MoireKP: An Automated Workflow for Symmetry-Constrained Moiré Continuum Models

Abstract

First-principles Hamiltonians contain the electronic information needed to study moiré materials, but their size makes subsequent calculations costly. We present MoireKP, an automated workflow for constructing compact continuum models from localized-orbital ab initio Hamiltonians. The workflow constructs a valley-resolved truncated atomic-plane-wave (TAPW) Hamiltonian, selects a low-energy basis, and projects the crystal-symmetry operations into this basis. These representations determine the symmetry-allowed Hamiltonian terms, whose coefficients are obtained by projecting the low-energy effective Hamiltonian onto the corresponding operator basis. The model dimension, localized reference states, and harmonic cutoff can be selected automatically or specified by the user. This Hamiltonian-based construction retains wave-function information within the selected low-energy subspace. We apply the workflow to AA-stacked twisted bilayer MoTe$_2$, AB-stacked twisted bilayer ZrS$_2$, and A--AB twisted trilayer MoTe$_2$, covering K, M, and $Γ$ valleys. All models reproduce TAPW band energies within 3.0 meV in the target windows along high-symmetry $k$ paths.