Atomic-size dependence of the cohesive energy, bandgap, Young's modulus, and Raman frequency in different MA₂Z₄: A bond relaxation investigation

Understanding the physical mechanism behind atomic-size dependence of the bandgap, phonon frequency, and mechanical strength in various monolayered MA₂Z₄ is of crucial importance for their electronic and photoelectronic applications. The density functional theory calculation results confirm that these physical quantities gradually decrease with the increasing periodicity of the atomic size (or radius) of the A or Z of MA₂Z₄. In order to clarify the common origin of the atomic-size dependence of these quantities, we establish these quantities as functions of bond length and bond energy by developing a bond relaxation theory approach. Theoretical reproduction of periodic trends confirms that bond expansion and energy weakening dominate their atomic-size dependence. The proposed approach is not only helpful to understand the physical origins of atomic-size dependence in different MA₂Z₄ monolayers but also can be extended to study the periodic trends of the related physical properties in other systems.