Quantum Monte Carlo Study of Semiconductor Artificial Graphene Nanostructures

TL;DR

This study uses advanced Monte Carlo simulations to explore phase transitions in semiconductor artificial graphene nanostructures, revealing how edge geometry and charge distribution influence magnetic and metallic phases.

Contribution

It provides the first detailed quantum Monte Carlo analysis of phase transitions in experimentally accessible artificial graphene nanostructures with varying edge types and geometries.

Findings

Transition from antiferromagnetic to metallic phases at specific lattice parameters

Edge geometry and charge distribution significantly influence phase transition characteristics

Triangular structures exhibit a smoother metal-insulator transition with edge polarization

Abstract

Semiconductor artificial graphene nanostructures where 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 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 analysing 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.