Electron tunnelling in metallic beads systems and slow electric relaxation

We study numerically and theoretically the electrical behavior of individual steel beads and the contact between 2 adjacent beads within a granular system. Due to the thin insulating oxide layer present at the surface of the beads, the coupling between neighboring beads is likely to occur through electron tunneling. The quantum tunneling dominates at low current where it generates a high resistance in the upwards characteristic. Retaining only fundamental ingredients such as modeling the tunneling contact as a parallel RC circuit, we show how our model agrees qualitatively and quantitatively with experimental results as the observed hysteretic features and the slow relaxation of the electrical properties of a large assembly of beads.