Theory of Infrared Hall Conductivity of Electron-doped Cuprates

It has been proposed by several experiments that the electron-doped cuprate Pr$_{2-x}$Ce$_x$CuO$_{4+\delta}$ undergoes a quantum phase transition to an antiferromegnetic state for the doping x smaller than 0.16. Here, we investigate the infrared Hall conductance of the electron-doped cuprates in the commensurate spin density wave state, using the linear response theory. The qualitative agreement between our results and the available experimental data provides strong evidence in favor of the spin density wave scenario and suggests that the magnitude of the gap is large, while quantitative discrepancies point towards additional physics which may be related to scattering of carriers off spin fluctuations. We also discuss the Hall conductivity sum rule and its connection to the experiments.