Inelastic electron transport in granular arrays

TL;DR

This paper investigates the low-temperature transport behavior of granular arrays, revealing insulating states at low coupling and a BKT transition to conduction at higher coupling in 2D systems, using instanton analysis.

Contribution

It introduces a dual charge representation approach to analyze Coulomb blockade effects in granular arrays, highlighting a BKT transition in 2D systems.

Findings

Arrays are insulating at low temperatures for any inter-grain coupling.

A BKT transition to conduction occurs in 2D arrays at a specific temperature.

Instanton analysis effectively maps phase and charge descriptions of granular systems.

Abstract

Transport properties of granular systems are governed by Coulomb blockade effects caused by the discreteness of the electron charge. We show that, in the limit of vanishing mean level spacing on the grains, the low-temperature behavior of 1d and 2d arrays is insulating at any inter-grain coupling (characterized by a dimensionless conductance g.) In 2d and g>>1, there is a sharp Berezinskii-Kosterlitz-Thouless crossover to the conducting phase at a certain temperature, T_{BKT}. These results are obtained by applying an instanton analysis to map the conventional `phase' description of granular arrays onto the dual `charge' representation.