Low magnetic field anomaly of the Hall effect in disordered 2D systems: Interplay between weak localization and electron-electron interaction

The nonlinear behavior of the Hall resistivity at low magnetic fields in single quantum well GaAs/In$_x$Ga$_{1-x}$As/GaAs heterostructures with degenerated electron gas is studied. It has been found that this anomaly is accompanied by the weaker temperature dependence of the conductivity as compared with that predicted by the first-order theory of the quantum corrections to the conductivity. We show that both effects in strongly disordered systems stem from the second order quantum correction caused by the effect of weak localization on the interaction correction and vice versa. This correction contributes mainly to the diagonal component of the conductivity tensor, it depends on the magnetic field like the weak localization correction and on the temperature like the interaction contribution.