The main focus of this thesis is the study of transport properties [thermomagnetic (Nernst) and thermoelectric (Seebeck) effects, Hall effect and magentoresistance in high magnetic field up to 58 T] of the electron-doped cuprate superconductor system Pr${2-x}$Ce${x}$CuO$_{4-\delta}$. One chapter of this thesis is devoted to a study of the vortex Nernst effect in Pr doped YBa$_2$Cu$3$O${7-\delta}$ films.

Electron-doped cuprate superconductors have demonstrated many distinct properties from their hole-doped counterparts. A few of them are investigated in this thesis. For example, by taking advantage of the low upper critical field, we investigated the field driven normal state thermoelectric power at low temperature in Pr${2-x}$Ce${x}$CuO$_{4-\delta}$ films with various doping. We observed an abrupt change of low temperature thermopower at a critical doping \textit{x}=0.16. The kink behavior in the doping dependent thermopower and the previously reported normal state Hall coefficient can be correlated via a simple model, strongly suggesting a Fermi surface rearrangement at the critical doping. This is taken as a further evidence for a quantum phase transition in the electron-doped cuprate superconductors.

Prior vortex Nernst effect measurements have shown a weak superconducting fluctuation effect in electron-doped cuprates, suggesting a more conventional superconductivity. We measured Nernst effect carefully through the entire range of doping and temperature. A stronger superconducting fluctuation effect is observed in the underdoped region compared to the overdoped region. This behavior is similar but weaker than in hole-doped cuprates. We explain this as a result of the incoherent phase fluctuations.

The large normal state Nernst effect observed around optimal doping in electron-doped cuprates has been interpreted as a result of two-carrier transport. Our thorough Nernst effect measurements have revealed a fairly large Nernst signal at the doping extremes (slightly underdoped and highly overdoped) in the normal state, implying that the band structure at these dopings is not a simple one carrier Fermi pocket as suggested by the photoemission experiments.

Hall effect and magnetoresistance measurements in pulsed magnetic field (58 T) were performed on Pr${2-x}$Ce${x}$CuO$_{4-\delta}$ films. A strong non-linear field dependent Hall resistivity is observed for doping \textit{x} above optimal doping in a certain temperature range, while the linearity persists up to 58 T in the underdoped region at all measured temperatures. Concomitant with the crossover of field dependent magnetoresistance in the overdoped regime, a spin density wave model is adapted to qualitatively explain the high field Hall effect. These results also imply that a quantum phase transition occurs under the superconductivity dome in electron-doped cuprates.

We also systematically measured the resistive superconducting transition in the electron-doped cuprates Pr${2-x}$Ce${x}$CuO${4-\delta}$ down to 1.5 K for magnetic field up to 58 T applied parallel to the conducting ab-planes. We found that the zero temperature parallel critical field (H${c2\parallel ab}$(0)) exceeds 58 T for the underdoped and optimally-doped films. For the overdoped films, 58 T is sufficient to suppress the superconductivity. We also find that the Zeeman energy $\mu_B$H${c2\parallel ab}$(0) reaches the superconducting gap ($\triangle_0$), i.e., $\mu_B$H${c2\parallel ab}(0)\simeq \triangle_0$, for all the dopings, strongly suggesting that the parallel critical field is determined by the Pauli paramagnetic limit in electron-doped cuprates.

Measurements of Nernst effect, resistivity and Hall angle on epitaxial films of Y$_{1-x}$Pr$_x$Ba$_2$Cu$3$O${7-\delta}$ (Pr-YBCO, 0$\leq x\leq$0.4) were performed over a broad range of temperature and magnetic field. While the Hall and resistivity data suggest a broad pseudogap regime in accordance with earlier results, these first measurements of the Nernst effect on Pr-YBCO show a large signal above the superconducting transition temperature T$_c$. This effect is attributed to vortex-like excitations in the phase incoherent condensate existing above T$_c$. A correlation between disorder and the width of the phase fluctuation regime has been established for the YBCO family of cuprates, which suggests a T$_c\simeq$110 K for disorder-free YBa$_2$Cu$3$O${7-\delta}$.