Theory of the Hall Effect in Disordered Systems: Impurity-Band Conduction

Abstract

A general quantum-mechanical formula for the low-field Hall effect is derived in the density matrix approach, thus making it possible to treat this effect in disordered systems. With some assumptions about the one-electron matrix elements involved, the Hall and ordinary conductivities are correlated for the impurity-band conduction in the "metallic range." According to our results, the sign of the Hall effect depends on the degree of filling of the impurity band.