HALL CONDUCTIVITY FOR 2-DIMENSIONAL MAGNETIC SYSTEMS

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a ga s of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (P auli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is wor ked out in detail. This system happens to display a transverse Hall co nductivity (P breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequencies Like 1/omega(2). A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the pl ane). At first order in perturbation theory, the Hall conductivity dis plays oscillations close to the classical straight line conductivity o f the mean magnetic field. (C) 1997 Elsevier Science B.V.