Nanopatterned semiconductor interfaces offer a versatile platform for creating quantum metamaterials and exploring novel electronic phenomena. In this study, we illustrate this concept using artificial graphene─a metamaterial featuring distinctive properties including Dirac and saddle points. We demonstrate that introducing additional nanopatterning can open a Dirac band gap, giving rise to what we term artificial hexagonal boron nitride (AhBN). The calculated valley Chern number of AhBN indicates the presence of topological valley Hall states confined to Dirac-gap domain walls. A key question is whether these one-dimensional edge states are topologically protected against disorder, given their vulnerability to Anderson localization. To this end, we perform band structure and electronic transport simulations under experimentally relevant disorder, including charge puddles and geometric imperfections. Our results reveal the resilience of the domain wall states against typical experimental disorder, particularly while the AhBN band gap remains open. The localization length along the domain wall can reach several microns─several times longer than the bulk electron mean free path─even though the number of bulk transport channels is greater. To enhance the effectiveness of the low-dissipation domain wall channel, we propose ribbon geometries with a large length-to-width ratio. These findings underscore both the potential and challenges of AhBN for low-energy, power-efficient microelectronic applications.
Pai et al. (Thu,) studied this question.