Nagaoka ferromagnetism in semiconductor artificial graphene

Abstract

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 $U/t \approx 60$.

Figures (5)

• Figure 1: Extrapolated spin-spin correlation function plotted against potential depth $V_{0}$ obtained using pair densities for potential radius $\rho = 25$ nm. Inset figures are extrapolated spin pair densities in the ground states. (a) $N_{e} = 41$, $V_{0} \approx -45$ meV, $S_{z} = 41/2$. (b) $N_{e} = 42$, $V_{0} \approx -45$ meV, $S_{z} = 0$. (c) $N_{e} = 41$, $V_{0} \approx -8.84$ meV, $S_{z} = 1/2$. (d) $N_{e} = 42$, $V_{0} \approx -8.84$ meV, $S_{z} = 0$.
• Figure 2: (a) Extrapolated spin-spin correlation function plotted against potential depth $V_{0}$ obtained using pair densities for potential radius $\rho = 17.5$ nm. (b) Ground state spin $S_{z}$ values plotted against potential depth $V_{0}$. (c) DMC energies plotted against $S_{z}$ at $V_{0} \approx -8.84$ meV for $N_{e} = 41$. (d) DMC energies plotted against $S_{z}$ at $V_{0} \approx -27$ meV for $N_{e} = 41$. For (a) and (b), the calculations are for $S_{z}$-min/max competition except "(scan)" results where we consider all $S_{z}$ values.
• Figure 3: Extrapolated spin pair densities for $N_{e} = 41$ electrons at several potential depth $V_{0}$ values. (a) $V_{0} \approx -8.84$ meV. (b) $V_{0} \approx -14.89$ meV. (c) $V_{0} \approx -19.74$ meV. (d) $V_{0} \approx -27$ meV.
• Figure 4: The ratio of onsite Coulomb interaction $U$ to nearest-neighbor hopping parameter $t$, $U/t$, plotted against $V_{0}$ for $\rho = 17.5$ nm and $k = 3.56 \times 10^{-4}$ meV/nm$^2$. (a) $U$ vs. $V_{0}$. (b) $t$ vs. $V_{0}$.
• Figure 5: Exact diagonalization results of the Hubbard Hamiltonian in a subspace of a single spin flip on $N = 42$ sites with $N_e=41$ electrons (one hole). The energy difference $\Delta E$ between $S=39/2$ and $S=41/2$ states' lowest energy states. Confining potential strength $\omega = 0.5 t / a^{2}$ where $a$ is the dot-to-dot distance.