Quantum Monte Carlo study of artificial triangular graphene quantum dots

Abstract

We investigate the magnetic phases of triangular graphene quantum dots (TGQDs) with zigzag edges using variational and quantum Monte Carlo methods. These systems serve as quantum simulators for bipartite lattices with broken sublattice symmetry, providing a platform to study the extended Hubbard model's emergent magnetic phenomena, including Lieb's magnetism at half-filling, edge depolarization upon single-electron addition, and Nagaoka ferromagnetism. Our non-perturbative quantum Monte Carlo simulations, performed for lattices of up to 61 sites, reveal that TGQDs transition from metallic to insulating regimes as a function of site radius size, while retaining edge-polarized ground states at half-filling. Notably, edge depolarization occurs upon single-electron doping in both metallic and insulating phases, contrasting with the Nagaoka ferromagnetism observed in hexagonal armchair geometries.

Figures (5)

• Figure 1: Potential profiles (left panels) and single-particle spectra (right panels) for a 33-site TGQD constructed using Gaussian-like potentials with radius (a) $\rho=15$ nm and (b) $\rho=30$ nm. Energy spectra are obtained using the real-space finite differences method and compared to TB solutions with fitted parameters. The total lateral size of the structure is approximately 250 nm.
• Figure 2: Diffusion Monte Carlo energies for charge-neutral TGQDs as a function of the quantum well radius $\rho$ for (a) $N_s=33$ sites and (b) $N_s=61$ sites, for all possible spin excitations within edge states, obtained using various trial wave functions. Insets (a) and (b) show the lowest energy spin densities for $\rho = 35$.
• Figure 3: Diffusion Monte Carlo energies for TGQDs with an additional electron as a function of the quantum well radius $\rho$ for (a) $N_s=33$ sites and (b) $N_s=61$ sites, for all possible spin excitations within edge states, obtained using various trial wave functions.
• Figure 4: (a) Extrapolated spin-spin correlation functions $g_p$ obtained via pair densities for neutral and gated TGQDs with $N_s=33, 46$, and $61$ sites. Corresponding statistical error bars are smaller than the size of the symbols. (b,c) Extrapolated pair-density results for $N_s = 33$ and $N = 34$, corresponding to the ground state at $\rho = 15\,\mathrm{nm}$ and $35\,\mathrm{nm}$. The fixed reference electron position is marked by x.
• Figure 5: Diffusion Monte Carlo energy difference between the Nagaoka ferromagnetic state and the edge-depolarized state, $E_{Nag}-E_{dep}$, for $N_s=33, 46,$ and $61$ site TGQDs, showing that Nagaoka ferromagnetism does not occur as the ground state. Statistical error bars are smaller than the size of the symbols.