The Hall effect in simple glassy structures

Abstract

The authors compute the Hall conductivity in a variety of model disordered two-dimensional systems by numerically evaluating the appropriate Kubo-Greenwood formula. Their models range from substitutional binary alloys to topologically disordered 'glasses', and include systems where the disorder is caused by the random small displacements of atoms from their positions in a crystalline lattice. Their Hamiltonian is reminiscent of the Kronig-Penney model in that delta -function-like atomic potentials are specified by a single parameter. The authors focus particularly on the sign of the Hall coefficient, and establish that the sign can be positive even when there is no well-defined dispersion relation for the electrons. They observe a correlation between the Hall coefficient and the derivative of the density of electron states.