Nagaoka ferromagnetism in semiconductor artificial graphene

We present the emergence of Nagaoka ferromagnetism in semiconductor-based artificial graphene with realistic Coulomb interaction using high-precision variational and diffusion Monte Carlo methods, complemented by exact diagonalization calculations of the generalized Hubbard model. We analyze models of armchair hexagonal geometries nanopatterned on GaAs quantum wells. Our results reveal a distinct magnetic phase transition driven by the absence/addition of a single electron at half-filling. This form of itinerant magnetism predicted rigorously for Hubbard model remained unascertained in large scale realistic systems. We demonstrate that Coulomb scattering terms play a crucial role in stabilizing Nagaoka ferromagnetism, enabling the observation of the phase transition for system parameters near $U/t \approx 60$.