With AC microwave measurements from 10 MHz up to 50 GHz and DC nano-volt level measurements we have investigated the superconducting phase transition of YBa ₂ Cu ₃ O _7-δ films in zero magnetic field and electrical transport properties of single walled carbon nanotube networks. We studied the microwave conductivity of YBa ₂ Cu ₃ O _7-δ thin films around T_c for different incident microwave power and observed that the microwave fluctuation conductivity deviates from scaling theory at low frequency around T_c. We systematically investigated the length scales involved in AC measurements and found the probed length scale depends on both frequency and current. At low current density J but high frequency ω, we observed critical behavior without hindrance from finite-size effects. However, at low current density J and low frequency ω, the experimentally probed length scale L_AC may approach the thickness d of the sample, and then the critical behavior will be destroyed by finite-size effects. In this regime, we can not observe the phase transition.

With very small applied microwave power, specifically -46dBm, and high frequency data, we have investigated the critical fluctuations of YBa₂ Cu ₃ O _7-δ thin films around T_c. It is shown that the determination of T_c is crucial for obtaining critical exponents. Improved temperature stability and conductivity calibration allow us to take high quality data at small temperature intervals (50mK). This improves the conventional data analysis method and allows a new method of extracting exponents to be developed. With these two methods, consistent values of T_c and the critical exponent were precisely determined. Experiments on 6 samples have been done and the results give a dynamical scaling exponent z=1.55±0.15. The scaling behavior of the fluctuation conductivity is also established.

We have also investigated fluctuation effects of YBa₂ Cu ₃ O _7-δ by doing frequency-dependent microwave conductivity measurements and dc current-voltage characteristics on the same film. The dc measurement verified that the applied microwave power -46dBm in our ac measurement is small enough for the correct determination of T_c and critical exponents. For both dc and ac experiments the scaling behavior of the data was investigated. We found that the dc measurement could be affected by disorder. For high quality YBCO films and crystal, the critical exponent z is also around 1.5, which is consistent with ac measurement.

Finally, using our broadband experimental technique and DC current-voltage characteristic measurement system, we measured the transport properties of single-walled carbon nanotube films. Based on the real and imaginary parts of the microwave conductivity, we calculated the shielding effectiveness for various film thickness. Shielding effectiveness of 43 dB at 10 MHz and 28 dB at 10 GHz is found for films with 90% optical transmittance, which suggests that single walled carbon nanotube(SWCNT) films are promising as a type of transparent microwave shielding material. We also investigated the frequency and electric field dependent conductivity of single walled carbon nanotube networks of various densities. We found the ac conductivity as a function of frequency follows the extended pair approximation model and increases with frequency above an onset frequency ω₀ which varies over seven decades with a range of film thickness from sub-monolayer to 200 nm. The nonlinear electric field-dependent conductivity shows strong dependence on film thickness as well. Measurement of the electric field dependence of the resistance allows for the determination of the localization length scale L of localized states, which is found to systematically decrease with increasing film thickness. The onset frequency ω₀ of enhanced ac conductivity and the localization length scale L of SWCNT networks are found to be correlated, and an empirical formula relating them has been proposed. Such studies will help the understanding of transport properties and broaden the applications of this novel material system.