Magnetic field induced directional localization in a 2D rectangular lattice

We study the effect of a perpendicular uniform magnetic field on the dissipative conductivity of a rectangular lattice with anisotropic hopping, $t_x\mathrm{\ne }{t}_y$. We show that the magnetic field may enhance dramatically the directional anisotropy in the conductivity. The effect is a measurable physical realization of Aubry’s duality in Harper systems.