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

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

2007-08-23

arxiv.org/abs/0708.3165v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevB.77.193308

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 $B$.

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