The linear and non-linear optical absorption and asymmetrical electromagnetic interaction in chiral twisted bilayer graphene with hybrid edges
Graphical abstract
Introduction
Two-dimensional materials have been widely used in many fields in recent years because of their strange properties different from bulk materials [[1], [2], [3]]. Graphene, as a representative of two-dimensional materials, has great research values [4]. Moreover, after many years of research and exploration, graphene has good applications in various fields because of its excellent mechanical [5,6], thermal [7,8], optical [9,10], electrical [[10], [11], [12]], and magnetic [13] properties, and commercial products have been put on the market. In 2018, Cao et al. [14,15] found that when the torsional angle between bilayer graphene (BLG) exceeds 1°, its physical properties will change dramatically. The situation of twisted bilayer graphene [16] (TwBLG) is quite different (the maximum angle is about 1°). In this case, the electrons occupy the flat band (a flat band is a very flat energy band). Because the bandwidth of these flat bands is very small, the interaction between electrons can no longer be treated as a perturbation. At this time, the physical properties of the system will strongly depend on the electron density. This strong interaction can even cause a phase that is not present in monolayer graphene [14,15,17] at a specific electron density, although the system should be metal in a free electron physical image, the actual system behaves as an insulator. The topological properties of TwBLG have been carefully studied theoretically and experimentally; however, its linear and non-linear optical absorption properties have not been fully studied theoretically. The topological properties of TwBLG have been carefully studied theoretically and experimentally. However, its linear and non-linear optical absorption properties have not been fully studied theoretically. The optical properties of graphene sheets have a great relationship with graphene edges, which have two forms of edges: armchair borders and zigzag edges. The orbital energy levels of these two kinds of edges are different so that the edge will affect the transition behavior [18]. Therefore, when the Moiré pattern and graphene edges in TwBLG are combined, the optical properties will change dramatically. Two-photon absorption (TPA), which differs from the one-photon absorption (OPA), requires two steps to transition through a different intermediate state, so its transition characteristics are more complicated than those of OPA. In the previous work, we developed a method that can effectively visualize the TPA two-step transition process [19]. In this work, we will use this method to visually analyze the OPA and TPA transition characteristics of different edge normal and twisted BLG. This method is based on the theoretical framework of sum of states (SOSs) [20,21]. This method is widely used in the calculation of non-linear optical coefficients. The TPA spectrum and quadratic response theory calculated by the SOS-based TPA analysis program have a good agreement with the experiments [22,23]. Recently, TwBLG was discovered with novel chiral properties. This property is explained as the energy level splitting of graphene after twisting. In our previous work, we developed a method to visually analyze the generalized chiral properties of molecules, clusters, and other systems [24]. This method can separate the electric and magnetic dipole moments in the visualization system and electromagnetic wave interaction process [25]. This is a generalized chiral analysis theory, which is different from the traditional chiral system classified according to symmetry. This method is based on the decomposition analysis of the electrical and magnetic responses in the interaction between light and matter, so it can be analyzed more generally. The physical mechanism of chirality in a specific system. Therefore, after the analysis of OPA and TPA, we discuss the influence of Moiré and edges on the chiral properties of BLG.
Section snippets
Method
All BLG geometric optimization processes are divided into two steps. The first step uses a combination of GFN2-XTB (Geometry, Frequency, Noncovalent, Extended Tight Binding) [26] and Gaussian 16 [27]. That is, the calculation of energy and gradient is performed using the GFN2-XTB program, and the construction of the density matrix and the calculation of the Hessian matrix are completed by Gaussian 16. A self-programmed script is used to pass the information required by the two programs. In the
OPA and TPA spectra and transition characteristic
When the graphene at the border of the two armchairs forms a BLG sheet, the plane is curved to some extent. After a certain twisted angle (28°) in the two layers of BLG, the degree of this twist is reduced, refer Fig. 1(a and b). This is due to the weakening of van der Waals forces in the Moiré region of the twisted BLG sheet, refer Fig. S1 in supporting information. Moiré can cause changes in the energy levels of BLG, which can cause changes in electronic transition behaviors [17,36]. This
Conclusion
In this work, we theoretically investigate the linear OPA and TPA absorption and their transition characteristics of BLG with different edges after in-plane twist with DFT calculations and SOS methods. The Moiré and edge pairs of charge transfer behavior during OPA and TPA are studied. It is found that the Moiré energy level is between the orbital energy levels of the zigzag edges and the armchair edge. The addition of Moiré energy can significantly enhance the interlayer charge transfer of
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (91436102 and 11374353), the fundamental Research Funds for the Central Universities, and the NSFC-BRICS STI (National Natural Science Foundation of China, Brics on Science, Technology and Innovation) Framework Program (grant 51861145309).
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