| In this thesis, I will describe our work on understanding the transport properties of two-dimensional spin-density-wave (SDW) systems, with potential application to the high-temperature copper-oxide superconductors.;We first demonstrate a mean-field calculation of the T → 0 limit of the Hall conductance of electron-doped cuprates such as Pr 2-xCexCuO4. In our model, as varying the doping x, there is a quantum phase transition at xc ≈ 0.16 from a state with the long-range commensurate SDW order at x < xc which is treated in the mean-field approximation to a normal Fermi liquid state at x > xc. Our results are found to be qualitatively in agreement with data for x < xc. Besides, the Hall conductance exhibits a non-analyticity at the quantum critical point for density wave ordering. To account for the experimental data for x > xc, we calculate the renorrnalization to the electron dispersion due to scattering from spin fluctuations in the leading order perturbation theory.;Next, we describe a mean-field calculation of the T → 0 limit of the Hall effect of stripe-ordered cuprates such as La 2-x-yNdySrxCuO4. We use a model in which, as varying doping x, there is a quantum phase transition at xc ≈ 0.24 from the long-range anti-phase stripe ordered state at x < x c, which is again treated at the mean-field level, to a normal Fermi liquid state at x > xc. We find that, by varying the stripe potential, the Hall effect can be strongly enhanced from the band value or can be made negative (with the electron-like sign), in semi-quatitative agreement with data. We also considered the case of strong stripe potential, such that the electron motion is quasi-one-dimensional. We find that the Hall effect depends on the details of the model parameters.;Then, we consider the calculation of the infrared Hall conductivity sigma xy(o) in a two-dimensional system with commensurate SDW order which is treated in the mean-field approximation. We use the linear response theory, and find that when the amplitude of the SDW gap value Delta is small, Imsigmaxy(o) remains positive in the whole frequency range, while when Delta is large, Imsigmaxy(o) is negative at small o, and positive at large o, with a zero-crossing at w∼Delta. This finding qualitatively agrees with experimental data on the electron-doped cuprates Pr2-xCexCuO4.;Then, we describe the use of the spin-fermion model to study the electron transport for two-dimensional systems close to antiferromagnetic ordering. We use, for the spin-spin correlation function, the phenomenological form proposed by Millis, Monien and Pines, and focus on the effects of thermal spin fluctuations. We argue that the Migdal's theorem is not applicable, and use perturbation theory to calculate the electron self-energy. We argue that in order to calculate the conductivity and the Hall conductivity, the current vertex corrections are not negligible, and show how to calculate the vertex corrections properly. We find that the conductivity and the Hall conductivity both show optical peaks which are precursors to the peaks in the state with SDW ordering. The DC conductivity has an unphysical suppression which we believe is an artifact of our approximation.;Finally, we study the effects of fluctuations around the long-range SDW order on the electron dynamics. Since the order parameter of the SDW order is a vector, the transverse fluctuations are massless Goldstone modes. We show that the scattering from long-wavelength transverse fluctuations is irrelevant, and that at zero or low temperatures, the transport properties are described by the Fermi liquid theory, provided that the system is not in the immediate vicinity of the quantum critical point. |
