Thickness and Layer Stacking Order Effects on Complex Optical Conductivity and Exciton Strength of Few-Layer Graphene: Implications for Optical Modulators and Photodetectors

The understanding and control of complex optical conductivity of graphene is the central endeavor in design and optimization of graphene-based optical modulators and photo-detectors. Here, we study the complex optical conductivities as a function of the thickness and stacking order in triple-layer graphene through spectroscopic ellipsometry and first-principles calculations. The increase in thickness allows for continuous shifting of the position of the zero-cross point in the imaginary part of the complex optical conductivity and leads to the tunable optical response of plasma in graphene. Two feature peaks are observed in the optical conductivity spectra of graphene, whose center energies are accurately determined and found to exhibit "V" shape evolutions versus the thickness. The first-principles results show that the excitonic strength decreases with the increasing layer, and the ABA stacking order in triple-layer graphene has a more localized and stronger exciton charge distributions and larger exciton strength than the ABC stacking order. The different excitonic strengths in two main stacking orders (i.e., ABA and ABC) of the triple-layer graphene are the key reason for different layer-dependent evolution trends of the center energies of feature peaks. By comparing the experimental and theoretical results, the triple-layer polycrystalline graphene in our experiment should mainly be the ABC stacking order.