法国巴黎综合理工学院Laurent Sanchez-Palencia团队研究了光学莫尔势中的有效紧束缚模型。相关论文于2025年4月9日发表在《物理评论A》杂志上。

两个周期系统之间的扭曲提供了彻底控制量子输运特性的可能性。在相应扭曲角度的离散集合中，形成莫尔周期图案，低能单粒子光谱形成不同的带和间隙。

研究组考虑由两个连续的空间周期势组成的成比例角度的扭曲系统。他们设计了一种基于能量尺度层次结构的通用方法，以推导出捕获能谱的有效紧束缚模型，重点关注方晶格的情况。莫尔晶胞中的局部状态通过强晶胞内和弱晶胞间隧道耦合，产生一系列对应于不同周期晶格的能带和子带。

对于足够深的势，研究组发现连续空间系统的谱与由此构建的紧束缚近似之间非常吻合。该方法可解释莫尔带结构并提取有效紧束缚模型的参数。研究组还讨论了多体系统物理学的应用以及对其他扭曲模型的扩展。

附：英文原文

Title: Effective tight-binding models in optical moiré potentials

Author: Dean Johnstone, Shanya Mishra, Zhaoxuan Zhu, Laurent Sanchez-Palencia

Issue&Volume: 2025/04/09

Abstract: A twist between two periodic systems offers the possibility to drastically control quantum transport properties. At discrete sets of commensurate twisting angles, a moiré periodic pattern is formed, and the low-energy single-particle spectrum forms distinct bands and gaps. Here, we consider twisted systems at a commensurate angle made of two continuous-space periodic potentials. We devise a general approach, based on a hierarchy of energy scales, to derive effective tight-binding models that capture the energy spectrum, focusing on the case of square lattices. Localized states in the moiré unit cell are coupled by strong intracell and weak intercell tunnelings, generating a series of energy bands and subbands that correspond to distinct, periodic lattices. For sufficiently deep potentials, we find excellent agreement between the spectrum of the continuous-space system and the tight-binding approximation thus constructed. Our approach allows for the interpretation of moiré band structures and the extraction of parameters for the effective tight-binding models. Applications to the physics of many-body systems and extensions to other twisted models are also discussed.

DOI: 10.1103/PhysRevA.111.043305

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.043305