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We study the formation of local moments in a metallic host due to a localized spin-orbit (Rashba) interaction. Using the Anderson model we describe the occurrence of magnetic moments through calculation of the magnetic-non-magnetic phase transition within the mean-field scenario. We compare our results with those in the absence of the Rashba interaction. The symmetry and regime of the magnetic phase demonstrates a dependence on the above interaction. The conductance values through the impurities are also exhibited for the above phases.

The NMR relaxation rate is studied on the magnetic states of an impurity in bilayer graphene within a tight-binding scenario. The dependencies of the relaxation rate on temperature, interlayer interaction and also the chemical potential have been considered. Although for low temperatures we observe the usual Korringa relation, a characteristic of the conventional fermions, the rate increases with the increase in temperature and tends to saturate for high temperatures. For small interlayer interactions ( t ⊥ ) the system can be either magnetic or non-magnetic. However for higher t ⊥ we observe the existence of only a pure magnetic state. In graphene this transition is also observed with two cusps related to the magnetic to non-magnetic transition, which modifies to a single hump for higher t ⊥ , where the system is purely magnetic for any value of chemical potential.

We study the effect of a magnetic field on the d-density wave (DDW) in the presence of d x 2 - y 2 superconducting order parameter (DSC) for high-temperature cuprates using a mean-field calculation of the tight binding model. The phase diagrams for the order parameter with doping are discussed. The phase diagram of the field with filling and also the dependence of the critical field ( H c ) on the critical temperature ( T c ) have been considered. The temperature dependence of the specific heat is also demonstrated. The effect of the field on the DDW order parameter and the superconducting gap are not alike. While the field suppresses the DSC gap, it tends to increase the DDW gap at the same doping. Moreover the gap to T c ratio increases with the field. The critical field has a power law dependence ( H c – T c 2 ).