Coherent transport in linear arrays of quantum dots: the effects of period doubling and of quasi-periodicity

TL;DR

This paper investigates phase-coherent electron transport in linear quantum dot arrays with periodic and Fibonacci quasi-periodic arrangements, revealing a metal-insulator transition in periodic arrays and pseudo-gaps in Fibonacci sequences.

Contribution

It introduces a decimation-renormalization method to analyze transport in quantum dot arrays, highlighting the effects of period doubling and quasi-periodicity on electronic properties.

Findings

Periodic arrays undergo a metal-insulator transition near single occupancy.

Fibonacci arrays exhibit prominent pseudo-gaps away from the band center.

Transport properties correlate with density of states in both array types.

Abstract

We evaluate the phase-coherent transport of electrons along linear structures of varying length, which are made from two types of potential wells set in either a periodic or a Fibonacci quasi-periodic sequence. The array is described by a tight-binding Hamiltonian and is reduced to an effective dimer by means of a decimation-renormalization method, extended to allow for connection to external metallic leads, and the transmission coefficient is evaluated in a T-matrix scattering approach. Parallel behaviors are found for the energy dependence of the density of electron states and of the transmittivity of the array. In particular, we explicitly show that on increasing its length the periodic array undergoes a metal-insulator transition near single occupancy per dot, whereas prominent pseudo-gaps emerge away from the band center in the Fibonacci-ordered array.