Weak Localization in Metallic Granular Media

TL;DR

This paper studies how weak localization affects electrical conductivity in metallic granular media, revealing a temperature-dependent crossover where the system transitions from behaving like a continuous medium to a regime dominated by single-junction effects.

Contribution

It demonstrates the crossover behavior of weak localization correction in granular metals and connects phase relaxation time with electron dwell time in grains.

Findings

Weak localization correction exhibits a crossover at temperature T~g_T^2δ.

Below the crossover, the array behaves as a continuous medium.

Above the crossover, weak localization is dominated by single-junction effects.

Abstract

We investigate the interference correction to the conductivity of a medium consisting of metallic grains connected by tunnel junctions. Tunneling conductance between the grains, $e^2g_{\rm T}/\pi\hbar$, is assumed to be large, $g_{\rm T}\gg 1$. We demonstrate that the weak localization correction to conductivity exhibits a crossover at temperature $T\sim g^2_{\rm T}\delta$, where $\delta$ is the mean level spacing in a single grain. At the crossover, the phase relaxation time determined by the electron-electron interaction becomes of the order of the dwell time of an electron in a grain. Below the crossover temperature, the granular array behaves as a continuous medium, while above the crossover the weak localization effect is largely a single-junction phenomenon. We elucidate the signatures of the granular structure in the temperature and magnetic field dependence of the weak localization correction.