Density of States and Conductivity of Granular Metal or Array of Quantum Dots

TL;DR

This paper explains the temperature-dependent conductivity in granular metals and quantum dot arrays by showing how doping-induced charge fluctuations create a soft Coulomb gap, with effects varying by array density.

Contribution

It demonstrates how doping-induced charge randomness leads to a soft Coulomb gap and causes oscillations in conductivity behavior in sparse quantum dot arrays.

Findings

Doping causes random charging and finite density of states at the Fermi level.

In sparse arrays, density of states oscillates with donor concentration.

In dense arrays, the density of states is smeared due to multiple donors per dot.

Abstract

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.