Hall Conductivity for Two Dimensional Magnetic Systems

Details Hall Conductivity for Two Dimensional Magnetic Systems Hall Conductivity for Two Dimensional Magnetic Systems

1996-12-09

arxiv.org/abs/cond-mat/9612080v1

Nucl.Phys. B500 (1997) 486

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

28 pages, latex, 2 figures

Scientific paper

10.1016/S0550-3213(97)00395-7

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas 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 (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity ($P$ breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like $1/\omega^2$. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.

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