Numerical investigation of the Hall effect in disordered materials

We undertake a systematic numerical study of the Hall effect in substitutionally disordered binary alloys and topologically disordered systems simulated by a molecular dynamics algorithm. As a Hamiltonian model, we use a tight-binding one with a set of explicit s-type orbitals. To compute the Hall coefficient, we numerically evaluate the appropriate Kubo–Greenwood formulae for the longitudinal and Hall conductivities in finite systems. We focus particularly on the sign of the Hall coefficient and obtain positive values for the Hall conductivity when the scattering is only s-type both in substitutionally and topologically disordered systems, in the weak and strong scattering regimes. Then, we establish that the already observed correlation between the sign of the Hall coefficient and the sign of the energy-derivative of the density of states is valid only for substitutionally disordered alloys in the weak scattering regime. We also found that localized states play a role in determining the positive sign of the Hall coefficient in topologically disordered systems.