Optically induced supercurrent modulation

Since Eq. (1-1) implies that the optically induced transient of the supercurrent 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. 4-19, we briefly recap the main observations described so far. With no bias current, no terahertz radiation is observed [Fig. 4-19(a)], indicating again the important role played by the supercurrent density. Figure 4-19(b) shows the pulse directly detected which presumably has been reshaped by the kinetic inductance. By using the transfer function expressed in the form of Eq. (4-7), the recovered pulse is depicted in Fig. 4-19(c). Finally, the irradiated E-field pulse is integrated over the sampling time to obtain the supercurrent

0 1 2 3 4 5 6 7 8 9 10 11 12

∆ J_s (d)

Supercurrent (a rb. units ) Time Delay (ps)

ETHzα ∆ J

s / ∆ t (c)

Pulse reshaping (b)

Electric Fie ld (arb. units)

(a) 0 mA

FIG. 4-19. A recap of terahertz generation related to nonequilibrium superconductivity: (a) no terahertz signal with zero bias current; (b) the detected

“raw” terahertz radiation; (c) the recovered terahertz radiation after removing kinetic inductance effect; (d) the “actual” supercurrent transient obtained by integrating the recovered radiation pulses.

density transient ∆ . As is evident from Fig. 4-19(d), J_s ∆ apparently exhibits two J_s characteristic time scales: a descending time of about 1 ps and a rising time of about 2.5 ps. If we attribute ∆ to be associated mainly with quasiparticle dynamics, the J_s two characteristic times should correspond to multiple excitation of hot-carrier thermalization-induced supercarrier reduction and to quasiparticle recombination to recover 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.

The transient change of optical reflectivity measured by the optical pump-probe method with femtosecond time response reveals that 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 logarithmic plots of ∆R /R reveal a break in slope near t=2.5 ps. Two relaxation processes [13,14] (fast component τ₁ and slow component τ₂) in our measured data can be clearly observed in YBCO films as shown in the Fig. 4-21. In this case, the two-component fit to the data yields two relaxation times with τ₁~0.7 ps and τ₂~2.3 ps at 60 K. Figure 4-20 shows the typical temperature dependence of relaxation times τ₁ and τ₂ for YBCO films obtained by pump-probe measurements.

For comparison, we also include the quasiparticle recombination characteristic time obtained from the recovered ∆ curves at various temperature [J_s ★ in Fig. 4-20].

The consistency between the two independent measurements is remarkable. 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 ∆ descending time scale. J_s

Finally, we turn our attention to the 70 K result [Fig. 4-13(c)]. The pulse appears to be only slightly modified by kinetic inductance due to drastic suppression of superconducting 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 [Figs 4-13(a) and 4-13(b)], the oscillation tail following the main pulse is suggestive of a reshaping effect. The oscillation tails can be significantly suppressed by removing the kinetic inductance effect and may have arisen from the absorption of atmospheric water vapor [87,88].

20 40 60 80 100 120 140 0

2 4 6 8 10

T

_c

=89.6 K

Relaxation Time (ps)

Temperature (K)

FIG. 4-20. Temperature-dependent the two relaxation times obtained from optical reflectivity transient measurements in YBCO films. The fast component, τ₁ (◇) in subpicosecond range appears to be insensitive to temperature, while the slow component, τ₂(□) diverging near Tc is frequently attributed to gap opening. The characteristic time of quasiparticle recombination calculated from terahertz generation results (30-60 K) denoted by (★) is also included for comparison.

0 2 4 6 8 10

1 10

(b)

T=60 K

τ2 ~ 2.3 ps τ1 < 1 ps

Time Delay (ps)

∆R/R (10-5 )

FIG. 4-21. The typical reflectivity transient R∆R / data used to obtain τ₁ and τ₂. The solid line is drawn to indicate the trend.

4.6 Summary

The origin of photogenerated terahertz radiation pulse emitted from current-biased superconducting YBa2Cu3O7-δ thin films excited by femtosecond optical laser pulses is delineated. The picosecond electromagnetic pulse (450-fs width), generated by the terahertz-field-induced phase retardation of the probe beam converted into an intensity modulation were obtained. The representative frequency spectrum derived by Fourier transform spans over 0.1-4 THz. The dynamics of the emitted terahertz transient related to the nonequilibrium superconductivity is investigated by measuring the dependence of the radiation on excitation power, bias current, and ambient temperature. The effect of the kinetic inductance originated from the superconducting charge carriers is identified to be solely responsible for the pulse reshaping of the original terahertz pulse. After recovering the original waveforms 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 distorted pulses inevitably result in unphysical time scales, which, in turn, have prevented a direct interpretation relating the supercurrent density 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 terahertz radiation in a consistent and physically plausible fashion.

Chapter 5

Terahertz Optical Conductivity of Superconducting YBa

2

Cu

3

O

7-δ

Thin Films

5.1 Principles of the terahertz time-domain spectroscopy

The essential concept of the terahertz time-domain spectroscopy (THz-TDS) can be briefly described as followings: The incident terahertz electric field is polarized parallel to the sample surface. A blank substrate identical to the one supporting the thin film is used as a reference. By doing the fast Fourier transform (FFT) of the temporal response data, we obtain simultaneously both the amplitude and the phase of the field transmitted through the thin-film/substrate composite in the frequency domain [5]. The experimental data usually exhibit a high signal-to-noise ratio; thus data smoothing is unnecessary for analysis. By analyzing the changes in the complex Fourier spectrum introduced by the sample, the spectrum of the index of refraction for the sample is obtained.

If we denote the Fourier transforms of the temporal profiles of the pulse

transmitted through a sample and the reference pulse as E^*_f(ω) and E_ref^* (ω), respectively, the complex transmittance of the sample can be expressed as:

) (

)) ( , )) (

( ,

( _*

*

*

*

*

ω ω ω ω

ω

ref f

E n n E

T = , Eq. (5-1)

The frequency dependence of the complex index of refraction n^*(ω) of the sample can then be determined by numerically solving the Eq. (5-1). The temperature- and frequency-dependent complex index of refraction thus obtained are expected to offer the information of both the phase and amplitude of pulsed terahertz generation in HTSC films. Furthermore, the complex optical conductivity can also yield the information for the London penetration depth and the quasiparticle scattering rate with the aid of a two-fluid model.

E

_substrate

(t) E

air

(t) E

THz

(t)

substrate

5.2 Theoretical treatment of the complex transmittance

In this section, we will focus on the data processing of the complex transmittance for thin film and substrate separately.

Analysis of substrate complex transmittance:

In this case, the substrate is regarded as the sample signal and air is used as the reference to determine the complex index of refraction of substrate by numerically solving the Eq. (5-1). Figure 5-3(a) schematically illustrates the circumstance of the transmission geometry. Ignoring the multiple reflections inside substrate, the complex transmission coefficient of substrate can be written as

] n the complex index of refraction of substrate, respectively. Hence, the complex s

transmission coefficient can be expressed directly as [89]

2

where t'(ω) is the transmission coefficient of vacuum. The experimental terahertz signals of the substrate and vacuum in the frequency domain is denoted as

FIG. 5-3(a). Schematic representation of the transmission geometry of the sample. The terahertz temporal profile enters from the left, travels past the substrate or nothing, and exits on the right.

E

_film

(t)

substrate n_s^*(ω,T)can be determined by minimizing the difference between the experimental data and the theoretical one on the right side of Eq. (5-3) at each frequency.

The case of thin films:

In this case, we regard the sample as a homogeneous dielectric films, and ignore reflections from the rear substrate/air interface, since reflections from this interface are widely separated in time from the leading pulse. Since we are interested only in the leading pulse, the expression for the complex transmission of the air/superconducting film/substrate system at normal incidence [as illustrated in Fig.

5-3(b)] can be written as [90] superconducting layer, and n₃ is the index of the substrate, which is to be determined by a separate measurement. Equation (5-4) accounts for multiple

FIG. 5-3(b). Schematic representation of the transmission geometry of the film. The terahertz temporal profile enters from the left, travels past the substrate or film/substrate, and exits on the right.

reflections within the superconducting layer but neglects reflections from the back of the substrate.

In addition, the expression of the transmission coefficient of the air/substrate can be written as dividing the experimental result of the component of thin film, E^*_film(ω), with that of

substrate, E_substrate^* (ω), and can be written as: From this one can directly determine the complex refractive index of thin film,

ik n

n₂ = + , by numerically minimizing the difference between the experimental data at each frequency [44].

5.3 Experimental setup

5.3.1 YBa2Cu3O7-δ thin films preparation

For this study, YBCO thin films were deposited on 0.5-mm-thick NdGaO3

(100) substrates by pulsed laser deposition. The excellent lattice match of NdGaO3 to YBCO is a necessity. The substrate NdGaO3 is specifically chosen because it remains transparent and non-dispersive over the entire spectral bandwidth of the incident pulses, as well as the entire range of temperatures investigated here. Owing to the strong reflection and absorption to the terahertz radiation of the superconducting films itself, the thinner superconducting films is required. In our experiments, the thickness of films about 30 ~ 50 nm is suitable. Thicker films will result in significant degradation in resolution and, hence, blurs the intrinsic characteristics of the sample.

We prepared two YBCO thin films with the same thickness of 30 nm. The critical temperature Tc’s, as shown in Fig. 5-1, are 87.8 K (sample A) and 86.6 K (sample B), respectively. In Fig. 5-1, sample A’s normal-state resistance of the YBCO film was linear in temperature and extrapolated to 0 Ω near T=0 K. Obviously, the sample A with higher Tc has better quality than sample B which is having higher residual resistance and noticeable deviation of linear temperature dependence in the normal-state resistance. In addition, for both samples, X-ray diffraction shown the presence of sharp (00l) peaks only; no traces of other phases can be detected.

0 50 100 150 200 250 300 0

2 4 6 8 10 12

R e sistance ( Ω )

Temperature (K)

Sample A Tc= 87.8 K

0 50 100 150 200 250 300

0 4 8 12 16 20 24 28

Sample B Tc= 86.6 K

FIG. 5-1. Temperature-dependent dc resistance of sample A and sample B.

5.3.2 Optical setup of terahertz time-domain spectroscopy (THz-TDS)

The idea of the established coherent terahertz time-domain spectroscopy technique has been shown in chapter 4 [as shown in Fig. 4-15]. The details of the optical setup of THz-TDS sampling system for measuring the transmission spectra is illustrated in Fig. 5-2. This setup consists of three parts: the pump-probe system, the electro-optic sampling detection, and the cryostat for low temperature measurements.

The ultrafast 20-fs optical pulse at 800 nm with a 75-MHz repetition rate is split into pump and probe beams. The pump beam is normally incident on the terahertz emitter to generate terahertz pulses. We use the SI-GaAs photoconductive switch as the terahertz radiation source. The terahertz pulses are collimated and focused on the sample (target) using a pair of off-axis paraboloidal mirrors. The samples are cooled using a Janis flow-through cold-finger cryostat. The terahertz radiation was passed through a 3-mm-thick vacuum window made of Teflon and focused on the sample.

After the pulses passed and defocused through the sample and the vacuum window, the terahertz pulse is collimated and re-focused on the terahertz electro-optic sampling detector by using another pair of off-axis paraboloidal mirrors to measure the instantaneous terahertz electric field. The terahertz temporal profile was sampled by scanning the delay between the pump and probe beam. The principle of the electro-optic sampling detection has been described in the previous chapter.

P.M.

FIG. 5-2. Illustration the optical setup of the coherent terahertz time-domain spectroscopy system. This setup is constructed from three parts: the pump-probe system、electro-optic sampling detection and the cryostat for low temperature measurements. Details are described in the text.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 10^-6

10^-5 10^-4

absorption of THz radiation in the air purged with dry nitrogen flow

Frequency (THz)

Spect ral Amplitude

FIG. 5-4. The absorption of terahertz radiation in the laboratory air compared to the frequency spectrum purged with dry nitrogen flow (dark line). The deep absorption in spectral amplitude is described in the text.

5.3.3 Water vapor absorption in terahertz frequency region

The absorption of the terahertz radiation by air has already been mentioned in the previous works (there existed the deep absorption in the frequency spectrum of the terahertz pulses). The THz-TDS can be effectively applied to characterize gases that have significant absorption in terahertz frequency region [40,91]. As shown in Fig.

5-4, it is apparent that there exists sharp absorption of the terahertz radiation by water vapor contained in the laboratory air. Hall et al. attributed the deep absorption to H2O molecule rotation transitions [91,92]. In order to suppress the humidity in the laboratory air, the THz-TDS system is put into a Plexiglas box and purged with dry nitrogen flow [as shown in Fig. 5-6]. Figs 5-4 and 5-5 display the influence of the water vapor absorption on the waveforms and spectra of terahertz pulses. The

-15 -12 -9 -6 -3 0 3 6 9 12 15 -1.0x10^-5

-5.0x10^-6 0.0 5.0x10^-6 1.0x10^-5 1.5x10^-5 2.0x10^-5

TH z electric field (arb. units)

Time Delay (ps)

FIG. 5-5. Illustration the influence of the water vapor absorption on the waveform of terahertz temporal profile (red line). After purged with dry nitrogen flow, the time profile displays no oscillation tail on the waveform (dark line).

oscillation tail in the temporal time profile apparently is caused by the water vapor absorption.

In general, the abrupt absorption at several frequencies will result in large errors in the estimation of sample’s intrinsic characteristics. It is essential that the influence of water vapor is minimized in order to obtain more precise information using the THz-TDS system. Table 5.1 shows the measured frequencies and wave numbers of the absorption lines compared to the results reported by Hall et al. [92].

The corresponding absorption lines located at 0.56 THz、0.76 THz、1.1 THz、1.4 THz and 1.7 THz are in good agreement with our data.

Table 5.1 Water vapor absorption lines in the terahertz range

Line # 1 2 3 4 5

f [THz] measured 0.56 0.76 1.10 1.17 1.42

f [cm^-1] measured 18.6 25.3 36.6 39 47.3

f [cm^-1] Hall et al. [92] 18.58 25.09 36.59 40.36 48.33

Line # 6 7 8 9 10

f [THz] measured 1.71 1.78 1.88 2.17 2.27

f [cm^-1] measured 57 59.3 62.6 72.3 75.6

f [cm^-1] Hall et al. [92] 57.29 59.68 62.24 72.2 75.52 FIG. 5-6 Display the experimental setup of terahertz time-domain spectroscopy in our laboratory. The system is put into a Plexiglas box and purged with dry nitrogen flow to suppress the humidity in the laboratory air.

-10 -5 0 5 10 15 20 -1.0x10^-5

0.0 1.0x10^-5 2.0x10^-5

E lectric F ield (arb. units)

Time Delay (ps)

air (reference signal)

NdGaO₃ substrate (sample's signal) T=300 K

multiple reflection SI-GaAs

signal cut off point

∆t

FIG. 5-7. Demonstration the terahertz time-domain spectra obtained for radiation through vacuum and with NdGaO3 substrate (red line).

5.3.4 Index of refraction of NdGaO3 substrate in terahertz region

This section presents the THz-TDS measurements of the dielectric substrate NdGaO3. Employing the method discussed previously, one can take the sample’s signal (substrate) and the reference signal (air) to determine the index of refraction of the sample quite accurately. In the case of a homogeneous sample the complex refraction index of substraten_s*=n+ikcan be then converted to complex dielectric function ε*=ε_r +iε_i using the relation n_s*= ε*.

Figure 5-7 demonstrates the time-domain spectra for radiations through vacuum and NdGaO3 substrate, respectively. The NdGaO3 substrate causes a time delay relative to vacuum by ∆t =(n_s −1)d/c. Where d is substrate’s thickness and c is the speed of light. The minor secondary signal appearing after about 15 ps delay of

the main terahertz pulse is believed to arise from the substrate (SI-GaAs) multiple reflections. After Fourier transforming the pulse with longer time scanning (terahertz signals including the part of multiple reflection), the effect of the multiple reflection in the GaAs, as shown in the Fig. 5-8(a), is seen in the spectrum. The periodic oscillation hinders the data processing in obtaining the material’s intrinsic characteristics. Hence, by losing some resolution, we choose a time scanning range which avoids the effect of the multiple reflection in the terahertz temporal profile. In Fig. 5-7, we collect the sampling range of time delay between -10 ps to 14 ps (Fig.

5-8(a) shown the Fourier transforms without the effect of multiple reflection). Then, according to Eq. (5-1) and by numerically solving Eq. (5-2), the amplitude of transmittance and the index of refraction of NdGaO3 substrate are plotted as a function of frequency. In Fig. 5-8(b), where we plot transmission data taken on a bare 0.5-mm NdGaO3 substrate at 300 K. The real part of the index of refraction n_s as a function of frequency is plotted in Fig. 5-9. The imaginary part, being nearly zero at all frequencies, is also plotted in Fig. 5-9. At 60 K, n varies slightly from 4.62 for low frequencies up to 4.7 for higher frequencies. The frequency dependence of the index of refraction remains approximately the same with temperature, displaying the linear dispersion. The value of index of refraction of substrate, for example at 0.5 THz, will vary with temperature from 4.65 at 60 K to 4.75 at 276 K. This variation must be taken into account in the data processing. Figure 5-10 shows the complex dielectric function as a function of frequencies for NdGaO3 substrate. In this case, k~0 leads to εi~0 and ε_r~n² over the whole range of frequencies and temperatures. Similarly, the frequency dependence of the real part of the dielectric function remains approximately the same over the entire temperature range studied. The value ε_r varies from 21.5 for low frequencies up to about 22.4 for higher frequencies at 60 K, while changes with temperature from 21.6 [T=60 K] to 22.6 [T=276 K] at 0.5 THz.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0

2.0x10^-4 4.0x10^-4 6.0x10^-4

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.0

0.2 0.4 0.6 0.8 1.0

Amplitude Transmittance

Frequency (THz)

Frequency (THz)

Amplitude

signal with multiple reflection remove the effect of multiple reflection

(a)

(b)

FIG. 5-8. (a) corresponding frequency spectrum by Fourier transform for radiation through vacuum. The multiple internal reflection of the SI-GaAs substrate is presented in the frequency spectra. The sampling range in time profile is collected (denoted in Fig. 5-7) to avoid the effect of the multiple reflection and shown in the frequency-domain (red line); (b) frequency-dependent transmission spectra of the NdGaO3 substrate at 300 K.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

FIG. 5-9. Calculated index of refraction of NdGaO3 substrate at various temperatures. .

FIG. 5-10 Dielectric function of NdGaO3 substrate versus frequency at various temperatures.

5.4 Optical conductivity in superconducting YBa

₂

Cu

₃

O

_7-δ

thin films

5.4.1 Motivation

The measurements of the low-frequency electrodynamics in high-temperature superconductors has been very important. A detailed review in microwave spectroscopy measurements has been given by Bonn and Hardy [93]. Recently, microstrip ring resonators made of double-side YBCO films were fabricated to investigate the temperature- and frequency-dependent penetration depth and microwave conductivity and furthermore to enlighten the properties of quasiparticles at microwave frequencies [94]. The optical conductivity σ^*(ω,T) in superconducting thin films at terahertz and submillimeter regime were carried out straight by using the newly developed technique of coherent terahertz time-domain spectroscopy [5,17,18,50,95-102]. However, the temperature dependence of the complex index of refraction n^*(ω,T) at terahertz frequencies is still not well characterized and it seems important to determine the spectral shape of the terahertz transmission temporal profile in the time-domain. Meanwhile, it seems that similar pulse reshaping phenomena have occurred in transmission spectra between the terahertz generation in FSEOS and the terahertz transmission in THz-TDS measurements by using YBCO thin films as sample. In addition, the method of the THz-TDS can also provide the necessary frequency-dependent information [103]. In particular, we are able to obtain the complex optical conductivity of the YBCO film and use it to directly extract the London penetration depth and the quasiparticle scattering rate with the aid of the two-fluid model.

5.4.2 Electrodynamics and the two-fluid model

5.4.2 Electrodynamics and the two-fluid model

在文檔中 兆赫輻射波的產生與應用於釔鋇銅氧超導薄膜特性之研究 (頁 79-0)