Sharp Magnetic Field Dependence of the 2D Hall Coefficient Induced by Classical Memory Effects

Abstract

We show that a sharp dependence of the Hall coefficient $R$ on the magnetic field $B$ arises in two-dimensional electron systems with randomly located strong scatterers. The phenomenon is due to classical memory effects. We calculate analytically the dependence $R(B)$ for the case of scattering by hard disks of radius $a$, randomly distributed with concentration $n_0\ll 1/a^2$. We demonstrate that in very weak magnetic fields (${\omega }_c\tau \lesssim n_0{a}^2$) memory effects lead to a considerable renormalization of the Boltzmann value of the Hall coefficient: $\delta R/R\sim 1.$ With increasing magnetic field, the relative correction to $R$ decreases, then changes sign, and saturates at the value $\delta R/R\sim -n_0{a}^2.$ We also discuss the effect of the smooth disorder on the dependence of $R$ on $B$.