In this thesis we synthesize Pr1.85Ce0.15CuO4 system by mean of X-ray diffraction, electrical resistivity, magnetic susceptibility and low-temperature specific heat. From these data analysis, we hope to more clearly understand the transition of electron-doped superconductor Pr2-xCexCuO4 (0.14<x<0.7) system. The main results show that the system is d-wave pairing symmetry. This conclusion is consisted with C. C. Tsuei¡¦s result. They present phase-sensitive evidence that the electron-doped cuprates Pr1.85Ce0.15CuO4 have d-wave pairing symmetry.

Since the discovery of high superconducting transition temperature in layered copper oxides, many researchers have searched for similar behavior in other layered metal oxides, such as cobalt and nickel. The sodium cobalt oxyhydrate is the first cobalt-oxide layered superconductor. We present the studies of low-temperature specific heat C(T, H) in NaxCoO2¡EyH2O (x ~ 0.35, y ~ 1.3). At H = 0, a very sharp anomaly was observed at T ~ 4.7 K indicating the existence of bulk superconductivity. There exists an £\T2 term in C(T, H=0) in the superconducting state manifesting the line nodal superconducting order parameter. The feature at the superconducting transition is rather sharp, becoming broad and strongly suppressed in an applied magnetic field. The transition temperature also changed in an applied magnetic field. Thus an abrupt change of slope in H vs. Tc curve was observed. Possible scenarios such as the multiple phase transitions in the mixed state are discussed.

Conventional superconductor could be explained by BCS theory (for Tc<35K), but the BCS theory is not valid for all superconductors with theincrease of critical temperature (Tc) in the continuous discovery of new superconductors. Later on, other theories, such as d-wave, line nodes, the point nodes, the s +g wave, the two gap model, have been proposed. After successfully applying the two-gap model on MgB2, we try to measure the magnetic field dependence of low-temperature specific heat on 2H-NbSe2. Subsequently, analysis is focused on checking whether the two-gap model could also be applied to NbSe2 . Based on this model, the corresponding two gap values are obtained. The nonlinear field dependence of electronic specific heat coefficient is also observed. Moreover, the positive curvature in Hc2(T) is similar to that in the other two-gap superconductor MgB2. Thus, the two-gap model appears to describe the superconducting gap function of 2H-NbSe2 better than s-wave and line nodes models.