AI 中文总结
该研究以扭转双层双层石墨烯为对象，采用微扰方法，发现莫尔平带可通过双共振效应大幅增强二次谐波产生，且不同堆叠构型在大偏置下存在π相移，为调控可调谐平带材料的非线性光学响应提供了通用机制。
AI 中文摘要
我们基于有效连续哈密顿量的微扰方法，从理论上研究了具有AB-AB和AB-BA堆叠构型的扭转双层双层石墨烯（Twisted Double Bilayer Graphene，TDBG）中的二次谐波产生（Second-Harmonic Generation，SHG）。我们系统分析了SHG响应随扭转角、垂直偏置电压、费米能量和堆叠构型的变化规律。研究发现，在小扭转角下，由于莫尔平带的出现及相关联合态密度的增加，SHG信号会显著增强。除了这种常规增强机制外，我们还证明，减小的带宽可实现显著的双共振过程，其中在莫尔布里渊区的扩展区域内，频率为ω和2ω的光学跃迁可同时满足。该机制会大幅放大SHG响应，与离散能级系统中的增强效应类似，但此处是在可调谐的莫尔能带结构中实现的。此外，我们还表明，在大偏置电压下，AB-AB和AB-BA构型的SHG响应会呈现系统性的π相移，这反映了它们不同的对称性和电子结构。我们的研究结果确定了双共振效应是增强莫尔系统中SHG的通用机制，并为理解和控制可调谐平带材料中的非线性光学响应提供了统一框架。
英文摘要
We theoretically investigate second-harmonic generation (SHG) in twisted double bilayer graphene (TDBG) with AB--AB and AB--BA stacking configurations using a perturbative approach based on an effective continuum Hamiltonian. We present a systematic analysis of the SHG response as a function of twist angle, vertical bias voltage, Fermi energy, and stacking configuration. We find that the SHG signal is strongly enhanced at small twist angles due to the emergence of moiré flat bands and the associated increase in the joint density of states. Beyond this conventional enhancement mechanism, we demonstrate that the reduced bandwidth enables a pronounced double-resonant process, in which optical transitions at both $ω$ and $2ω$ are simultaneously satisfied over extended regions of the moiré Brillouin zone. This mechanism leads to a substantial amplification of the SHG response, analogous to the enhancement observed in systems with discrete energy levels, but realised here in a tuneable moiré band structure. Furthermore, we show that the AB--AB and AB--BA configurations exhibit a systematic $π$ phase shift in the SHG response at large bias voltages, reflecting their distinct symmetry and electronic structure. Our results identify double-resonance effects as a generic mechanism for enhancing SHG in moiré systems and provide a unified framework for understanding and controlling nonlinear optical responses in tuneable flat-band materials.
