Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe\(_2\) and WSe\(_2\)

• Published in: arXiv.org 2024-11
• Main Authors: Zhang, Yan, Pi, Hanqi, Liu, Jiaxuan, Miao, Wangqian, Ziyue Qi, Regnault, Nicolas, Weng, Hongming, Dai, Xi, Bernevig, B Andrei, Wu, Quansheng, Yu, Jiabin
• Format: Article
• Language: English
• Subjects: Continuum modeling; Energy bands; First principles; Many body problem; Mathematical analysis; Parameter robustness; Principles; Wave functions
• ISSN: 2331-8422

We develop a comprehensive method to construct analytical continuum models for moiré 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 moiré 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 moiré materials accessible by first-principles calculations.