Engineering Hubbard models with gated two-dimensional moiré systems

TL;DR

The work demonstrates that a two-dimensional electron gas confined in a moiré potential and screened by dual gates can be tuned to realize square-lattice Hubbard physics, including AFM order at half-filling and stripe phases at $1/8$ doping, by controlling gate separation $d$ and moiré depth $V_m$. It combines LSDA-based DFT with a gate-screened exchange-correlation functional and ab initio Wannierization with cRPA downfolding to extract effective lattice parameters, enabling quantitative mapping to $U_0/t_1$, $t_2/t_1$, and related Hubbard-model quantities. The results reveal how interaction range and strength control ground-state orders and identify regimes where the system behaves as the simple Hubbard model or as an extended Hubbard model, with consistent cross-checks between continuum and lattice descriptions. The analysis extends to triangular moiré geometries to connect with current experiments and outlines concrete routes for experimental realization and exploration of magnetic and potentially superconducting phases in moiré materials.

Abstract

Lattice models are powerful tools for studying strongly correlated quantum many-body systems, but their general lack of exact solutions motivates efforts to simulate them in tunable platforms. Recently, a promising new candidate has emerged for such platforms from two-dimensional materials. A subset of moiré systems can be effectively described as a two-dimensional electron gas (2D EG) subject to a moiré potential, with electron-electron interactions screened by nearby metallic gates. In this paper, we investigate the realization of lattice models in such systems. We show that, by controlling the gate separation, a 2D EG in a square moiré potential can be systematically tuned into a system whose ground state exhibits orders analogous to those of the square lattice Hubbard model, including the stripe phase. Furthermore, we study how variations in gate separation and moiré potential depth affect the ground-state orders. A number of antiferromagnetic phases, as well as a ferromagnetic phase and a paramagnetic phase, are identified. We then apply our quantitative downfolding approach to triangular moiré systems closer to current experimental conditions, compare them with the square lattice parameters studied, and outline routes for experimental realization of the phases.

Figures (13)

• Figure 1: The schematic of a dual-gate screened 2D EG in a moiré potential. In the left panel, electrons denoted by the red dots are confined in a 2D plane with a moiré potential. The squares above and below the 2D EG represent metallic gates, which screen the electron-electron interaction. The middle three panels are moiré potential of various geometries, where the blue color represent potential valleys and the red color represent potential peaks. From top to bottom, the potential minima form triangular, honeycomb, and square lattices, respectively. The right panel illustrates that the dual-gate screening shortens the range of the electron-electron interaction.
• Figure 2: Phase diagram for the square moiré potential at $1/8$ hole doping
• Figure 3: Charge and spin patterns in the ground state of system $\nu=1$, $r_s=5\; a_B^*$, $V_m/W=1.6$, and $d=0.3\; a_B^*$. The upper panel is the charge density and the lower panel the spin density. Both densities are normalized by the average charge density $\rho_0=N_e/A$, where $N_e$ is the number of electrons and $A$ the area of the simulation cell.
• Figure 4: Charge and spin patterns in the ground state of system $\nu=7/8$, $r_s=5\; a_B^*$, $V_m/W=1.6$, and $d=0.3\; a_B^*$. Setting and conventions are similar to Fig. \ref{['fig:checkerboard']}.
• Figure 5: Diagonal charge and spin patterns in the ground state of system $V_m/W=1.6$ and $d=0.4\; a_B^*$. In this plot, the horizontal and vertical axes, denoted by $x'$ and $y'$, represent the $(1,1)$- and $(-1,1)$-directions, respectively. That is, they are rotated by $45\degree$ with respect to the $x$- and $y$-axes in Figs. \ref{['fig:checkerboard']} and \ref{['fig:spinNcharge']}; other conventions are the same.