Superconducting terahertz (THz) metamaterial (MM) made from niobium (Nb) film has been investigated using a continuous-wave THz spectroscopy. The quality factors of the resonance modes at 0.132 THz and 0.418 THz can be remarkably increased when the working temperature is below the superconducting transition temperature of Nb, indicating that the use of superconducting Nb is a possible way to achieve low loss performance of a THz MM. In addition, the tuning of superconducting THz MM by a magnetic field is also demonstrated, which offers an alternative tuning method apart from the existing electric, optical and thermal tuning methods.
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Metamaterial (MM) is an arrangement of artificial structure elements to achieve advantageous and unusual electromagnetic properties, which cannot be realized with natural material . These properties make it possible to manipulate the propagation of electromagnetic waves, giving rise to a variety of applications such as planar superlens and invisible cloaks at microwave band as well as functional devices at THz [2–6].
Metallic structures on dielectric substrates are commonly used in MMs . They have relative low losses at microwaves, and allow us to demonstrate experimentally the extraordinary properties of the MMs. However, as the frequency is pushed higher towards terahertz (THz), the ohmic losses become prominent and the desired functions may not be implemented by using the current MM designs. Thus, an urgent problem is to reduce the loss of THz MMs. Recently, metallic THz MM operating at cryogenic temperature and superconducting THz MM based on yttrium-barium-copper oxide (YBCO) film are proposed for this purpose [8,9]. In the former case, simulations show that the quality factor of the MM can be increased by 40% when the normal metal is kept at 1 K. In the latter case, i.e. superconducting THz MM made from YBCO film, although experimentally the loss does decrease as the temperature decreases, the surface resistance Rs of YBCO film at 0.1 THz and 77 K is comparable to that of the normal metal, implying that YBCO film may not be a very good candidate for superconducting THz MMs .
In this paper, THz MM made from superconducting Nb films is studied. Encouraged by the previous report that up to 0.3 THz the Rs value of Nb film at 4.2 K is lower than that of YBCO film  by at least one order of magnitude, we successfully demonstrate experimentally that the quality factor of the MM can be increased when the Nb film is in the superconducting state. Besides, the tuning of superconducting MMs by a magnetic field is realized at THz in this paper, while in earlier days this tuning possibility was demonstrated only at microwave frequencies [11,12]. Thus we have provided another method to control THz wave propagation apart from the existing electric , optical [13,14] and thermal tuning methods .
2. Experiments and discussions
The sample is a square array of double-split-ring-resonators (double SRR) as shown in Fig. 1a [7,16]. In fact a double-split-ring-resonator consists of two concentric split rings, the outer one and the inner one. The outer one measures 120 μm × 120 μm, while the inner one 80 μm × 80 μm. The widths of the both rings, the spacing between them, and the splits on them are all 10 μm. In the array the distances between neighboring double-split-ring-resonators are 20 μm, making each cell of the sizes 140 μm × 140 μm. The transmission property of this MM is simulated by the commercially available code. In the simulation, the superconducting thin film is assumed to be a normal metal with a conductivity of 5 × 107 S/m. The wave propagates perpendicular to the plane of SRR, with the ac electric field parallel to the gap (shown in Fig. 1). Three resonance dips below 0.5 THz are obtained at 0.13 THz, 0.24 THz and 0.41 THz, respectively.
To carry out experimental studies, Niobium (Nb) film is deposited on 400 μm-thick Si (111) substrate by DC magnetron sputtering. The resistivity of the Si substrate is larger than 1000 Ω • cm. The thickness of Nb film is about 200 nm. The superconducting transition temperature, Tc, is measured to be about 9 K by four-probe technique. The films are polycrystalline with a cubic structure. The standard photolithography and reactive ion etching are used to pattern the sample.
Transmission experiments are carried out using continuous-wave THz spectroscopy, and the necessary DC magnetic field, Hdc, can be provided by a superconducting split-coil magnet . We measure the transmission spectra at 6 K and 26 K in two frequency ranges, one from 0.10 to 0.18 THz and the other from 0.30 to 0.55 THz, corresponding to the ranges in which the simulations find the first and third resonance modes (Fig. 1). Indeed in Fig. 2a and Fig. 2b two dips are experimentally observed respectively at 0.132 THz and 0.418 THz at 6 K in the absence of Hdc.
The resonance curves can be expressed as Eq. (1) to fit the measured results we can easily get QL and Qu. For the resonance mode at 0.132 THz, we get QL = 5 and 1 + β/2 = 17.3, yielding Qu = 86.5 at 6 K, and QL = 2.3 and 1 + β/2 = 2.7, yielding Qu = 6.2 at 26 K. Similarly, for the resonance mode at 0.418 THz, we get Qu = 36.6 at 6 K, and Qu = 22.35 at 26 K, respectively. With Nb film superconducting at 6 K and normal at 26 K, this remarkable improvement in Qu is expected. This result demonstrates that low loss can be achieved as the Nb film is in the superconducting state. The physical reason is clear because superconducting Nb film has a lower surface resistance Rs than that in the normal state. At 6 K, the complex conductivity of Nb film, σ, from the previous measurement are about (2-j6) × 105 Ω−1 cm−1 at 0.15 THz (close to 0.132 THz) and (1.2-j3) × 105 Ω−1 cm−1 at 0.45 THz . This gives Rs of 20.6 mΩ at 0.15 THz and 62.7 mΩ at 0.45 THz, respectively. The normal resistivity of Nb film just above Tc is about 4 μΩ• cm. This value is approximately equal to the one at 26 K since the normal resistivity in the low temperature is almost temperature independent. So, Rs at 26 K is about 154 mΩ at 0.15 THz and 266 mΩ at 0.45 THz, which are all much larger than the ones at 6 K. Therefore, the superconducting THz MM made of Nb film is a very nice candidate for low-loss THz devices.
We can get a lower loss if the working temperature is decreased further. However, it is hindered by the residual surface resistance of the film and the radiation loss of MM. As the temperature tends to zero, Rs approaches to a finite value, i.e., residual surface resistance, which is determined by the impurity in the superconducting films. The radiation loss is another important factor to be considered especially at THz since it is proportional to f4 . It cannot be reduced for fixed SRR structure, essentially limits the loss performance of THz MM. Hence, the fabrication of the film with lower density defects and the adjustment of the geometry of the unit cell will be further directions to reduce the loss of THz MM.
In addition to the low loss properties, DC magnetic field tuning of superconducting MM can be implemented. Figure 3(a) and Fig. 3(b) show respectively the transmission spectra at 6 K and different magnetic fields (0-1 Tesla) for two resonance modes. In Fig. 3(a), the resonance frequency decreases with the increase of the magnetic field and we can clearly see the shift of the transmission vs frequency curves until 0.7 T, above which all the transmission vs frequency curves tends to be the same and the resonance frequencies do not change any more. Similar changes can be seen in Fig. 3(b) except that the resonance frequency increases with the increase of magnetic field [compare Fig. 4(a) with Fig. 4(b)]. The physical reason of tuning is that the superconducting properties of Nb film, such as the magnetic penetration depth and critical current density, strongly depend upon Hdc [12,20]. When Hdc is large enough, superconductivity is quenched and the film goes normal. As a support to this argument, in Fig. 3(a) and Fig. 3(b) we use solid triangles to show the transmission data for the same sample but at 26 K and no magnetic field applied. These points scatter, very closely, around the transmission vs frequency curves for the sample at 6 K and with magnetic fields above 0.7T. This seems to suggest that the upper critical field of the sample is 0.7 T. Although we do not measure it experimentally, we believe this is a reasonable estimate because reported values of the critical field at low temperatures range from 1.0 T to 4.6 T  and at 6 K it should be in a range from 0.4 T to 1.8 T according to the temperature dependence of Hc2(T) = Hc2(0)(1-t2) /(1 + t2)  where t = T/Tc and T is the working temperature.
As mentioned above, the increase of the magnetic field may result in either the decrease or the increase of the resonance frequency (Fig. 4a and Fig. 4b). For the resonance mode at 0.132 THz, the frequency decreases with the increasing Hdc. The total frequency change is about 3 GHz. But, for the resonance mode at 0.418 THz, the frequency increases with Hdc with a total frequency change of about 20 GHz. The different tuning behaviors come from the different current distributions in these resonance modes. Figure 5 shows the simulated current distributions. For the resonance mode at 0.132 THz, there is a circulating current in the outer ring. In this case, this ring acts as an inductor and the gap is like a capacitor . The magnetic penetration depth of superconducting film increases with Hdc, leading to the increase of the inductor, and the decrease of the frequency. For the resonance at 0.418 THz, the current distribution is symmetric. The current in the outer ring has the same direction as the one in the adjacent outer ring, leading to attractive forces between them. As the film goes to the superconducting state, this attraction become larger and the current prefers to distribute in the outer edge of the outer ring. Effectively, the electric length of the outer ring is extended, and the resonance frequency is reduced.
In conclusion, we successfully demonstrated the low loss and magnetic field tuning superconducting THz MM. The unloaded Q values of the MM at 0.132 THz and 0.418 THz can reach 86.5 and 36.6, respectively. We hope our results can contribute to paving the way for making THz devices based on superconducting THz MM.
This work is supported by the MOST 973 project of China (No. 2007CB310404), the Program for New Century Excellent Talents in University (NCET-07-0414), Ministry of Education, China, and Qing Lan Program of JiangSu Province, China.
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