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A residual disorder in the gate system is the main problem on the way tocreate artificial graphene based on two-dimensional electron gas. The disordercan be significantly screened/reduced due to the many-body effects. To analysethe screening/disorder problem we consider AlGaAs/GaAs/AlGaAs heterostructurewith two metallic gates. We demonstrate that the design least susceptible tothe disorder corresponds to the weak coupling regime (opposite to tightbinding) which is realised via system of quantum anti-dots. The most relevanttype of disorder is the area disorder which is a random variation of areas ofquantum anti-dots. The area disorder results in formation of puddles. Othertypes of disorder, the position disorder and the shape disorder, arepractically irrelevant. The formation/importance of puddles dramaticallydepends on parameters of the nanopatterned heterostructure. A variation of theparameters by 20--30\% can change the relative amplitude of puddles by ordersof magnitude. Based on this analysis we formulate criteria for the acceptabledesign of the heterostructure aimed at creation of the artificial graphene.

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