Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons

TL;DR

This paper investigates how density inhomogeneity causes a percolation-driven metal-insulator transition in graphene nanoribbons, revealing a dimensional crossover from 2D to 1D behavior and confirming the transition through conductivity measurements.

Contribution

It predicts a density inhomogeneity driven percolation transition in graphene nanoribbons and identifies a dimensional crossover in the transport behavior, supported by experimental consistency.

Findings

Percolation transition in graphene nanoribbons at low density

Dimensional crossover from 2D to 1D in narrow ribbons

Consistency of measured exponents with percolation theory

Abstract

Transport in graphene nanoribbons with an energy gap in the spectrum is considered in the presence of random charged impurity centers. At low carrier density, we predict and establish that the system exhibits a density inhomogeneity driven two dimensional metal-insulator transition that is in the percolation universality class. For very narrow graphene nanoribbons (with widths smaller than the disorder induced length-scale), we predict that there should be a dimensional crossover to the 1D percolation universality class with observable signatures in the transport gap. In addition, there should be a crossover to the Boltzmann transport regime at high carrier densities. The measured conductivity exponent and the critical density are consistent with this percolation transition scenario.