Narrow Results

Using a model spectral function of the electron, the Hall conductivity in the normal metallic state of the Pr${}_{2-x}$Ce_xCuO₄ (PCCO) superconductor is calculated neglecting the current vertex-correction. The result is qualitatively consistent with the experiment. Consequently, the reason becomes clear why the Fermi-liquid theory fails to explain the anomaly of the Hall conductivity. The inconsistency of the fluctuation-exchange approximation also becomes clear.

Recently, the measurement of the polar Kerr effect (PKE) in the quasi two-dimensional superconductor Sr₂RuO₄, which is motivated to observe the chirality of p_x + ip_y-wave pairing, has been reported. We clarify that the PKE has intrinsic and extrinsic (disorder-induced) origins. The extrinsic contribution would be dominant in the PKE experiment.

In this paper we study the electron energy spectrum corresponding to Landau levels in doped graphene when an external magnetic field is applied in the direction normal to the graphene planar sheet. The derived dispersion relation for the electrons in the doped graphene allows us to determine the dependence of the electrical conductivity on the applied magnetic field. This relationship between electrical conductivity and applied magnetic field is further analyzed for different characteristics of the impurities; specifically the potential of hybridization and the energy of the adsorbed atom.

We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating the spin Hall conductivity. Focusing on the high frequency regime, we obtain a diagonalized Hamiltonian. After getting the corresponding spectrum, we show that there is a Hall conductivity without an external magnetic field, which is noncommutativity parameter θ-dependent. This allows us to make contact with the spin Hall effect and also give different interpretations. Fixing θ, one can recover three different approaches dealing with the phenomenon.