Equilibrial Charge of Grains and Low-temperature Conductivity of Granular Metals

TL;DR

This paper investigates the low-temperature equilibrium state of granular metals, revealing that grain charging arises from surface energy fluctuations rather than quantum state quantization, leading to a gapless insulating behavior with charge transport governed by charging energy.

Contribution

It introduces the concept of a gapless Hubbard insulator where charge fluctuations dominate over quantum state quantization, providing new insights into low-temperature conductivity of granular metals.

Findings

Grains are charged due to surface energy fluctuations, not quantization.

The system exhibits a gapless insulating state with finite energy for electron transfer.

Hopping transport is governed by charging energy, leading to gapless conduction at low temperatures.

Abstract

The low-temperature equilibrial state of a system of small metal grains, embedded into insulator, is studied. We find, that the grains may be charged due to the fluctuations of the surface energy of electron gas in grains, rather than quantization of electron states. The higherst-occupied level in a grain fluctuates within the range of order of charging energy below the overall chemical potential. The system, called a gapless Hubbard insulator, has no overall energy gap, while the transfer of an electron on finite distances costs finite energy. The ionization energy is determined mostly by the intragrain Coulomb repulsion, rather than a weak intergrain interaction, responsible for the Coulomb gap. The hopping transport in the system is studied. The hopping energy is determined by the charging energy. At low temperature the transport has gapless character.