利用環形共振器研究釔系高溫超導薄膜之微波物理性質

Abstract

我們成功地研發在鋁酸鑭(LAO)基板的上、下二面蒸鍍釔鋇銅氧（YB2Cu3O7-d）之高溫超導薄膜技術，並將薄膜研製成有隙縫或沒有隙縫之超導環形共振器。量測其微波表面阻抗，Zs(T) = Rs(T) + jXs(T)，可獲知在ab平面上的複數導電率s(T)。利用上述之結果，輔以二流體模型，我們可獲知倫敦穿透深度及準粒子(quasiparticle)散射之鬆弛時間對溫度和頻率的關係。同時為了進一步瞭解不同氧含量對於同一樣品之物理特性的影響，我們針對此樣品作了一系列氧含量變化的研究，其結果如下： I.從量測環形共振器之共振頻率的變化，可估算基板之介電常數。在5K時，我們獲得LAO基板之介電常數為25.7。 II.我們在環形共振器耦合線的對稱位置，蝕刻一個窄的隙縫，發現原有之共振頻率將因此而分裂，此分裂的共振頻率分別位於1/2和3/2倍原來共振頻率(環形共振器)的位置。分析以上共振頻率的變化，可輕易的驗證在同一微結構下，其物理特性隨頻率之變化。此外，我們還應用等效互感模型來說明此一共振頻率分裂結果。由於模型準確性，使吾人得以證實表面損耗與w2成正比。 III.(a) YBCO薄膜環形共振器在滿氧(d = 0.05)的狀態下，其品質因子在15 K時達到一萬單位以上。同時其穿透深度Dl(T) = l(T) - l(5K) 對溫度(T < Tc/3)的變化維持線性增加之關係(Dl/T = 4.8 Å/K)；當YBCO樣品之氧含量逐漸的減少時（例如d = 0.2，0.4），此線性關係依舊不變，但隨著氧缺陷的增加其Dl/T之斜率因而變大。 (b) 依據Scalapiano之模型，可獲致能隙對臨界溫度的關係。在微波量測上，我們獲得此比例常數為2D(0)/kBTc = 5.3 ± 1.4，而且此結果與樣品之氧原子缺陷無關。 (c) 在不同之氧含量下，樣品的穿透深度l(T)對歸一化溫度T/Tc展示一致化結果，這顯示YBCO樣品之高溫超導的機制主要由氧化銅平面所操控。此外，我們也獲得樣品在不同氧含量下之l(5K)的大小，分別為：l(5K) = 150±14 (d = 0.05)、216±16 (d = 0.2)和 282±20 nm (d = 0.4)；並發現共振頻率改變不致對其造成影響。 IV.在我們的研究裡，準粒子的散射速率與歸一化溫度T/Tc存在著指數的關係：1/t(T) µ eaT/Tc。此外，在低溫(5K)時其鬆弛時間t大約是3.76 ´ 10-11秒，此數值較臨界溫度時高了500倍。利用測不準原理估計此散射時間所對應之能量大約為1.75 ´ 10-2 mev。 V.導電率s1(T)在低溫時不再明顯隨溫度變化而趨平，此與YBCO單晶所獲得之結果迥異，可能是因為我們所製作的樣品薄膜在ab平面上有許多的錯位分佈，此錯位的缺陷在低溫時對準粒子的散射影響較大。此外，殘留導電率會隨著氧含量的摻雜濃度(underdoped)變化。 VI.Wen及Lee理論估算高溫超導體之費米液體修正常數a2約為0.5附近，這表示準粒子係為一不正常費米液體。此外，當氧含量摻雜濃度改變，其高溫超導的機制或許為單一玻色凝態(single Boson condensation)的結果。

Superconducting ring resonators with or without a gap were successfully fabricated using double-side YBa2Cu3O7-δ (YBCO) films deposited on LaAlO3 (LAO) substrates. Measurement of the microwave surface impedance, Zs(T) = Rs(T) + jXs(T), allows us to determine the complex conductivity, s(T), in the ab-plane of YBCO thin films. Using results of Zs(T) and s(T) together with the modified two-fluid model, the temperature and frequency dependences of London penetration depth and quasiparticle scattering lifetime can be systematically studied by varying the oxygen contents of the same resonator structure. Some salient results found in the dissertation are listed below: I.Form the measurement of the resonance frequency and thus the phase velocity in the ring resonator the dielectric constant of the LAO substrate was estimated to be er @ 25.7 at 5 K. II.By placing a narrow gap located at symmetrical position with respect to the coupling lines in the ring resonator, we observed that original fundamental resonating modes splits into a dual-mode with different resonating frequencies. One occurs at one half and the other at three halves of the original frequency, respectively. It leads us to easily provide some behaviors of frequency dependence of several physical quantities with the same microstructure in a unique manner. Moreover, an equivalent mutual-inductance circuit model is suggested to account for the occurrence of the dual mode resonance. The validity of the model let us easily give the justification of the relation between the surface loss and frequencies, i.e., Rs µ w2. III.(a) For fully oxygenated case (d = 0.05), the resonator exhibits a quality factor Q > 104 around 15 K, and Dl(T) = l(T)-l(5K) displays a linear behavior (Dl/T = 4.8 Å/K) at the low temperature regions (T < Tc/3). With increasing d (e.g. d = 0.2, 0.4), although Dl is still linear in temperature, the slope changes with increasing oxygen deficiency. (b) Following the model suggested by Scalapiano et al., the energy gap could be derived and the value of the ratio of energy gap to the critical temperature, we found 2D(0)/kBTc, around 5.3±1.4, which is independent of the doping concentrations. (c) The function of l(T) versus the normalized temperature T/Tc exhibits a universal form. It implies a unique high-Tc mechanism in the underdoped cuprate, which is occurred in the CuO2 planes only. The values of l(5K) with various oxygen contents are 150±14 (d = 0.05), 216±16 (d = 0.2) and 282±20 nm (d = 0.4), respectively and found to be independent of frequencies. IV.The scattering rate of the low-excitation quasiparticles versus normalized temperature appears as a universal exponential form, 1/t(T) µ eaT/Tc. The relaxation time in the low temperature limit is around t @ 3.76 ´ 10-11 sec, which is 500 times more than that at the critical temperature. Then the energy due to such scattering from the uncertainty principle is found to be around 1.75 ´ 10-2 mev. V.The real part of the complex conductivity s(T) after reaches a plateau in the low temperature limit. The effect is clearly contradicted to that found by a single crystal. We prospect that it might be a lot of dislocation distributed in the ab plane for our samples thin films. Such defect of dislocation takes a great effect on the quasiparticle scattering in the low temperature limit. We also found that the residual conductivity depends upon the doping concentration of oxygen contents. VI.The current model suggested by Wen and Lee was analyzed in a quantitative manner. We noted that the Fermi-liquid correction factor, a2, predicted by the model could be obtained with the values around 0.5, which might correspond to prospect the mechanism of high-Tc in the underdoped case to be a single Boson condensation possibly.