Artificial moiré engineering for an ideal BHZ model

TL;DR

This work proposes artificial moiré engineering in (001)-oriented Cd3As2 thin films to realize a moiré BHZ model using a patterned gate. By combining a BHZ Hamiltonian with a real-space moiré potential and a Hartree-Fock mean-field framework projected to the active minibands, the authors identify parameter regions that yield topological, flat mini-bands with $C_s=\pm1,\pm2$ and demonstrate that a spin-polarized state can drive a moiré-induced quantum anomalous Hall effect. In multi-band HF analyses, a spin-polarized order emerges as a robust ground state under appropriate $\delta$ and moiré strength, with a CI phase stabilized in the $C_{6z}$ case and an adjacent anomalous Hall metal region; interaction strength can further tune phase boundaries and induce band mixing. The results provide a clean, tunable platform for interaction-driven topological phases in artificial moiré lattices, offering a pathway to QAH effects without lattice relaxation or twisting, and suggesting future exploration of density-wave competition and spontaneous long-period modulations.

Abstract

We demonstrate that (001) grown Cd3As2 thin films with a superlattice-patterned gate can potentially realize the moiré Bernevig-Hughes-Zhang (BHZ) model. Our calculations identify the parameterization region necessary to achieve topological flat mini-bands with a C4z symmetric and a C6z symmetric potential. Additionally, we show that a spin-polarized state can serve as the minimal platform for hosting the moiré induced quantum anomalous Hall effect, supported by Hartree Fock interaction kernel analysis and self-consistent mean field calculations.

Figures (10)

• Figure 1: A proposed experimental device architecture in which a patterned gate metal creates a moiré potential in the Cd3As2 thin film. (a) illustration of the double gated device. The patterned gate sets the Fermi level in the film while the top gate controls the potential under the holes, generating an effective moiré superlattice. (b) A scanning electron microscope image of a patterned Ru gate metal realized by electron beam lithography and dry etching. The holes are around 20 nm in diameter while the pitch size is 45 nm.
• Figure 2: Topological phase diagram of the moiré BHZ model. (a) The calculated spin Chern number ($C_s$) of the first valence bands when a $C_{4z}$ symmetric potential is applied, $\delta$ characterize the original band gap and $V_0$ is the strength of moiré potential. (b) Same as (a) but with a $C_{6z}$ symmetric moiré potential. (c) The bandwidth $\Delta$ of the first valence bands in the topological region when a $C_{4z}$ symmetic potential is applied. (d) Same as (c) but with a $C_{6z}$ symmetric moiré potential.
• Figure 3: (a) Single particle band structures for the moiré BHZ model when a $C_{4z}$ symmetric potential is applied ($\delta=-5$ meV, $V_0$ = 4 meV). The first valence bands and the first conduction bands are labeled and are relatively flat. (b) Wannier charge center (WCC) flow of the first valence bands (VB1). The non-trivial winding feature indicates the band topology which is consistent with the spin Chern number calculation.
• Figure 4: (a) Eigenvalues of different modes of the Hartree Fock interaction kernel. Three discrete modes are separated from others, correspond to one spin polarized mode ($s_z (\mathbf{k})$, labeled in blue) and two spin coherent modes ($s_{x/y}(\mathbf{k})$, labeled in orange). The single particle Hamiltonian is solved on a $40\times 40$$k$-mesh when a $C_{4z}$ symmetric potential is applied ($\delta=-5$ meV, $V_0$ = 4 meV) (b-c) The $k$ space distribution of the Hartree Fock eigenmodes for the spin-polarized mode and two degenerate spin-coherent modes.
• Figure 5: Two band Hartree Fock calculations when a $C_{4z}$ symmetric potential ($\delta=-5$ meV, $V_0$ = 4 meV) is applied and a $C_{6z}$ symmetric potential ($\delta=-5$ meV, $V_0$ = 3.5 meV) is applied. The self-consistent Hartree Fock calculations are performed on a 40 $\times$ 40 $k$-mesh for the $C_{4z}$ symmetric case and on a 30 $\times$ 30 $k$-mesh for the $C_{6z}$ symmetric case. (a), (d) Hartre -Fock band structures for the spin-coherent state, exhibiting a topological semimetal (TSM) phase. The original bands are labeled in grey dashed line. (b), (e) Hartree Fock band structures for the spin-polarized state, indicative of a quantum anomalous Hall (QAH) phase. (c), (f) Berry curvature distribution in the moiré Brillouin zone (mBZ), with labeled high-symmetry points.