The two-dimensional electron gas and effects of a moiré potential: a quantum Monte Carlo perspective

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. The addition of a moiré potential can stabilize a variety of electronic phases such as generalized Wigner crystal (GWC), ferromagnet, fractional Chern insulator, and superconductor. Accurate computations in such systems, with reliable treatment of strong long-range Coulomb interaction in large system sizes, are mostly missing.

In this talk, I will present a series of studies using quantum Monte Carlo (QMC) to examine the phase behavior of the 2DEG under external moiré potentials. For a moiré potential with triangular symmetry, we identify a GWC exhibiting noncollinear magnetism [1]. In contrast, a honeycomb moiré potential stabilizes distinct phases, including ferromagnetic semimetal and charge density wave [2]. By benchmarking density functional theory (DFT) calculations with QMC, we identify functionals useful for efficiently exploring certain 2D continuum Hamiltonians. We use QMC calculations to parametrize a dual-gate screened local density approximation (LDA) functional [3], enabling future DFT studies to model a wider range of experimentally relevant device configurations. Further, machine learned wavefunctions are being explored as an even more accurate method to discover correlated electronic phases [4].

[1] Yubo Yang, Miguel Morales, Shiwei Zhang, “Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction,” PRL 132, 076503 (2024).

[2] Yubo Yang, Miguel A. Morales, Shiwei Zhang, “Ferromagnetic semimetal and charge-density wave phases of interacting electrons in a honeycomb moiré potential,” arXiv: 2406.01715.

[3] Yiqi Yang, Yubo Yang, Kun Chen, Miguel A. Morales, Shiwei Zhang, “The two-dimensional homogeneous electron gas with symmetric dual-gate screening: exchange-correlation functional and other ground-state properties,” arXiv: 2410.07445.

[4] Conor Smith, Yixiao Chen, Ryan Levy, Yubo Yang, Miguel A. Morales, Shiwei Zhang, “Ground state phases of the two-dimension electron gas with a unified variational approach,” arXiv: 2405.19397.