Lai, Liang-Shing, and 賴良星. "Study of Physical Properties of YBCO and Ca-YBCO Thin Films Using Microstrip Ring and Line Resonators." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/34479860965227823154.
Abstract:
博士<br>國立交通大學<br>電子物理系所<br>94<br>Superconducting microstrip ring and line resonators were successfully fabricated using double-side YBa2Cu3O7-δ (YBCO) and Y0.7Ca0.3Ba2Cu3O7-δ (Ca-YBCO) thin films deposited on LaAlO3 (LAO) substrates by pulsed laser deposition. By controlling the oxygen contents of the same resonator, the hole concentration p determined from the empirical relation, Tc/Tc,max=1-82.6(p-0.16)2, was controlled from the over- to the underdoped regime. The microwave surface impedance measurements, Zs(T) = Rs(T) + jXs(T), allow us to determine the complex conductivity, ��(T), in the ab-plane of YBCO and Ca-YBCO thin films. Using results of Zs(T) and ��(T) together with the modified two-fluid model, the doping and temperature dependences of London penetration depth, superfluid density and complex conductivity can be systematically studied. In particular, these experimental results can be used to test the current theoretical models of high-Tc superconductivity, especially for Lee’s model, Wen and Lee’s model, Emery and Kivelson’s model and Vishveshwara and Fisher’s model. Some salient results found in the dissertation are listed below:
I. From the measurements of the temperature dependence of resonance frequency in the microstrip ring and line resonators, the absolute values of the ab-plane London penetration depth at 5K were obtained for YBCO and Ca-YBCO thin films with various hole concentrations by using Chang’s formula together with the help of THz measurements. For example, was obtained to be at optimum doping, and this result was consistent with the one obtained from single crystal measurement ( ) or thin film measurement ( ).
II. In the underdoped regime, the measured superfluid density is proportional to critical temperature Tc. This relation has been revealed by the Uemura relation. However, for all doping levels (from over- to underdoped regime), the measured superfluid density is proportional to the product of critical temperature (Tc) and the d.c. conductivity at Tc. This universal relation can be explained by using Ferrell-Glover-Tinkham (FGT) sum rule. Furthermore, the doping dependence of the normalized superconducting energy gap can be obtained from the FGT sum rule. Compare to the doping dependence of the superconducting d-wave gap directly measured by scanning tunneling spectroscopy (STS), the doping dependence of is consistent with that measured by STS. This indirect evidence not only leads further support that the superconducting energy gap is of d-wave symmetry but also point out that the charge is conserved in the ab-plane of the cuprates.
III. The complex conductivity �� = ��1 - j��2 extracted from experiments together with the help of some theoretical model gives the evidence that the real part of complex conductivity, ��1, and the imaginary part of it, ��2, both have thermal activation gap. This result is consistent with the prediction of Lee’s model. It thus points out that the classical thermal fluctuations play an important role on physical properties of the high temperature state of high-Tc superconducting cuprates. Also, by fitting ��2 with , it was found that a characteristic energy scale emerges. is higher than Tc, when . The phase diagram of versus hole concentration p is similar to that predicted by Emery and Kivelson’s model. Hence, we propose that would be the upper bound on the phase ordering temperature in the underdoped regime, and in the overdoped regime, is corresponding to the mean field transition temperature .
IV. There are two cases for the temperature dependence of ��1 in the low temperature regime (T < 0.1 Tc). Case 1, ��1(T) reaches a plateau in the low temperature limit. Case 2, ��1(T) decreases with temperature in the low temperature limit. However, in both cases, ��1(T) contains a thermal activation gap . The meaning of the thermal activation gap in ��1(T) can be attributed to the energy barrier for quasiparticle tunneling in the weak-link structures. And also, in case 1, the cuprate is the thermal insulator in the superconducting state according to the Vishveshwara and Fisher’s model. But for case 2, the real part conductivity ��1(T) contains an extra linear-T contribution, which has been also observed for pure crystals, as reported by Hardy et al. We propose that the linear-T contribution is due to the delocalized quasiparticles free from the effects of weak links. According to Vishveshwara and Fisher, the delocalized quasiparticles would further result in the thermal metal phase in the superconducting state. Thus, for case 2, the ��1(T) results imply that there are two phases, the thermal-metal and the thermal-insulator, in the superconducting state of some samples displaying the clean limit behaviors similar to those observed in high purity single crystal. The fact reveals that the feature of is very sensitive to the degree of disorder in the cuprate samples.
V. As the temperature approaching 0 K, ��1(T) has a finite residual value, which we denoted as ��1(5K). According to Lee’s model, impurity scattering, particularly in the unitary limit, produces low energy quasiparticles in a two-dimensional d-wave superconductor even with small impurity concentrations. In our thin film samples, these quasiparticles are localized because the mean free path of quasiparticles ( ) is smaller than the localization length ( ). In this condition, the conductivity ��1(T) approaches to a universal value at , where is the coherence length and is the lattice constant. Moreover, Durst and Lee proposed a theoretical model based on Lee’s model that the universal value should be corrected by the Fermi liquid correction factor ��2 and the vertex correction factor , which accounts for the charge current renormalization and anisotropic impurity potential, respectively. Based on the residual conductivity ��1(5K) obtained in our experiments, we found that the value of is about 1.5±1.0, which is consistent with that predicted by the Durst and Lee’s model. In fact, we have observed that a flattening of the temperature dependence of in the low temperature limit, which is also consistent with that predicted by Lee’s model. All of these results revealed that the quasiparticles have the tendency of being localized in a two-dimensional superconductor with small impurity concentrations or disorder.
VI. The Fermi-liquid model, proposed by Wen and Lee in 1998 to describe the basic nature of low-lying excitations, was analyzed in a quantitative manner. The obtained Fermi-liquid correction factor, ��, was formed to be always smaller than one ( ) over the entire doping range (from underdoped to overdoped) and is almost independent of hole concentration p, which is consistent with that predicted by Wen and Lee’s model ( ). The results revealed that the basic nature of quasiparticles in the superconducting state can be attributed to the normal Fermi-liquid in all doping levels.
VII. The imaginary part of complex conductivity ��2(T) has a thermal activation gap , which shows the thermal-averaged Josephson coupling energy of superfluid (Cooper pairs) in forming the long range order across the barriers macroscopically.
VIII. A closed form of the empirical formula of the real part and the imaginary part is obtained respectively. From that, the phase diagram of several energy scales versus hole concentration p was presented. The phase diagram is very similar to the one predicted by Emery and Kivelson’s model based on the classical phase fluctuations on explaining the Cooper pair formation for high-Tc superconductors. We conjecture that the formation of superconducting state in the high-Tc superconducting thin films is owing to the phase fluctuations mechanism.
The experimental results have revealed that a number of the basic natures of quasiparticles in the superconducting state can be attributed to the normal Fermi liquid in the all levels of doping. When T > Tc, the classical phase fluctuations play a key role in forming the Cooper pairs of short range order. When T �� Tc, the superconductivity with a long range order is formed by the Josephson tunneling of superfluid (Cooper pairs). In the superconducting state (T < Tc), the ��2(T) was attributed to the effect of Josephson tunneling in the weak links in our disordered samples. However, for all of the experiments in the microwave measurements till now there are two cases for ��1(T). One of them is that ��1(T) can be completely attributed to the effect of quasiparticle tunneling in the weak links. It means that the quasiparticles are localized, and ��1(T) is in thermal insulator phase in the superconducting state. Another is that ��1(T) can be partly attributed to the effect of quasiparticle tunneling through the weak links, i.e. quasiparticles are localized, and partly attributed to the effect of delocalized quasiparticles. In this case, ��1(T) indicates that the system contains both the thermal insulator and the thermal metal phases. All of the above results have led us to the conjecture that in the HTSC, there are two different energy scales which correspond to two temperatures: Tc below which coherence is established, and some higher temperature where the pairs are formed. These two scales are close to each other, in the all levels of doping. The conjecture is also to endow the two associated superconducting phases - the thermal metal and the thermal insulator – and the critical point between them.