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    Area of Science:

    • Condensed Matter Physics
    • Materials Science
    • Optics

    Background:

    • Multilayer graphene structures exhibit unique optical absorption properties.
    • Coherent Perfect Absorption (CPA) is a phenomenon of significant interest in optical applications.
    • Understanding the role of interlayer separation is key to controlling optical properties.

    Purpose of the Study:

    • To investigate the sensitivity of multilayer graphene optical absorption to subnanometer interlayer separation.
    • To derive theoretical expressions for optical absorption considering interlayer effects.
    • To establish the critical interlayer separation limit (Dlim) for maintaining theoretical absorption bounds.

    Main Methods:

    • Utilized a transfer-matrix formalism to derive semi-analytical expressions for far-field observables.
    • Developed a continued-fraction analysis for an infinite layer model.
    • Compared theoretical predictions with experimental data for Van der Waals crystals.

    Main Results:

    • Neglecting interlayer separation yields an upper absorption bound of 50% for real conductivities, essential for CPA.
    • A critical interlayer separation (Dlim), often smaller than realistic values, limits the existence of this absorption bound.
    • Absorption becomes highly sensitive to interlayer separation beyond Dlim.
    • Derived a closed-form expression for absorption in infinite graphene layers and for Dlim.

    Conclusions:

    • Subnanometer interlayer separation critically influences optical absorption in multilayer graphene.
    • Accurate modeling of multilayer Van der Waals crystals for CPA requires careful consideration of interlayer separations.
    • Treating layers as electronically independent is valid only up to a certain interlayer separation.