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

TL;DR

This paper demonstrates that classical memory effects cause a sharp magnetic field dependence of the Hall coefficient in 2D electron systems with strong scatterers, showing significant renormalization and sign change.

Contribution

The paper provides an analytical calculation of the magnetic field dependence of the Hall coefficient due to classical memory effects in 2D systems with strong scatterers, highlighting a novel sharp dependence.

Findings

Memory effects cause a significant renormalization of the Hall coefficient at weak magnetic fields.

The Hall coefficient's correction changes sign and saturates at higher magnetic fields.

The study discusses the influence of smooth disorder on the Hall coefficient dependence.

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 $n_0\ll1/a^2$. We demonstrate that in very weak magnetic fields ($\omega_c\tau \lesssim n_0a^2$) 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 $\delta R / R \sim -n_0a^2 .$ We also discuss the effect of the smooth disorder on the dependence of $R$ on $B$.