Quantum Monte Carlo study of semiconductor artificial graphene nanostructures

Semiconductor artificial graphene nanostructures where the Hubbard model parameter U/t can be of the order of 100, provide a highly controllable platform to study strongly correlated quantum many-particle phases. We use accurate variational and diffusion Monte Carlo methods to demonstrate a transition from antiferromagnetic to metallic phases for an experimentally accessible lattice constant a = 50 nm in terms of lattice site radius rho, for finite-sized artificial honeycomb structures nanopatterned on GaAs quantum wells containing up to 114 electrons. By analyzing spin-spin correlation functions for hexagonal flakes with armchair edges and triangular flakes with zigzag edges, we show that edge type, geometry, and charge nonuniformity affect the steepness and the crossover rho value of the phase transition. For triangular structures, the metal-insulator transition is accompanied with a smoother edge polarization transition.