Electron transport in two-dimensional arrays

TL;DR

This paper investigates charge transport in two-dimensional granular arrays, revealing a Berezinskii-Kosterlitz-Thouless transition from conducting to insulating states influenced by temperature and gate voltage, with a theoretical framework based on charge-phase correspondence.

Contribution

It introduces a theoretical analysis of the BKT crossover in 2D granular arrays, connecting charge and phase models using instanton gas summation.

Findings

Identifies a BKT transition at a critical temperature T_{BKT} rom conducting to insulating state.

Shows gate voltage can induce a transition from insulator to conducting charge liquid and then to a Wigner crystal.

Establishes a theoretical framework linking charge and phase representations in granular arrays.

Abstract

We study charge transport in a granular array with high inter-grain conductances. We show that the system exhibits a Berezinskii-Kosterlitz-Thouless crossover from the high-temperature conducting state into a low-temperature insulating state. The crossover takes place at a critical temperature T_{BKT} \propto E_c exp{-g}, where E_c is the charging energy of a grain and g >> 1 is the dimensionless inter-grain conductance. A uniformly applied gate voltage drives the insulator into a conducting charge liquid state followed by an insulating lattice-pinned Wigner crystal state at larger values of the gate voltage. Technically, we establish correspondence between the charge and phase representations, employing the instanton gas summation in the framework of the phase model.