Two-dimensional magnetic Hamiltonians

Two-dimensional magnetic Hamiltonians : Hall conductivity, persistent currents, magnetization

Electronic transport: Study of the Hall conductivity for a gas of electrons submitted to a random magnetic field

A 2d model for an electron submitted to the random magnetic field created by a set of point-like magnetic vortices randomly distributed was studied by Desbois, Furtlehner & Ouvry (Nucl.Phys.B453, 1995). Since the electron only feels the Aharonov-Bohm vector potential of the vortices, this model has no classical counterpart. The spectral properties of the model were studied by Desbois et al. by using the relation with the some winding properties of the planar Brownian motion. It was shown that, in the limit where the flux carried by the vortices tends to zero, the spectrum is reminiscent of a Landau spectrum with broadened Landau levels.

In the next article we study the electronic transport in this model. The Hall conductivity is analyzed by some perturbative arguments.

  • Jean Desbois, Stéphane Ouvry and Christophe Texier,
    Hall conductivity for two-dimensional magnetic systems
    Nucl. Phys. B 500 [FS], (1997), 486-510.
    cond-mat/9612080.
  • Jean Desbois, Stéphane Ouvry and Christophe Texier,
    Hall conductivity in the presence of repulsive magnetic impurities
    Eur. Phys. J. B 7, (1999), 527-528.
    cond-mat/9807243.

Persistent currents and magnetization for two-dimensional magnetic Hamiltonians

Definition of persistent current in 2d systems is analyzed. Orbital and spin contributions are defined. Relation with magnetization is discussed.

  • Jean Desbois, Stéphane Ouvry and Christophe Texier,
    Persistent currents and magnetization in two-dimensional magnetic systems
    Nucl. Phys. B 528 [FS], (1998), 727-745.
    cond-mat/9801106.

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