Effects of Coulomb screening and disorder on artificial graphene based on nanopatterned semiconductor

TL;DR

This paper analyzes how Coulomb screening and disorder affect the creation of artificial graphene in nanopatterned semiconductor heterostructures, identifying design strategies to minimize disorder effects and optimize system performance.

Contribution

It provides a detailed analysis of disorder types in nanopatterned heterostructures and formulates design criteria to reduce disorder impact for artificial graphene creation.

Findings

Area disorder causes puddle formation, significantly affecting system properties.

Weak coupling regime with quantum anti-dots is less susceptible to disorder.

Parameter variations can change puddle amplitudes by orders of magnitude.

Abstract

A residual disorder in the gate system is the main problem on the way to create artificial graphene based on two-dimensional electron gas. The disorder can be significantly screened/reduced due to the many-body effects. To analyse the screening/disorder problem we consider AlGaAs/GaAs/AlGaAs heterostructure with two metallic gates. We demonstrate that the design least susceptible to the disorder corresponds to the weak coupling regime (opposite to tight binding) which is realised via system of quantum anti-dots. The most relevant type of disorder is the area disorder which is a random variation of areas of quantum anti-dots. The area disorder results in formation of puddles. Other types of disorder, the position disorder and the shape disorder, are practically irrelevant. The formation/importance of puddles dramatically depends on parameters of the nanopatterned heterostructure. A variation of the parameters by 20--30\% can change the relative amplitude of puddles by orders of magnitude. Based on this analysis we formulate criteria for the acceptable design of the heterostructure aimed at creation of the artificial graphene.