Papers › Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe₂ and WSe₂
Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe₂ and WSe₂
Yan Zhang, Hanqi Pi, Jiaxuan Liu, Wangqian Miao, Ziyue Qi, Nicolas Regnault, Hongming Weng, Xi Dai, B. Andrei Bernevig, Quansheng Wu, Jiabin Yu
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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 MoTe₂ and WSe₂ with twist angles ranging from 2.13° to 3.89°, 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.
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