An extensive analytical and numerical investigation has been carried out to examine the role played by many-body effects on various $\alpha$-$\mathcal{T}_3$ materials under an off-resonance optical dressing field. Additionally, we explore its dependence on the hopping parameter $\alpha$ as well as the electron-light coupling strength $\lambda_0$. The obtained dressed states due to mutual interaction between Dirac electrons and incident light are shown to demonstrate rather different electronic and optical properties in comparison with those in the absence of incident light. Specifically, various collective transport and optical properties of these electron dressed states are discussed in detail and compared for both single- and double layer $\alpha$-$\mathcal{T}_3$ lattices. All of these novel properties are due to the presence of a middle flat band and the interband transitions between it and an upper conduction band. Also, coupled plasmon dispersions for interacting double layer $\alpha$-$\mathcal{T}_3$ lattices are calculated, revealing a lower acoustic-like plasmon branch with tunable group velocity determined by both the layer separation and Fermi energy of each layer. Finally, a many-body theory is presented within the random-phase approximation for calculating the optical absorbance of doped multi-layered $\alpha$-$\mathcal{T}_3$ lattices in a linearly-polarized light field. We anticipate that the discoveries reported here could impact the design of the next-generation nano-optical and nano-plasmonic devices.

中文翻译：

---

单双层α-T ₃晶格的多体效应和光学性质

已经进行了广泛的分析和数值研究，以检查多体效应在非共振光学修整场下对各种 $\alpha$-$\mathcal{T}_3$ 材料的作用。此外，我们探索了它对跳跃参数 $\alpha$ 以及电子-光耦合强度 $\lambda_0$ 的依赖。与没有入射光的情况相比，由于狄拉克电子和入射光之间的相互作用而获得的修饰状态显示出相当不同的电子和光学性质。具体而言，详细讨论并比较了单层和双层 $\alpha$-$\mathcal{T}_3$ 晶格的这些电子修饰态的各种集体传输和光学特性。所有这些新特性都是由于中间平坦带的存在以及它与上导带之间的带间跃迁。此外，计算了相互作用双层 $\alpha$-$\mathcal{T}_3$ 晶格的耦合等离子体色散，揭示了较低的类似声学的等离子体分支，其群速度由每层的层间距和费米能量决定. 最后，在随机相位近似中提出了多体理论，用于计算线性偏振光场中掺杂的多层 $\alpha$-$\mathcal{T}_3$ 晶格的光吸收率。我们预计这里报告的发现可能会影响下一代纳米光学和纳米等离子体设备的设计。计算了相互作用双层 $\alpha$-$\mathcal{T}_3$ 晶格的耦合等离子体色散，揭示了较低的类声子等离子体分支，其群速度可调，由每层的层间距和费米能量决定。最后，在随机相位近似中提出了多体理论，用于计算线性偏振光场中掺杂的多层 $\alpha$-$\mathcal{T}_3$ 晶格的光吸收率。我们预计这里报告的发现可能会影响下一代纳米光学和纳米等离子体设备的设计。计算了相互作用双层 $\alpha$-$\mathcal{T}_3$ 晶格的耦合等离子体色散，揭示了较低的类声子等离子体分支，其群速度可调，由每层的层间距和费米能量决定。最后，在随机相位近似中提出了多体理论，用于计算线性偏振光场中掺杂的多层 $\alpha$-$\mathcal{T}_3$ 晶格的光吸收率。我们预计这里报告的发现可能会影响下一代纳米光学和纳米等离子体设备的设计。在随机相位近似中提出了多体理论，用于计算线性偏振光场中掺杂的多层 $\alpha$-$\mathcal{T}_3$ 晶格的光吸收率。我们预计这里报告的发现可能会影响下一代纳米光学和纳米等离子体设备的设计。在随机相位近似中提出了多体理论，用于计算线性偏振光场中掺杂的多层 $\alpha$-$\mathcal{T}_3$ 晶格的光吸收率。我们预计这里报告的发现可能会影响下一代纳米光学和纳米等离子体设备的设计。