Received 19 December 2003; accepted 18 March 2004兲
The origin of photogenerated terahertz radiation pulse emitted from current-biased superconducting YBa2Cu3O7⫺␦thin films excited by femtosecond optical laser pulses is delineated. By investigating the performance of the transient terahertz radiation generated under different operating parameters, pulse reshaping in the measured terahertz electric field caused by the kinetic inductance of the superconducting charge carriers is identified. After recovering the original wave forms of the emitted terahertz pulses, the transient supercurrent density directly correlated to the optically excited quasiparticle dynamics is obtained. A fast decreasing component of about 1.0 ps and a slower recovery process with a value of 2.5 ps are unambiguously delineated in the optically induced supercurrent modulation. The radiation mechanism of the transient terahertz pulse related to nonequilibrium superconductivity is discussed. © 2004 American Institute of Physics.
关DOI: 10.1063/1.1738537兴
INTRODUCTION
The ultrafast photoresponse of high-Tcsuperconductors
共HTSCs兲 has attracted much attention due to its unique
ca-pacity in uncovering the nonequilibrium dynamics of the op-tically excited quasiparticles. The photoinduced transient re-flectivity change measured by the optical pump-probe method has identified two distinct characteristic relaxation times in the superconducting state, linked to the information of the energy gap.1Using a subpicosecond electro-optic sam-pling system, the typical nonequilibrium kinetic-inductance photoresponse of voltage transient2was ascribed to the non-equilibrium quasiparticle generation and recombination in the presence of an applied dc bias current.3
Recently, the modulation of kinetic inductance by ul-trafast laser pulses has been utilized as a sampling technique for measuring ultrafast electric wave forms.4 On the other hand, the reshaping of terahertz共THz兲 pulses upon transmis-sion through superconducting thin films caused by the ki-netic inductance of the superconducting charge carriers was detected by using coherent THz time-domain spectroscopy.5,6 In general, the kinetic inductance of charge carriers is ne-glected since the intrinsic impedance is usually dominated by the resistance. In a superconducting state, however, the ki-netic inductance becomes more significant and must be con-sidered as an important parameter. This pulse reshaping ef-fect is, unfortunately, mostly ignored 共unintentionally兲 in interpreting the observed picosecond electromagnetic pulses emitted from optically excited superconducting bridges, which have revived interest in using HTSC films as potential THz radiation sources.7–9As a result, depending on the ra-diation and detection schemes employed, there have been
discrepancies in trying to directly associate the resultant pulse shape with the characteristic times of the optically in-duced quasiparticle generation and recombination. Further-more, although THz radiation based on the supercurrent modulation has been proposed,8the radiation mechanism of photogenerated THz radiation is still obscure because it is largely inconsistent with the characteristics of optically ex-cited quasiparticle dynamics obtained by femtosecond time-resolved spectroscopy.
Coherent THz radiation emitted from biased photocon-ductive switches has been investigated and explained as follows.10,11The externally biased constant voltage drives the photogenerated carriers to form a transient photocurrent across the field region. A radiated THz electric field is ob-tained by the time derivative of the net current. It acts as the source term in Maxwell’s equation, given as
ETHz⬀
J
t. 共1兲
It is natural to suggest that the amplitude of transient THz electric field in superconducting films can be similarly interpreted as the time derivative of the supercurrent density. The dynamics of the quasiparticles optically induced by the ultrafast laser pulses then determines the performance of the transient THz radiation generated under different operating parameters. Since the THz electric field is measured at the backside of substrate, the pulse may be reshaped by the ki-netic inductance of the superconducting charge carriers before reaching the detector. In this article we report the observation of THz generation from superconducting YBa2Cu3O7⫺␦ 共YBCO兲 thin films by using a free-space electro-optic sampling 共FSEOS兲 technique. By taking into account of the effect of kinetic inductance on the pulse
re-a兲Electronic mail: glinpi.ep87g@nctu.edu.tw
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shaping, our results demonstrate the direct connection be-tween the quasiparticle dynamics and the detected THz ra-diation. Indeed, by transforming the pulse shape back to the original circumstance, the time integral of the original THz pulse reveals a fast decreasing component of about 1.0 ps and a slower recovery process, with a value of 2.5 ps for the optically induced supercurrent modulation, consistent with that obtained from the optical reflectivity measurements. These results not only remove the discrepancies just men-tioned, but also indicate that the THz generation is a direct manifestation of quasiparticle dynamics in response of the optical excitations.
EXPERIMENTAL DETAILS
Schematics of the experimental setup are shown in Fig. 1共a兲. YBCO thin films were deposited on 0.5-mm-thick MgO共100兲 substrates by pulsed-laser deposition. The films were c-axis oriented, and had a typical thickness of 110 nm for the THz generation experiments. The YBCO thin films were patterned into a bow-tie antenna structure using stan-dard photolithography and wet chemical etching. The center
bridge is 200 m long and 100m wide with the bow-tie angle of 60°. The critical temperature Tc was 88 K after patterning into the antenna structure and the critical current densities (Jc) were 1.7⫻106 A/cm2 at 77 K and
1.0⫻107 A/cm2 at 50 K. In addition, for optical reflectivity measurements, 300-nm-thick YBCO film was deposited on SrTiO3(100) substrate. The details of the optical setup of transient reflectance (⌬R/R) measurements were similar to those reported previously.12
The generation and detection of THz radiation was real-ized by using FSEOS technique. A cw argon-laser-pumped, compact, mode-locked Ti:sapphire laser 共Femtosource C20兲 provides 20-fs optical pulses at 800 nm共1.55 eV兲 with a 75 MHz repetition rate. The pump beam focused into a spot size about 50 m in diameter was modulated by a mechanical chopper which operated at 1.3 kHz and incident normal to the center bridge of YBCO bow-tie antenna. The electric field of the THz pulse was sampled by scanning the delay between the pump and probe beam. The superconducting YBCO bow-tie antenna, triggered by femtosecond optical laser pulses, radiates the THz signals. The THz radiation emitted through the backside of the MgO substrate was col-limated by an MgO hemispherical lens with a diameter of 5 mm attached to the backside of the substrate. The THz radia-tion was then passed through a 3-mm-thick vacuum window made of Teflon™ and focused by a pair of off-axis parabo-loidal mirrors onto the 1.0-mm-thick ZnTe共110兲 sensor crys-tal. For low-temperature measurements, the samples were cooled using a Janis flow-through cold-finger cryostat. In the detection segment, the orientation dependence of THz beam detection in ZnTe crystal was accomplished by using an un-doped semi-insulating GaAs 共SI-GaAs兲 photoconductive switch. The shape of THz pulses remains, but the peak am-plitude of the signal and the polarity vary with the probe beam polarization and the THz beam polarization with re-spect to the 共001兲 axis of the 共110兲-oriented ZnTe crystal. The results were then used to determine the optimal operat-ing parameters for our THz detection setup. Further details of the experimental setup can be found in our previous publication.9
RESULTS AND DISCUSSION
The typical photogenerated THz radiation共THz electric field pulse ETHz) as a function of the scanning delay time obtained from a current-biased superconducting YBCO bow-tie antenna measured at 50 K is shown in Fig. 1共b兲. The optical excitation power was 190 mW and the biased cur-rents were⫹100 mA, 0 mA, and ⫺100 mA, respectively. A sharp pulse about 450 fs wide is observed. The figure also shows that the polarity of the THz electric field is reversed by reversing the bias current direction, and that no signal is observed when no bias current is applied, revealing the es-sentiality of the optically induced transient supercurrent den-sity. This consequence can be understood from Eq. 共1兲, in which the change of photocurrent with time can be treated as the supercurrent transient in superconductors.
We note that in order to describe the generation of the THz radiation, two major points have to be clarified. The first FIG. 1. 共a兲 Schematic diagram of the free-space THz generation in the
experimental setup in which tpis pulse duration of either laser or THz pulse.
The enlarged portion denotes the matter of the original THz pulses Ei(t) and
the reshaping of THz pulses Eo(t) that transmission through the
supercon-ducting YBCO film and substrate in the time domain.共b兲 Measured transient THz radiation from superconducting YBCO bow-tie antenna at 50 K. The polarity of the THz wave forms measured with bias currents of⫹100 mA and⫺100 mA. No signal is observed when zero bias current is applied.
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one is the carrier dynamics giving rise to the generation of the THz electric field pulse, and the other one is the output coupling of the radiation from the superconducting thin films. The dynamics of the emitted THz transient related to the nonequilibrium superconductivity is investigated by mea-suring the dependence of the radiation on optical excitation power, bias current, and ambient temperature. The peak strength of the transient THz radiation was found to increase linearly with optical excitation power as well as the bias current, indicating the superradiant character of the emission.9 Next, it would be interesting to see whether the wave form changes with ambient temperature. Figure 2 shows a series of emitted THz pulses obtained at several temperatures. The phase and the shape of the transient change significantly at different ambient temperatures. It is evident that the shape of the transient terahertz pulses is al-most the same in each case, except for the 70 K results, in which the shape after the main pulse followed a slower com-ponent with a characteristic time of about 2.5 ps. It is noted that the phase of the pulse also shifts with increasing the temperature. With regard to the peak amplitude of THz sig-nals, the radiation amplitude rapidly increases with increas-ing temperature. This phenomenon has been attributed to the reduced superconductor energy gap and associated temperature-dependent transmission and absorption coefficients.7
As far as classical electromagnetic dynamics is con-cerned, a far-field radiated THz electric field is proportional to the time derivative of the net current. From the results just presented it is natural to suggest that the THz electric field
ETHzfrom YBCO films is generated by the temporal modu-lation of the supercurrent densityJs/t. Within the
frame-work of the two-fluid model, the bias current density Js can
be described as
Js⫽2enss, 共2兲
where e is the charge of the carrier; Jsis expected to change
when an optical transient is illuminated at the bridge region. The time derivative of Jsthus gives a transient wave form of
the induced radiation. On the other hand, the time integral of the observed E-field amplitude correspondently gives the current transient in the time domain. An unphysical time
scale was obtained, however, if one interprets the transient wave forms shown in Fig. 2 as direct manifestation of
Js/t. The response time obtained this way appears to be
too fast for supercurrent transient associated with quasiparti-cle dynamics. Similar difficulties have been encountered when trying to assign the subpicosecond recovering time to quasiparticle recombination response time,3,8which is about an order of magnitude shorter than normally conceived values.1,12
In general, the frequency-dependent conductivitys()
of the superconducting carriers is purely imaginary, indicat-ing that the superconductindicat-ing films may act as an ideal induc-tor. This property is referred to as kinetic inductance, since the effect is a consequence of the superconducting carrier’s kinetics.2,13,14 The phase sensitivity of the THz pulse spec-trometer allows us to observe directly the kinetic inductance of the carriers. The results are illustrated in Fig. 3, which shows the time-domain spectroscopy taken on the YBCO film at 50 K. The output共measured兲 electric field of the THz pulse is determined by the response of the film and the di-electric properties of the substrate. MgO substrate turns out to be an excellent material with sufficiently low loss to allow for the extended propagation of subpicosecond electromag-netic pulses. The influence of the substrate on pulse shape can be neglected. Notice that there is a dramatic change of the pulse shape in Figs. 3共a兲 and 3共c兲 for results measured at 50 K and 70 K, respectively. In order to yield the original THz pulse关Ei(t) denoted in the enlarged graph of Fig. 1共a兲兴,
which emitted from the superconducting microbridge, propa-gated through the superconducting film itself, passed through the substrate and lens, and then transmitted to the free space, the output THz electric field Eo(t) is transformed via a
trans-fer function. The transtrans-fer function T(), relating the original pulse Ei() and output pulse Eo(), is expressed as5
T共兲⫽Eo共兲 Ei共兲 ⬀共⫺
i兲, 共3兲
where the pulse Eo(t) is Fourier transformed to get Eo(),
divided by (⫺i), and inversely Fourier transformed to yield Ei(t).
The calculated pulse Ei(t)共the original one兲 is shown in
Fig. 3共b兲. This original pulse has the shape of the initial THz
FIG. 2. Temperature dependence of emitted THz wave forms. The excitation power is 190 mW. The dramatic change in pulse shape is shown in the figure.
FIG. 3. 共a兲 Measured 共output兲 THz pulse Eo(t) at 50 K,共b兲 original THz
pulse Ei(t) obtained by Eq.共3兲 using the data in 共a兲, and 共c兲 measured THz
pulse at 70 K.
electric field that is not affected by the kinetic inductance of superconducting film itself. It is interesting to note that the
recovered pulse关Fig. 3共b兲兴 has a wave form similar to the 70 K result 关Fig. 3共c兲兴. It is indicative that for the 70 K result, due to having fewer participating superconducting charge carriers, the effect of kinetic inductance is insignificant.
共With the excitation power illuminated in the region of the
superconducting bridge, a rise of about 10 K is estimated to drive the actual sample temperature to near Tc.) It appears
that the pulse reshaping is a direct result of the superconduc-tor’s kinetic inductance. Moreover, the phase of the transient also changes significantly in the time domain and is consis-tent with that reported earlier.15
As can be seen in Fig. 2, the phase shift of the propa-gated transient is roughly 240 fs below Tc. Taking the
ab-sorption coefficient ␣⫽1.1⫻10⫺5 cm⫺1 for YBCO thin films, an optical penetration depth of␦⫽1/␣⬃90 nm above
Tc is estimated.16 The value of ␦ will rapidly reduce upon
decreasing temperature below Tcdue to the variations in the heat capacity as well as the temperature transient irradiated by the laser pulse. We note that, in the more established coherent THz time-domain spectroscopy technique, which uses SI-GaAs photoconductive switch as the THz radiation source, similar pulse reshaping of transient THz was ob-served共not shown here兲 from a 30-nm-thick YBCO film de-posited on NdGaO3 substrate. In that case, the pulse reshap-ing was modeled as a transmission line shunted by an inductor having an impedance Z⫽⫺iL to act as a
high-pass filter.5 In principle, the inductance L as a function of temperature must be taken into account in the transfer func-tion T() in Eq.共3兲. In particular, since YBCO is known to have d-wave pairing, the nodal regions can lead to strong temperature dependence of the kinetic inductance even well below Tc.17However, in our case, although L may affect the
absolute pulse amplitude, it does not change the genuine characteristics of the radiation. This explains the essentially similar behaviors observed for temperatures below 60 K. For the 70 K result, the influence of temperature-dependent in-ductance and the enhanced optical penetration depth in the superconductor sets in, leading to a very different behavior shown in Fig. 2.
Following the previous discussion, the temperature de-pendence of the original THz pulses from YBCO films are obtained and shown in Fig. 4. The fact that all the recovered pulses exhibit almost the same behavior not only lends strong support to our previous conjectures, but also is indica-tive of one essential underlying mechanism. Since Eq. 共1兲 implies that the optically induced transient of the supercur-rent density in the time domain can be subsequently obtained by integrating the recovered emitted electric field pulses as long as the supercurrent transient is the only prominent mechanism giving rise to the observed radiation.
In Fig. 5, we briefly recap the main observations de-scribed so far. With no bias current, no THz radiation is observed 关Fig. 5共a兲兴, indicating again the important role played by the supercurrent density. Figure 5共b兲 shows the pulse directly detected which presumably has been reshaped by the kinetic inductance. By using the transfer function ex-pressed in the form of Eq. 共3兲, the recovered pulse is
de-picted in Fig. 5共c兲. Finally, the irradiated E-field pulse is integrated over the sampling time to obtain the supercurrent density transient ⌬Js. As is evident from Fig. 5共d兲, ⌬Js
apparently exhibits two characteristic time scales: a descend-ing time of about 1 ps and a risdescend-ing time of about 2.5 ps. If we attribute ⌬Js to be associated mainly with quasiparticle dy-namics, the two characteristic times should correspond to multiple excitation of hot-carrier thermalization-induced su-percarrier reduction and to quasiparticle recombination to re-cover supercarriers, respectively. The latter usually is related to the superconducting energy gap and has been employed ubiquitously in pump-probe measurements to infer energy gap evolutions.
Usually, the optical reflectivity measured by the optical pump-probe method has a femtosecond time response, while the gap opening is manifested by a rapid increase in the amplitude of the photogenerated transient reflectance in the superconducting state. The ultrafast rise of the reflectivity after excitation of the YBCO is attributed to Cooper pairs breaking, and the subsequence decrease of the reflectivity results from quasiparticle relaxation. Below Tc, the
logarith-mic plots of ⌬R/R reveal a break in slope near t⫽2.5 ps. Two relaxation processes1,12 共fast component 1 and slow component2) in our measured data can be clearly observed in YBCO films, as shown in the Fig. 6共b兲. In this case, the two-component fit to the data yields two relaxation times
FIG. 4. Temperature dependence of the recovered THz pulses calculated from the data in Fig. 2 and the transfer function.
FIG. 5. A recap of THz generation related to nonequilibrium superconduc-tivity: 共a兲 no THz signal with zero bias current, 共b兲 the detected ‘‘raw’’ terahertz radiation,共c兲 the recovered terahertz radiation after removing the kinetic inductance effect, and 共d兲 the ‘‘actual’’ supercurrent transient ob-tained by integrating the recovered radiation pulses.
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with 1⬃0.7 ps and2⬃2.3 ps at 60 K. Figure 6共a兲 shows the typical temperature dependence of relaxation times 1 and 2 for YBCO films obtained by pump-probe measuments. For comparison, we also include the quasiparticle re-combination characteristic time obtained from the recovered
⌬Js curves at various temperature关쐓 in Fig. 6共a兲兴. The
con-sistency between the two independent measurements is re-markable. It is noted that the fast relaxation process of about 1.0 ps in pump-probe⌬R/R is also very close to the present
⌬Js descending time scale.
Finally, we turn our attention to the 70 K result 关Fig. 3共c兲兴. The pulse appears to be only slightly modified by ki-netic inductance due to drastic suppression of superconduct-ing carriers when T→Tc. Thus, it is difficult to identify an
appropriate transfer process to remove the reshaping effect. Nonetheless, by comparing with the reshaped and recovered pulses at lower temperatures关Figs. 3共a兲 and 3共b兲兴, the oscil-lation tail following the main pulse is suggestive of a reshap-ing effect. Although there have been suggestions that the
oscillation tails in various THz radiations may have arisen from the absorption of atmospheric water vapor,18 the fact that it can be significantly suppressed by removing the ki-netic inductance effect indicates the antenna circuit itself might be important as well. Analyses along this direction are in progress and will be reported separately.19
CONCLUSIONS
In conclusion, we report a free-space electro-optic sam-pling of the terahertz pulse generation from current-biased superconducting YBCO thin films with excitations of femto-second optical laser pulses. The effect of the kinetic induc-tance originated from the superconducting charge carriers is identified to be solely responsible for the pulse reshaping of the original terahertz pulse. The distorted pulses inevitably result in unphysical time scales, which, in turn, have pre-vented a direct interpretation relating the supercurrent den-sity transient-induced radiation to quasiparticle dynamics. By including a proper transfer function to remove the effect of kinetic inductance and to recover the original shape of the radiation pulses, we have been able to relate the quasiparticle dynamics associated with nonequilibrium superconductivity to the photogenerated THz radiation in a consistent and physically plausible fashion.
ACKNOWLEDGMENTS
This work was supported by the National Science Coun-cil of Taiwan, R.O.C. under grant NSC 92-2112-M-009-031.
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共unpublished兲. FIG. 6. 共a兲 The two temperature-dependent relaxation times obtained from
optical reflectivity transient measurements in YBCO films. The fast compo-nent1共〫兲 in subpicosecond range appears to be insensitive to
tempera-ture, while the slow component 2 共䊐兲 diverging near Tc is frequently
attributed to gap opening. The characteristic time of quasiparticle recombi-nation calculated from THz generation results共30–60 K兲 denoted by 共쐓兲 is also included for comparison. 共b兲 The typical reflectivity transient ⌬R/R data used to obtain1and2. The solid line is drawn to indicate the trend.
