Rf-induced dc voltages across unbiased terminals and current–voltage characteristics of microwave-driven high-Tc SQUIDs

Quantized voltage across the unbiased terminals of a bicrystal YBa2Cu3O7 dc SQUID exposed to microwave radiation has been observed at 77 K. Using this voltage as an indication of the microwave power coupled to the junctions, we identified three distinct regions in the I–V curves as the microwave power was tuned, similar to those reported for low-Tc SQUID. Pronounced double period steps were observed when the microwave radiation power was high enough to suppress the dc Josephson current completely. Half-integer steps also appeared as the applied dc-magnetic flux was close to half-integers of flux quanta. The experimental phenomenon was explained based on the resistively shunted Josephson junction model. It is well known that when a Josephson junction (JJ) is driven by a microwave of frequency ν, there will be Shapiro steps appearing on the current–voltage (I–V ) curve at constant voltages V = nhν/2e, which correspond to the locking of the Josephson oscillation and the harmonics of the external microwave field. A Bessel-function dependence of the step heights on the applied microwave power is usually expected for an ideal JJ, though deviations from the Bessel-function behaviour have been widely observed experimentally [1–5]. Vanneste et al have presented a numerical calculation using the resistively shunted JJ (RSJ) model, and identified the existence of three distinct regions in I–V curves and two different types of microwave steps [1]. Their theoretical predictions have been verified in conventional low-Tc tunnel junctions and SQUIDs [1, 2]. On the other hand, quantized microwaveinduced dc voltages across low-Tc junctions, in the absence of the bias voltage and external dc magnetic field, have also been theoretically predicted and experimentally verified by Chen et al [6, 7]. However, several issues remain unanswered: (1) Will the I–V characteristics and the microwave-induced steps for high-Tc SQUID behave similarly as their counterparts in low-Tc SQUID? (2) Will the microwave-induced voltage across an unbiased high-Tc junction be quantized as observed in the case of low-Tc? (3) Will the direct measurement on variation of the rf-induced voltage with the applied microwave power help to explain the observed I–V characteristics? The above issues are important in order to develop the high-Tc SQUID as an oscillator. In order to shed some light on the above issues, we developed a method to monitor the amplitude of the unbiased microwave-induced voltage |Vn|, and by recording the I–V curves at fixed microwave powers corresponding to certain |Vn|, we obtained the relationship between the effective microwave voltage and the three separated regions in the I–V curves, as defined by Vanneste, for a high-Tc YBa2Cu3O7 (YBCO) bicrystal SQUID. The dc-SQUID we studied was fabricated on a 24◦ bicrystal (001)-SrTiO3 substrate, on which epitaxial high-Tc YBCO thin film was grown using pulsed laser deposition (PLD) technique [8]. The superconducting transition temperature Tc measured away from the grain boundary was above 90 K and the critical current density Jc > 1.6 × 106 A cm−2. A conventional photolithography technique was 0953-2048/02/020226+04$30.00 © 2002 IOP Publishing Ltd Printed in the UK 226 Rf-induced dc voltages across unbiased terminals of high-Tc dc SQUIDs Figure 1. Microwave power dependence of the rf-induced dc voltages across the unbiased terminals of the high-Tc dc SQUID. Frequency of the microwave applied was 10 GHz. The drawing of the SQUID on a 10 × 10 mm2 substrate and the zoom-in SQUID loop are inserted. employed to pattern the dc-SQUID, which consists of two identical grain-boundary junctions each with a line width of ∼9μm after etching. The fairly wide junction is a compromise on the technology limitation of our mask supplier. The area of the superconducting loop was about 1 × 104 μm2 and the dimension of the square washer was 4 × 4 mm2. The drawing of the SQUID on a 10 × 10 mm2 substrate and the zoom-in SQUID loop are shown in figure 1 as an inset. Working at 77 K, the typical critical current of the dc-SQUID, 2Ic0, was about 2 mA, and the junction resistance Rn was 0.15 . The field-to-flux coefficient of the SQUID, a field in which one flux quantum generated through the SQUID loop, was calculated as 2.0 × 10−3 Oe, and experimentally obtained from the voltage versus flux curve as around 1 × 10−4 Oe, due to the flux focusing effect [9]. For I–V curve measurements, the conventional fourprobe method was employed. During the microwave power dependence study, the termination of the microwave coaxial line was set in the dewar as inductive-coupled and its position was adjusted first to optimize the coupling between the microwave and the junction, and then fixed. The microwave radiation employed was generated by a Hewlett Packard 83640B signal generator, and the rf frequencies selected were 10 and 20 GHz. The SQUID voltage output was connected to an amplifier with noise level 4 nV Hz−1/2, input impedance 0–30 and gain 1000, followed by an oscilloscope. Firstly, we applied a dc current Idc ≈ Ic to the SQUID so that the bias voltage across the terminals was zero. Then we tuned the microwave power, and measured the dc voltage induced by the rf radiation across the two terminals of the SQUID. Figure 1 shows the voltages recorded, as varying with the microwave power. It is clear that the induced voltage |Vn| is discrete, i.e. it stayed prominently at a certain value for a limited range of microwave power, though a drift to a higher or lower level was observed. Careful investigation suggests that these values are integers of the particular voltage hν/2e = 20.7μV, where the Shapiro step on the I–V curve appears. Figure 2. I–V characteristics of the dc SQUID under a microwave radiation of frequency 10 GHz, and different powers labelled by the alphabets, as indicated in table 1. The inset shows the double period steps on the I–V curve when the SQUID was driven by a microwave of 12 dBm. According to the study of Chen et al [6], in case of ‘unbiased’ (both the bias dc voltage and the external dc magnetic field are absent), the dc voltage developed across a junction is controlled by the external rf radiation, following −n R = IJ ∣∣∣Jn ( 2eVrf hν ∣∣∣ sin n (1) whereVn is the nth voltage induced by microwave, R is the total resistance in the external circuit, IJ is the Josephson current amplitude, Jn is the nth Bessel function, Vrf is the peak voltage of the microwave applied, and n is the relative phase between the Josephson junction and the nth harmonic of the microwave. Since sin n 1, it is only if ∣∣Jn ( 2eV rf h̄ν )∣∣ ∣∣ Vn RIJ ∣∣, i.e. only for a large enough R and for a certain range of Vrf , can Vn be a stable voltage across the junction. Each stable voltage scope starts as Jn → max and ends as Jn → 0. It is clear that the |Vn| recorded in figure 1 are in fact the amplitude, or the largest Vn at a particular microwave power. Therefore we may say that the microwave-induced dc voltage in our high-Tc SQUID is quantized, which we can monitor directly. It is worthwhile to mention that, after n = 5 (|Vn| ∼= 100μV), |Vn| start to depart from the theoretical prediction. It no longer increases with the microwave power even as the later rises up to 25 dBm. This suggests that the coupling of the junction to the microwave radiation is weakened at higher microwave powers. Adjusting the microwave power to a certain |Vn| level, and then fixing the power and increasing the bias dc current, we obtained the corresponding I–V characteristics, the unperturbed I–V curve (curve a in figure 2), and the curves corresponding to different |Vn |, (b–l in figure 2). The alphabets labelled in the figure stand for cases of different powers related to different |Vn| values, as indicated in table 1. Curve a is nonhysteretic, which suggests that the Stewart–McCumber parameter βc = 2eRIcC/h̄ of the junction is less than 1, and the capacitance is negligible (∼0.3 pF). This means that the RSJ model is suitable for this SQUID if the phases of the two junctions are locked. As we adjusted |Vn| to a value lower than 20 μV, no steps appeared on the corresponding I–V curves.