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 $\ensuremath{\rho}$, 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 $\ensuremath{\rho}$ value of the phase transition. For triangular structures, the metal-insulator transition is accompanied with a smoother edge polarization transition.