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Universal Moir\'e-Model-Building Method without Fitting: Application to Twisted MoTe$_2$ and WSe$_2$
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abstract
We develop a comprehensive method to construct analytical continuum models for moir\'e systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum model as a basis, allowing us to determine model parameters as coefficients of this basis through Gram-Schmidt orthogonalization. We apply our method to twisted MoTe$_2$ and WSe$_2$ with twist angles ranging from 2.13$^\circ$ to 3.89$^\circ$, producing continuum models that exhibit excellent agreement with both energy bands and wavefunctions obtained from first-principles calculations. We further propose a strategy to integrate out the higher-energy degrees of freedom to reduce the number of the parameters in the model without sacrificing the accuracy for low-energy bands. Our findings reveal that decreasing twist angles typically need an increasing number of harmonics in the moir\'e potentials to accurately replicate first-principles results. We provide parameter values for all derived continuum models, facilitating further robust many-body calculations. Our approach is general and applicable to any commensurate moir\'e materials accessible by first-principles calculations.
Forward citations
Cited by 7 Pith papers
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At ν=1 in 3.65°-twisted WSe2, Hartree-Fock predicts that the 120° antiferromagnet gives way to coplanar or non-coplanar multi-Q magnetic order with four ordering wavevectors and soft M-point spin fluctuations.
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Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe$_2$
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Twisted SnSe2 realizes quasi-1D triangular (AA) and kagome (AB) interacting models with predicted dimer, valence-bond-solid, and frustrated spin-liquid phases.
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MoireStudio: A Universal Twisted Electronic Structure Calculation Package
MoireStudio is a Python package that finds commensurate moiré angles, builds tight-binding and k·p Hamiltonians, and includes Fourier-based relaxation for twisted 2D materials.
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